# Rama

## Divide Whole Numbers Go Math Grade 5 Chapter 2 Answer Key Pdf

Apply the math to real-time examples by learning the tricks using HMH Go Math Grade 5 Answer Key. The quick way of solving math problems will help the students to save time. So, students can practice more questions utilizing the time properly. If you want the best way of learning then you must use Go Math Grade 5 Chapter 2 Divide Whole Numbers Answer Key.

Lesson 1: Place the First Digit

Lesson 2: Divide by 1-Digit Divisors

Lesson 3: Investigate • Division with 2-Digit Divisors

Lesson 4: Partial Quotients

Mid-Chapter Checkpoint

Lesson 5: Estimate with 2-Digit Divisors

Lesson 6: Divide by 2-Digit Divisors

Lesson 7: Interpret the Remainder

Lesson 9: Problem Solving • Division

Review/Test

### Place the First Digit – Share and Show – Page No. 63

Divide.

Question 1.
3)$$\overline { 579 }$$
_____

193

Explanation:
Divide integers 57/3 = 19
Multiply 19 x 3 = 57; Subtract 57 – 57 = 0
Write down 9 and divide integers 9/3 = 3.
Multiply 3 x 3 = 9. Subtract 9 – 9 = 0.
The remainder is 0.

Question 2.
5)$$\overline { 1,035 }$$
_____

207

Explanation:
Divide integers 10/5 = 2
Multiply 2 x 5 = 10; Subtract 10 – 10 = 0
Write down 35 and divide integers 35/5 = 7.
Multiply 7 x 5 = 35. Subtract 35 – 35 = 0.
The remainder is 0.

Go Math Book 5th Grade Place The First Digit Lesson 2.1 Question 3.
8)$$\overline { 1,766 }$$
_____ R _____

220 R 6

Explanation:
Divide integers 17/8 = 2
Multiply 2 x 8 = 16; Subtract 17 – 16 = 1
Write down 16 and divide integers 16/8 = 2.
Multiply 2 x 8 = 16. Subtract 16 – 16 = 0.
Write down 6; 6 < 8. There are not enough tens
So, the remainder is 6

Divide.

Question 4.
8)$$\overline { 275 }$$
_____ R _____

43 R 3

Explanation:
Divide integers 27/8 = 3
Multiply 8 x 3 = 24; Subtract 27 – 24= 3
Write down 3 and divide integers 35/8 = 4.
Multiply 8 x 4 = 32. Subtract 35 – 32 = 3.
The remainder is 3.

Question 5.
3)$$\overline { 468 }$$
_____

155 R 3

Explanation:
Divide integers 46/3 = 15
Multiply 3 x 15 = 45; Subtract 46 – 45= 1
Write down 18 and divide integers 18/3 = 5.
Multiply 3 x 5 = 15. Subtract 18 – 15 = 3.
The remainder is 3.

Question 6.
4)$$\overline { 3,220 }$$
_____

805

Explanation:
Divide integers 32/4 = 8
Multiply 4 x 8 = 32; Subtract 32 – 32 = 0
Write down 20 and divide integers 20/4 = 5.
Multiply 4 x 5 = 20. Subtract 20 – 20= 0.
The remainder is 0.

Question 7.
6)$$\overline { 618 }$$
_____

103

Explanation:
Divide integers 61/6 = 10
Multiply 6 x 10 = 60; Subtract 61 – 60 = 1
Write down 18 and divide integers 18/6 = 3.
Multiply 6 x 3 = 18. Subtract 18 – 18 = 0.
The remainder is 0.

Question 8.
4)$$\overline { 716 }$$
_____

179

Explanation:
Divide integers 71/4 = 17
Multiply 4 x 17 = 68; Subtract 71 – 68 = 3
Write down 36 and divide integers 36/4 = 9.
Multiply 4 x 9 = 36. Subtract 36 – 36 = 0.
The remainder is 0.

Question 9.
9)$$\overline { 1,157 }$$
_____ R _____

128 R 5

Explanation:
Divide integers 11/9 = 1
Multiply 9 x 1 = 9; Subtract 11 – 9 = 2
Write down 25 and divide integers 25/9 = 2.
Multiply 9 x 2 = 18. Subtract 25 – 18 = 7.
Write down 77 and divide integers 77/9 = 8.
Multiply 9 x 8 = 72. Subtract 77 – 72= 5.
The remainder is 5.

Question 10.
6)$$\overline { 6,827 }$$
_____ R _____

1,137 R 5

Explanation:
Divide integers 6/6 = 1
Multiply 6 x 1 = 6; Subtract 6 – 6 = 0
Write down 82 and divide integers 82/6 = 13.
Multiply 6 x 13 = 78. Subtract 82 – 78 = 4.
Write down 47 and divide integers 47/6 = 7.
Multiply 6 x 7 = 42. Subtract 47 – 42= 5.
The remainder is 5.

7)$$\overline { 8,523 }$$
_____ R _____

1,217 R 4

Explanation:
Divide integers 8/7 = 1
Multiply 7 x 1 = 7; Subtract 8 – 7 = 1
Write down 15 and divide integers 15/7 = 2.
Multiply 7 x 2 = 14. Subtract 15 – 14 = 1.
Write down 12 and divide integers 12/7 = 1.
Multiply 7 x 1 = 7. Subtract 12 – 7= 5.
Write down 53 and divide integers 53/7 = 7.
Multiply 7 x 7 = 49. Subtract 53 – 49= 4.
The remainder is 4.

Practice: Copy and Solve Divide.

Question 12.
645 ÷ 8 = _____ R _____

645 ÷ 8 = 80 R 5

Explanation:
Divide integers 64/8 = 8
Multiply 8 x 8 = 64; Subtract 64 – 64 = 0
Write down 05; 5 < 8; There are not enough tens
The remainder is 5.

Question 13.
942 ÷ 6 = _____

157

Explanation:
Divide integers 9/6 = 1
Multiply 6 x 1 = 6; Subtract 9 – 6 = 3
Write down 34 and divide integers 34/6 = 5.
Multiply 6 x 5 = 30. Subtract 34 – 30 = 4.
Write down 42 and divide integers 42/6 = 7.
Multiply 6 x 7 = 42. Subtract 42 – 42 = 0.
The remainder is 0.

Question 14.
723 ÷ 7 = _____ R _____

103 R 2

Explanation:
Divide integers 7/7 = 1
Multiply 7 x 1 = 7; Subtract 7 – 7 = 0
Write down 23 and divide integers 23/7 = 3.
Multiply 7 x 3 = 21. Subtract 23 – 21 = 2.
The remainder is 2.

Question 15.
3,478 ÷ 9 = _____ R _____

386 R 4

Explanation:
Divide integers 34/9 = 3
Multiply 9 x 3 = 27; Subtract 34 – 27 = 7
Write down 77 and divide integers 77/9 = 8.
Multiply 9 x 8 = 72. Subtract 77 – 72 = 5.
Write down 58 and divide integers 58/9 = 6.
Multiply 9 x 6 = 54. Subtract 58 – 54= 4.
The remainder is 4.

Question 16.
3,214 ÷ 5 = _____ R _____

642 R 4

Explanation:
Divide integers 32/5 = 6
Multiply 5 x 6 = 30; Subtract 32 – 30 = 2
Write down 21 and divide integers 21/5 = 4.
Multiply 5 x 4 = 20. Subtract 21 – 20 = 1.
Write down 14 and divide integers 14/5 = 2.
Multiply 5 x 2 = 10. Subtract 14 – 10 = 4.
The remainder is 4.

Question 17.
492 ÷ 4 = _____

123

Explanation:
Divide integers 4/4 = 1
Multiply 4 x 1 = 4; Subtract 4 – 4 = 0
Write down 9 and divide integers 9/4 = 2.
Multiply 4 x 2 = 8. Subtract 9 – 8 = 1.
Write down 12 and divide integers 12/4 = 3.
Multiply 4 x 3 = 12. Subtract 12 – 12 = 0.
The remainder is 0.

Question 18.
2,403 ÷ 9 = _____

267

Explanation:
Divide integers 24/9 = 2
Multiply 9 x 2 = 18; Subtract 24 – 18 = 6
Write down 60 and divide integers 60/9 = 6.
Multiply 9 x 6 = 54. Subtract 60 – 54 = 6.
Write down 63 and divide integers 63/9 = 7.
Multiply 9 x 7 = 63. Subtract 63 – 63 = 0.
The remainder is 0.

Question 19.
2,205 ÷ 6 = _____ R _____

367 R 3

Explanation:
Divide integers 22/6 = 3
Multiply 6 x 3 = 18; Subtract 22 – 18 = 4
Write down 40 and divide integers 40/6 = 6.
Multiply 6 x 6 = 36; Subtract 40 – 36 = 4
Write down 45 and divide integers 45/6 = 7.
Multiply 6 x 7 = 42; Subtract 45 – 42 = 3
The remainder is 3.

Question 20.
2,426 ÷ 3 = _____ R _____

808 R 2

Explanation:
Divide integers 24/3 = 8
Multiply 3 x 8 = 24; Subtract 24 – 24 = 0
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
The remainder is 2.

Question 21.
1,592 ÷ 8 = _____ R _____

199

Explanation:
Divide integers 15/8 = 1
Multiply 8 x 1 = 8; Subtract 15 – 8 = 7
Write down 79 and divide integers 79/8 = 9.
Multiply 8 x 9 = 72; Subtract 79 – 72 = 7
Write down 72 and divide integers 72/8 = 9.
Multiply 8 x 9 = 72; Subtract 72 – 72 = 0
The remainder is 0.

Question 22.
926 ÷ 4 = _____ R _____

231 R 2

Explanation:
Divide integers 9/4 = 2
Multiply 4 x 2 = 8; Subtract 9 – 8 = 1
Write down 12 and divide integers 12/4 = 3.
Multiply 4 x 3 = 12; Subtract 12 – 12 = 0
Write down 6 and divide integers 6/4 = 1.
Multiply 4 x 1 = 4; Subtract 6 – 4 = 2
The remainder is 2.

Question 23.
6,033 ÷ 5 = _____ R _____

1,206 R 3

Explanation:
Divide integers 6/5 = 1
Multiply 5 x 1 = 5; Subtract 6 – 5 = 1
Write down 10 and divide integers 10/5 = 2.
Multiply 5 x 2 = 10; Subtract 10 – 10 = 0
Write down 33 and divide integers 33/5 = 6.
Multiply 5 x 6 = 30; Subtract 33 – 30 = 3
The remainder is 3.

### Place the First Digit – UNLOCK the Problem – Page No. 64

Question 24.
Rosa has a garden divided into sections. She has 125 daisy plants. If she plants an equal number of daisy plants in each section of daisies, will she have any left over? If so, how many daisy plants will be left over?

a. What information will you use to solve the problem?
Type below:
__________

We can use the fact that she has 125 daisy plants and she plants an equal number of the daisy plants in each of 3 sections.

Question 24.
b. How will you use division to find the number of daisy plants left over?
Type below:
__________

We have to do 125/3
Divide integers 12/3 = 4
Multiply 3 x 4 = 12; Subtract 12 – 12 = 0
Write down 5 and divide integers 5/3 = 1.
Multiply 3 x 1 = 3; Subtract 5 – 3 = 2
The remainder is 2.
41 daisy plants in each section.
2 daisy plants left over

Question 24.
c. Show the steps you use to solve the problem. Estimate: 120 ÷ 3 = _____
Type below:
__________

Divide integers 12/3 = 4
Multiply 3 x 4 = 12; Subtract 12 – 12 = 0
The remainder is 0.

Question 24.
d. Complete the sentences:
Rosa has _____ daisy plants.
She puts an equal number in each of _____ sections.
Each section has _____ plants.
Rosa has _____ daisy plants left over.
Type below:
__________

Rose has 125 daisy planes.
She puts an equal number in each of 3 sections.
Each section has 41 plants.
Rosa has 2 daisy plants left over.

Question 25.
One case can hold 3 boxes. Each box can hold 3 binders. How many cases are needed to hold 126 binders?
_____ cases

14 cases

Explanation:
One case can hold 3 boxes. Each box can hold 3 binders. 3 x 3 = 9.
For 12 binders,
126/ (3 x 3) = 126/9 = 14

Question 26.
Test Prep In which place is the first digit in the quotient 1,497 ÷ 5?
Options:
a. thousands
b. hundreds
c. tens
d. ones

b. hundreds

Explanation:
1,497 ÷ 5 = 499. The first digit 4 is in hundreds place.

### Divide by 1-Digit Divisors – Share and Show – Page No. 67

Question 1.
8)$$\overline { 624 }$$
Check
_____

78

Explanation:
Divide integers 62/8 = 7
Multiply 8 x 7 = 56; Subtract 62 – 56 = 6
Write down 64 and divide integers 64/8 = 8.
Multiply 8 x 8 = 64. Subtract 64 – 64 = 0.
The remainder is 0.
Check:
78 x 8 = 624;
624 = 624

Question 2.
4)$$\overline { 3,220 }$$
Check
_____

805

Explanation:
Divide integers 32/4 = 8
Multiply 4 x 8 = 32; Subtract 32 – 32 = 0
Write down 20 and divide integers 20/4 = 5.
Multiply 4 x 5 = 20. Subtract 20 – 20 = 0.
The remainder is 0.
Check:
805 x 4 = 3,220;
3,220 = 3,220.

Question 3.
4)$$\overline { 1,027 }$$
Check
_____ R _____

256 R 3

Explanation:
Divide integers 10/4 = 2
Multiply 4 x 2 = 8; Subtract 10 – 8 = 2
Write down 22 and divide integers 22/4 = 5.
Multiply 4 x 5 = 20. Subtract 22 – 20= 2.
Write down 27 and divide integers 27/4 = 6.
Multiply 4 x 6 = 24. Subtract 27 – 24 = 3.
The remainder is 3.
So, 256 R 3.
Check:
256 x 4 = 1,024;
1,024 + 3 = 1,027.
1,027 = 1,027

Divide.

Question 4.
6)$$\overline { 938 }$$
_____ R _____

156 R 2

Explanation:
Divide integers 9/6 = 1
Multiply 6 x 1 = 6; Subtract 9 – 6 = 3
Write down 33 and divide integers 33/6 = 5.
Multiply 6 x 5 = 30. Subtract 33 – 30 = 3.
Write down 38 and divide integers 38/6 = 6.
Multiply 6 x 6 = 36. Subtract 38 – 36 = 2.
The remainder is 2.
So, 156 R 2.

Question 5.
4)$$\overline { 762 }$$
_____ R _____

190 R 2

Explanation:
Divide integers 7/4 = 1
Multiply 4 x 1 = 4; Subtract 7 – 4 = 3
Write down 36 and divide integers 36/4 = 9.
Multiply 4 x 9 = 36. Subtract 36 – 36 = 0.
Write down 2. 2 < 4; There are not enough tens
The remainder is 2.
So, 190 R 2.

Question 6.
3)$$\overline { 5,654 }$$
_____ R _____

1884 R 2

Explanation:
Divide integers 5/3 = 1
Multiply 3 x 1 = 3; Subtract 5 – 3 = 2
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
Write down 25 and divide integers 25/3 = 8.
Multiply 3 x 8 = 24. Subtract 25 – 24 = 1.
Write down 14 and divide integers 14/3 = 4.
Multiply 3 x 4 = 12. Subtract 14 – 12 = 2.
The remainder is 2.
So, 1884 R 2.

Question 7.
8)$$\overline { 475 }$$
_____ R _____

59 R 3

Explanation:
Divide integers 47/8 = 5
Multiply 8 x 5 = 40; Subtract 47 – 40 = 7
Write down 75 and divide integers 75/8 = 9.
Multiply 9 x 8 = 72. Subtract 75 – 72 = 3.
The remainder is 3.
So, 59 R 3.

Practice: Copy and Solve Divide.

Question 8.
4)$$\overline { 671 }$$
_____ R _____

167 R 3

Explanation:
Divide integers 6/4 = 1
Multiply 4 x 1 = 4; Subtract 6 – 4 = 2
Write down 27 and divide integers 27/4 = 6.
Multiply 4 x 6 = 24. Subtract 27 – 24 = 3.
Write down 31 and divide integers 31/4 = 7.
Multiply 4 x 7 = 28. Subtract 31 – 28 = 3.
The remainder is 3.
So, 167 R 3.

Question 9.
9)$$\overline { 2,023 }$$
_____ R _____

224 R 7

Explanation:
Divide integers 20/9 = 2
Multiply 9 x 2 = 18; Subtract 20 – 18 = 2
Write down 22 and divide integers 22/9 = 2.
Multiply 9 x 2 = 18. Subtract 22 – 18 = 4.
Write down 43 and divide integers 43/9 = 4.
Multiply 9 x 4 = 36. Subtract 43 – 36 = 7.
The remainder is 7.
So, 224 R 7.

Question 10.
3)$$\overline { 4,685 }$$
_____ R _____

1,561 R 2

Explanation:
Divide integers 4/3 = 1
Multiply 3 x 1 = 3; Subtract 4 – 3 = 1
Write down 16 and divide integers 16/3 = 5.
Multiply 3 x 5 = 15. Subtract 16 – 15 = 1.
Write down 18 and divide integers 18/3 = 6.
Multiply 3 x 6 = 18. Subtract 18 – 18 = 0.
Write down 5 and divide integers 5/3 = 1.
Multiply 3 x 1 = 3. Subtract 5 – 3 = 2.
The remainder is 2.
So, 1,561 R 2.

Question 11.
8)$$\overline { 948 }$$
_____ R _____

118 R 4

Explanation:
Divide integers 9/8 = 1
Multiply 8 x 1 = 8; Subtract 9 – 8 = 1
Write down 14 and divide integers 14/8 = 1.
Multiply 8 x 1 = 8. Subtract 14 – 8 = 6.
Write down 68 and divide integers 68/8 = 8.
Multiply 8 x 8 = 64. Subtract 68 – 64 = 4.
The remainder is 4.
So, 118 R 4.

Question 12.
1,326 ÷ 4 = _____ R _____

331 R 2

Explanation:
Divide integers 13/4 = 3
Multiply 4 x 3 = 12; Subtract 13 – 12 = 1
Write down 12 and divide integers 12/4 = 3.
Multiply 4 x 3 = 12. Subtract 12 – 12 = 0.
Write down 6 and divide integers 6/4 = 1.
Multiply 4 x 1 = 4. Subtract 6 – 4 = 2.
The remainder is 2.
So, 331 R 2.

Question 13.
5,868 ÷ 6 = _____

978

Explanation:
Divide integers 58/6 = 9
Multiply 6 x 9 = 54; Subtract 58 – 54 = 4
Write down 46 and divide integers 46/6 = 7.
Multiply 6 x 7 = 42. Subtract 46 – 42 = 4.
Write down 48 and divide integers 48/6 = 8.
Multiply 6 x 8 = 48. Subtract 48 – 48 = 0.
The remainder is 0.
So, 978.

Question 14.
566 ÷ 3 = _____ R _____

188 R 2

Explanation:
Divide integers 5/3 = 1
Multiply 3 x 1 = 3; Subtract 5 – 3 = 2
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
Write down 26 and divide integers 26/3 = 8.
Multiply 3 x 8 = 24. Subtract 26 – 24 = 2.
The remainder is 2.
So, 188 R 2.

Question 15.
3,283 ÷ 9 = _____ R _____

364 R 7

Explanation:
Divide integers 32/9 = 3
Multiply 9 x 3 = 27; Subtract 32 – 27 = 5
Write down 58 and divide integers 58/9 = 6.
Multiply 9 x 6 = 54. Subtract 58 – 54 = 4.
Write down 43 and divide integers 43/9 = 4.
Multiply 9 x 4 = 36. Subtract 43 – 36 = 7.
The remainder is 7.
So, 364 R 7.

Algebra Find the value of n in each equation. Write what n represents in the related division problem.

Question 16.
n = 4 × 58
Value of n = _______
Represents: _______

Value of n = 232
Represents: dividend

Explanation:
n = 4 × 58;
232 = 4 x 58;
n is the dividend

Question 17.
589 = 7 × 84 + n
Value of n = _______
Represents: _______

Value of n = 1
Represents: remainder

Explanation:
589 = 7 × 84 + n
589 = 588 + n;
589 – 588 = n;
1 = n
n is the remainder

Go Math Grade 5 Chapter 2 Assessment Question 18.
n = 5 × 67 + 3
Value of n = _______
Represents: _______

Value of n = 338
Represents: dividend

Explanation:
n = 5 × 67 + 3
n = 335 + 3
n = 338
n is the dividend

### Divide by 1-Digit Divisors – Problem Solving – Page No. 68

Use the table to solve 19–20.

Question 19.
If the Welcome gold nugget were turned into 3 equal-sized gold bricks, how many troy ounces would each brick weigh?
_____ troy ounces

739 troy ounces

Explanation:
Welcome gold nugget = 2,217 troy ounces.
If it turned into 3 equal-sized gold bricks, 2,217/3 = 739.
739 troy ounces

Question 20.
Pose a Problem Look back at Problem 19. Write a similar problem by changing the nugget and the number of bricks. Then solve the problem.
Type below:
__________

571 troy ounces

Explanation:
If Welcome Stranger nugget were turned into 4 equal-sized gold bricks, how many troy ounces would each brick weigh?
Welcome Stranger nugget = 2,284.
If it turned into 4 equal-sized gold bricks, 2,217/3 = 571.
571 troy ounces

Question 21.
There are 246 students going on a field trip to pan for gold. If they are going in vans that hold 9 students each, how many vans are needed? How many students will ride in the van that isn’t full?
The number of vans: _________
_________ students in the van that isn’t full

The number of vans: 27
3 students will ride in the van that isn’t full

Explanation:
There are 246 students going on a field trip to pan for gold. If they are going in vans that hold 9 students each, 246/9 = 27 R 3
The number of vans: 27
3 students will ride in the van that isn’t full
Question 22.
One crate can hold 8 cases of trading cards. How many crates are needed to hold 128 cases of trading cards?
_____ crates

16 crates

Explanation:
One crate can hold 8 cases of trading cards. To hold 128 cases of trading cards, 128/8 = 16 crates needed.

Question 23.
Test Prep At a bake sale, a fifth-grade class sold 324 cupcakes in packages of 6. How many packages of cupcakes did the class sell?
Options:
a. 1,944
b. 108
c. 64
d. 54

d. 54

Explanation:
At a bake sale, a fifth-grade class sold 324 cupcakes in packages of 6. 324/6 = 54

### Division with 2-Digit Divisors – Share and Show – Page No. 71

Use the quick picture to divide.

Question 1.

143 ÷ 13 = _____

143 ÷ 13 = 11

Explanation:
143 = 100 + 40 + 3
Model the first partial quotient by making a rectangle with the hundred and 3 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10) = 100 + 30 = 130.
The rectangle shows 10 groups of 13.
Model the second partial quotient by making a line with the ten and 3 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1) = 10 + 3 = 13
130 + 13 = 143;
So, the answer is 10 + 1 = 11

Divide. Use base-ten blocks.

Question 2.
168 ÷ 12 = _____

168 ÷ 12 = 14

Explanation:
168 ÷ 12
Model the first partial quotient by making a rectangle with the hundred and 2 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10) = 100 + 20 = 120.
The rectangle shows 10 groups of 12.
Model the second partial quotient by making a line with the ten and 2 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1) = 10 + 2 = 12.
Repeat the above step more three times to get
120 + 12 + 12 + 12 + 12 = 168;
So, the answer is 10 + 1 + 1 + 1 + 1 = 14

Question 3.
154 ÷ 14 = _____

154 ÷ 14 = 11

Explanation:
154 ÷ 14
Model the first partial quotient by making a rectangle with the hundred and 4 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10) = 100 + 40 = 140.
The rectangle shows 10 groups of 14.
Model the second partial quotient by making a line with the ten and 4 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1) = 10 + 4 = 14.
Repeat the above step more three times to get
140 + 14 = 154;
So, the answer is 10 + 1 = 11

Question 4.
187 ÷ 11 = _____

187 ÷ 11 = 17

Explanation:
187 ÷ 11 =
Model the first partial quotient by making a rectangle with the hundred and 1 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10) = 100 + 10 = 110.
The rectangle shows 10 groups of 11.
Model the second partial quotient by making a line with the ten and 1 ones. In the Record section, cross out the ten and ones you use.
10 + (1) = 10 + 1 = 11.
Repeat the above step more six times to get
110 + 11 + 11 + 11 + 11 + 11 + 11 + 11 = 187;
So, the answer is 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 17

Divide. Draw a quick picture.

Question 5.
165 ÷ 11 = _____

165 ÷ 11 = 15

Explanation:
165 ÷ 11
Model the first partial quotient by making a rectangle with the hundred and 1 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10) = 100 + 10 = 110.
The rectangle shows 10 groups of 11.
Model the second partial quotient by making a line with the ten and 1 ones. In the Record section, cross out the ten and ones you use.
10 + (1) = 10 + 1 = 11.
Repeat the above step more four times to get
110 + 11 + 11 + 11 + 11 + 11 = 165;
So, the answer is 10 + 1 + 1 + 1 + 1 + 1 = 15

Question 6.
216 ÷ 18 = _____

216 ÷ 18 = 12

Explanation:
216 ÷ 18
Model the first partial quotient by making a rectangle with the hundred and 8 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10 + 10 + 10 + 10 + 10) = 100 + 80 = 180.
The rectangle shows 10 groups of 18.
Model the second partial quotient by making a line with the ten and 8 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1) = 10 + 8 = 18.
Repeat the above step to get
180 + 18 + 18  = 216;
So, the answer is 10 + 1 + 1 = 12

196 ÷ 14 = _____

196 ÷ 14 = 14

Explanation:
196 ÷ 14
Model the first partial quotient by making a rectangle with the hundred and 4 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10) = 100 + 40 = 140.
The rectangle shows 10 groups of 14.
Model the second partial quotient by making a line with the ten and 4 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1) = 10 + 4 = 14.
Repeat the above step more three times to get
140 + 14 + 14 + 14 + 14  = 196;
So, the answer is 10 + 1 + 1 + 1 + 1 = 14

Question 8.
195 ÷ 15 = _____

195 ÷ 15 = 13

Explanation:
195 ÷ 15
Model the first partial quotient by making a rectangle with the hundred and 5 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 + 10 + 10) = 100 + 50 = 150.
The rectangle shows 10 groups of 15.
Model the second partial quotient by making a line with the ten and 5 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1 + 1 + 1) = 10 + 5 = 15.
Repeat the above step more three times to get
150 + 15 + 15 + 15  = 195;
So, the answer is 10 + 1 + 1 + 1 = 13

Question 9.
182 ÷ 13 = _____

182 ÷ 13 = 14

Explanation:
182 ÷ 13
Model the first partial quotient by making a rectangle with the hundred and 3 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10 + 10 ) = 100 + 30 = 130.
The rectangle shows 10 groups of 13.
Model the second partial quotient by making a line with the ten and 3 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1 + 1) = 10 + 3 = 13.
Repeat the above step more four times to get
130 + 13 + 13 + 13 + 13 = 182;
So, the answer is 10 + 1 + 1 + 1 + 1 = 14

Question 10.
228 ÷ 12 = _____

228 ÷ 12 = 19

Explanation:
228 ÷ 12
Model the first partial quotient by making a rectangle with the hundred and 2 tens. In the Record section, cross out the hundred and tens you use.
(10 x 10) + (10 + 10) = 100 + 20 = 120.
The rectangle shows 10 groups of 12.
Model the second partial quotient by making a line with the ten and 2 ones. In the Record section, cross out the ten and ones you use.
10 + (1 + 1) = 10 + 2 = 12.
Repeat the above step more eight times to get
120 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 228;
So, the answer is 10 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 19

### Division with 2-Digit Divisors – Connect to Social Studies – Page No. 72

Pony Express

The Pony Express used men riding horses to deliver mail between St. Joseph, Missouri, and Sacramento, California, from April, 1860 to October, 1861. The trail between the cities was approximately 2,000 miles long. The first trip from St. Joseph to Sacramento took 9 days 23 hours. The first trip from Sacramento to St. Joseph took 11 days 12 hours.

Solve.

Question 11.
Suppose two Pony Express riders rode a total of 165 miles. If they replaced each horse with a fresh horse every 11 miles, how many horses would they have used?
_____ horses

16 horses

Explanation:
Suppose two Pony Express riders rode a total of 165 miles. If they replaced each horse with a fresh horse every 11 miles. Then, 16 horses used.

Question 12.
Suppose a Pony Express rider was paid $192 for 12 weeks of work. If he was paid the same amount each week, how much was he paid for each week of work?$ _____

$16 Explanation: Suppose a Pony Express rider was paid$192 for 12 weeks of work.
For each week. $192/12 =$16.

Question 13.
Suppose three riders rode a total of 240 miles. If they used a total of 16 horses, and rode each horse the same number of miles, how many miles did they ride before replacing each horse?
_____ miles

15 miles

Explanation:
Assuming each horse was only ridden once then a total of 16 horses were ridden for a total of 240 miles
240 miles/16 horses = 15 miles/horse
if each horse was ridden more than once before being replaced the distance between replacements could be reduced.
The fact that there were 3 riders is irrelevant.

Question 14.
Suppose it took 19 riders a total of 11 days 21 hours to ride from St. Joseph to Sacramento. If they all rode the same number of hours, how many hours did each rider ride?
_____ hours

15 hours

Explanation:
Suppose it took 19 riders a total of 11 days 21 hours to ride from St. Joseph to Sacramento.
(11 x 24 + 21)/19 = (264 + 21)/19 = 285/19 = 15 hours.

### Partial Quotients – Share and Show – Page No. 75

Divide. Use partial quotients.

Question 1.
18)$$\overline { 648 }$$
_____

36

Explanation:
Multiply 18 x 10 = 180; Subtract: 648 – 180 = 468.
partial quotient = 10
Multiply 18 x 10 = 180; Subtract: 468 – 180= 288.
partial quotient = 10
Multiply 18 x 10 = 180; Subtract: 288- 180= 108.
partial quotient = 10
Multiply 18 x 6 = 108; Subtract: 108 – 108 = 0.
partial quotient = 6;
The remainder is 0;
Add the partial quotient to find the whole number quotient;
10 + 10 + 10 + 6 = 36 R 0

Question 2.
62)$$\overline { 3,186 }$$
_____ R _____

Explanation:
Multiply 62 x 10 = 620; Subtract: 3,186 – 620 = 2,566.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 2,566 – 620 = 1,946.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 1,946 – 620 = 1,326.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 1,326 – 620 = 706.
partial quotient = 10
Multiply 62 x 10 = 620; Subtract: 706 – 620 = 86.
partial quotient = 10
Multiply 62 x 1 = 62; Subtract: 86 – 62 = 24.
partial quotient = 1
The remainder is 24;
Add the partial quotient to find the whole number quotient;
10 + 10 + 10  + 10 + 1 = 51 R 24

Question 3.
858 ÷ 57
_____ R _____

Explanation:
Multiply 57 x 10 = 570; Subtract: 858 – 570 = 288.
partial quotient = 10
Multiply 57 x 5 = 285; Subtract: 288 – 285 = 3.
partial quotient = 5
The remainder is 3;
Add partial quotient to find the wholenumber quotient;
10 + 5 = 15 R 3

Divide. Use partial quotients.

Question 4.
73)$$\overline { 584 }$$
_____

8

Explanation:
Multiply 73 x 8 = 584; Subtract: 584 – 584 = 0.
partial quotient = 8
The remainder is 0;

Question 5.
51)$$\overline { 1,831 }$$
_____ R _____

35 R 46

Explanation:
Multiply 51 x 10 = 510; Subtract: 1,831 – 510 = 1,321.
partial quotient = 10
Multiply 51 x 10 = 510; Subtract: 1,321 – 510 = 811.
partial quotient = 10
Multiply 51 x 10 = 510; Subtract: 811 – 510 = 301.
partial quotient = 10
Multiply 51 x 5 = 255; Subtract: 301 – 255 = 46.
partial quotient = 5
The remainder is 46;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 5 = 35 R 46

Question 6.
82)$$\overline { 2,964 }$$
_____ R _____

36 R 12

Explanation:
Multiply 82 x 10 = 820; Subtract: 2,964 – 820 = 2,144.
partial quotient = 10
Multiply 82 x 10 = 820; Subtract: 2,144 – 820 = 1,324.
partial quotient = 10
Multiply 82 x 10 = 820; Subtract: 1,324 – 820 = 504.
partial quotient = 10
Multiply 82 x 6 = 492; Subtract: 504 – 492= 12.
partial quotient = 6
The remainder is 12;
Add partial quotient to find the whole number quotient;
10 + 10 + 10 + 6 = 36 R 12

Question 7.
892 ÷ 26
_____ R _____

34 R 8

Explanation:
Multiply 26 x 10 = 260; Subtract: 892 – 260 = 632.
partial quotient = 10
Multiply 26 x 10 = 260; Subtract: 632 – 260 = 372.
partial quotient = 10
Multiply 26 x 10 = 260; Subtract: 372 – 260 = 112.
partial quotient = 10
Multiply 26 x 4 = 104; Subtract: 112 – 104 = 8.
partial quotient = 4
The remainder is 8;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 4 = 34 R 8

Question 8.
1,056 ÷ 48
_____

22

Explanation:
Multiply 48 x 10 = 480; Subtract: 1,056 – 480 = 576.
partial quotient = 10
Multiply 48 x 10 = 480; Subtract: 576 – 480 = 96.
partial quotient = 10
Multiply 48 x 2 = 96; Subtract: 96 – 96 = 0.
partial quotient = 2
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 2 = 22

Question 9.
2,950 ÷ 67
_____ R _____

44 R 2

Explanation:
Multiply 67 x 10 = 670; Subtract: 2,950 – 670 = 2,280.
partial quotient = 10
Multiply 67 x 10 = 670; Subtract: 2,280 – 670 = 1,610.
partial quotient = 10
Multiply 67 x 10 = 670; Subtract: 1,610 – 670 = 940.
partial quotient = 10
Multiply 67 x 10 = 670; Subtract: 940 – 670 = 270.
partial quotient = 10
Multiply 67 x 4= 268; Subtract: 270 – 268 = 2.
partial quotient = 4
The remainder is 2;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 4 = 44 R 2

Practice: Copy and Solve Divide. Use partial quotients.

Question 10.
653 ÷ 42
_____ R _____

15 R 23

Explanation:
Multiply 42 x 10 = 420; Subtract: 653 – 420 = 233.
partial quotient = 10
Multiply 42 x 5 = 210; Subtract: 233 – 210 = 23.
partial quotient = 5
The remainder is 23;
Add partial quotient to find the wholenumber quotient;
10 + 5 = 15 R 23

Question 11.
946 ÷ 78
_____ R _____

12 R 10

Explanation:
Multiply 78 x 10 = 780; Subtract: 946 – 780 = 166.
partial quotient = 10
Multiply 78 x 2 = 156; Subtract: 166 – 156 = 10.
partial quotient = 2
The remainder is 10;
Add partial quotient to find the wholenumber quotient;
10 + 2 = 12 R 10

412 ÷ 18
_____ R _____

22 R 16

Explanation:
Multiply 18 x 10 = 180; Subtract: 412 – 180 = 232.
partial quotient = 10
Multiply 18 x 10 = 180; Subtract: 232 – 180 = 52.
partial quotient = 10
Multiply 18 x 2 = 36; Subtract: 52 – 36 = 16.
partial quotient = 2
The remainder is 16;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 2 = 22 R 16

Question 13.
871 ÷ 87
_____ R _____

10 R 1

Explanation:
Multiply 87 x 10 = 870; Subtract: 871 – 870 = 1.
partial quotient = 10
The remainder is 1;
10 R 1

Question 14.
1,544 ÷ 34
_____ R _____

45 R 14

Explanation:
Multiply 34 x 10 = 340; Subtract: 1,544 – 340 = 1,204.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 1,204 – 340 = 864.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 864 – 340 = 524.
partial quotient = 10
Multiply 34 x 10 = 340; Subtract: 524 – 340 = 184.
partial quotient = 10
Multiply 34 x 5 = 170; Subtract: 184 – 170 = 14.
partial quotient = 5
The remainder is 14;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 5 = 45 R 14

Question 15.
2,548 ÷ 52
_____ R _____

47 R 14

Explanation:
Multiply 52 x 10 = 520; Subtract: 2,548 – 520 = 2028.
partial quotient = 10
Multiply 52 x 10 = 520; Subtract: 2028- 520 = 1508.
partial quotient = 10
Multiply 52 x 10 = 520; Subtract: 1508- 520 = 988.
partial quotient = 10
Multiply 52 x 10 = 520; Subtract: 988 – 520 = 468.
partial quotient = 10
Multiply 52 x 9 = 468; Subtract: 468 – 468= 0.
partial quotient = 9
The remainder is 0;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 9 = 49 R 0

Question 16.
2,740 ÷ 83
_____ R _____

33 R 1

Explanation:
Multiply 83 x 10 = 830; Subtract: 2,740 – 830= 1910.
partial quotient = 10
Multiply 83 x 10 = 830; Subtract: 1910 – 830= 1080.
partial quotient = 10
Multiply 83 x 10 = 830; Subtract: 1080 – 830= 250.
partial quotient = 10
Multiply 83 x 3 = 249; Subtract: 250 – 249 = 1.
partial quotient = 3
The remainder is 1;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 3 = 33 R 1

Question 17.
4,135 ÷ 66
_____ R _____

62 R 43

Explanation:
Multiply 66 x 10 = 660; Subtract: 4,135 – 660 = 3475.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 3475 – 660 = 2815.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 2815 – 660 = 2155.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 2155 – 660 = 1495.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 1495 – 660 = 835.
partial quotient = 10
Multiply 66 x 10 = 660; Subtract: 835 – 660 = 175.
partial quotient = 10
Multiply 66 x 2 = 132; Subtract: 175 – 132 = 43.
partial quotient = 2
The remainder is 43;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 10 + 10 + 2 = 62 R 43

### Partial Quotients – Problem Solving – Page No. 76

Use the table to solve 18–20 and 22.

Question 18.
How many years would it take for a person in the United States to eat 855 pounds of apples?
_____ years

45 years

Explanation:
Each year a person eats 19 pounds of apples. So, to eat 855 pounds of apples, it takes 855/19 = 45 years.

Question 19.
How many years would it take for a person in the United States to eat 1,120 pounds of turkey?
_____ years

80 years

Explanation:
Each year a person eats 14 pounds of turkey. So, to eat 1,120 pounds of turkey, it takes 1,120/14 = 80 years.

Question 20.
If 6 people in the United States each eat the average amount of popcorn for 5 years, how many quarts of popcorn will they eat?
_____ quarts

2,040 quarts

Explanation:
1 person eats 68 quarts of popcorn each year. 6 people = 6 x 68 quarts of popcorn = 408 quarts of popcorn for each year.
For 5 years, they will eat popcorn = 5 x 408 = 2,040 quarts

Question 21.
In a study, 9 people ate a total of 1,566 pounds of potatoes in 2 years. If each person ate the same amount each year, how many pounds of potatoes did each person eat in 1 year?
_____ pounds

87 pounds

Explanation:
9 people ate a total of 1,566 pounds of potatoes in 2 years. If each person ate the same amount each year, 1,566/2 = 783.
To calculate how many pounds of potatoes did each person eat in 1 year, 783/9 = 87 pounds.

Question 22.
Sense or Nonsense? In the United States, a person eats more than 40,000 pounds of bread in a lifetime if he or she lives to be 80 years old. Does this statement make sense, or is it nonsense? Explain.
__________

nonsense; 40,000 pounds / 80 years = 4,000 pounds / 8 years = 2,000 pounds (1 ton) / 4 years = 1,000 pounds / 2 years = 1,000 pounds / 2 years = 500 pounds per year = almost 1 and 1/2 pounds of bread every day of your life.

Question 23.
Test Prep The school auditorium has 448 seats arranged in 32 equal rows. How many seats are in each row?
Options:
a. 14,336
b. 480
c. 416
d. 14

d. 14

Explanation:
The school auditorium has 448 seats arranged in 32 equal rows.
Each row = 448/32 = 14

### Mid-Chapter Checkpoint – Page No. 77

Concepts and Skills

Question 1.
Explain how estimating the quotient helps you place the first digit in the quotient of a division problem.
Type below:
__________

Let’s do 5980 divided by 347
Estimate: 6000/300 = 20
So, I now know my first digit will go into the 10’s place
or 57890 divided by 34
that is 60,000 divided by 30 = 2000
my first digit goes into the thousands place.

Question 2.
Explain how to use multiplication to check the answer to a division problem.
Type below:
__________

Take 739/9 = 82 R 1.
Check: 9 x 82 + 1 = 739.
divisor x quotient + remainder = dividend.

Divide.

Question 3.
633 ÷ 3 = _____

211

Explanation:
Divide integers 6/3 = 2
Multiply 3 x 2 = 6; Subtract 6 – 6 = 0
Write down 3 and divide integers 3/3 = 1.
Multiply 3 x 1 = 3. Subtract 3 – 3 = 0.
Write down 3 and divide integers 3/3 = 1.
Multiply 3 x 1 = 3. Subtract 3 – 3 = 0.
The remainder is 0.

Question 4.
487 ÷ 8 = _____ R _____

60 R 7

Explanation:
Divide integers 48/8 = 6
Multiply 8 x 6 = 48; Subtract 48 – 48 = 0
Write down 7;7 < 8.
The remainder is 7.
So, 60 R 7.

Question 5.
1,641 ÷ 4 = _____ R _____

410 R 1

Explanation:
Divide integers 16/4 = 4
Multiply 4 x 4 = 16; Subtract 16 – 16 = 0
Write down 4 and divide integers 4/4 = 1.
Multiply 4 x 1 = 4; Subtract 4 – 4 = 0
Write down 1; 1<4
The remainder is 1.
So, 410 R 1.

Question 6.
2,765 ÷ 9 = _____ R _____

307 R 2

Explanation:
Divide integers 27/9 = 3
Multiply 9 x 3 = 27; Subtract 27 – 27 = 0
Write down 65 and divide integers 65/9 = 7.
Multiply 9 x 7 = 63. Subtract 65 – 63 = 2.
The remainder is 2.
So, 307 R 2.

Divide. Use partial quotients.

Question 7.
156 ÷ 13 = _____

12

Explanation:
Multiply 13 x 10 = 130; Subtract: 156 – 130 = 26.
partial quotient = 10
Multiply 13 x 2 = 26; Subtract: 26 – 26 = 0.
partial quotient = 2
The remainder is 0;
Add the partial quotient to find the whole number quotient;
10 +2 = 12 R 0

Question 8.
318 ÷ 53 = _____

6

Explanation:
Multiply 53 x 6 = 318; Subtract: 318 – 318= 0.
partial quotient = 6
The remainder is 0;
quotient = 6

Question 9.
1,562 ÷ 34 =
_____ r _____

45 R 32

Explanation:
Multiply 34  x 10 = 340; Subtract: 1,562 – 340 = 1,222.
partial quotient = 10
Multiply 34  x 10 = 340; Subtract: 1,222 – 340 = 882.
partial quotient = 10
Multiply 34  x 10 = 340; Subtract: 882 – 340 = 542.
partial quotient = 10
Multiply 34  x 10 = 340; Subtract: 542 – 340 = 202.
partial quotient = 10
Multiply 34  x 5 = 170; Subtract: 202 – 170 = 32.
partial quotient = 5
The remainder is 32;
Add partial quotient to find the whole number quotient;
10 + 10 + 10 + 10 + 5 = 45 R 32

Question 10.
4,024 ÷ 68 =
_____ r _____

59 R 12

Explanation:
Multiply 68 x 10 = 680; Subtract: 4,024 – 680 = 3,344.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 3,344 – 680= 2664.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 2664 – 680 = 1984.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 1984 – 680= 1304.
partial quotient = 10
Multiply 68 x 10 = 680; Subtract: 1304 – 680 = 624.
partial quotient = 10
Multiply 68 x 9 = 612; Subtract: 624 – 612 = 12.
partial quotient = 9
The remainder is 12;
Add partial quotient to find the wholenumber quotient;
10 + 10 + 10 + 10 + 10 + 9 = 59 R 12

### Mid-Chapter Checkpoint – Page No. 78

Question 11.
Emma is planning a party for 128 guests. If 8 guests can be seated at each table, how many tables will be needed for seating at the party?
_____ tables

16 tables

Explanation:
Emma is planning a party for 128 guests. If 8 guests can be seated at each table 128/8 = 16.

Question 12.
Tickets for the basketball game cost $14 each. If the sale of the tickets brought in$2,212, how many tickets were sold?
_____ tickets

158 tickets

Explanation:
Tickets for the basketball game cost $14 each. If the sale of the tickets brought in$2,212, $2,212/$14 = 158

Question 13.
Margo used 864 beads to make necklaces for the art club. She made 24 necklaces with the beads. If each necklace has the same number of beads, how many beads did Margo use for each necklace?
_____

Explanation:
Margo used 864 beads to make necklaces for the art club. She made 24 necklaces with the beads. If each necklace has the same number of beads, 864/24 = 36 beads

Go Math Grade 5 Chapter 2 Test Pdf Question 14.
Angie needs to buy 156 candles for a party. Each package has 8 candles. How many packages should Angie buy?
_____ packages

20 packages

Explanation:
Angie needs to buy 156 candles for a party. Each package has 8 candles.
156/8 = 20

Question 15.
Max delivers 8,520 pieces of mail in one year. About how many pieces of mail does he deliver in 2 months? Explain your steps.
_____ pieces

1,420 pieces

Explanation:
Max delivers 8,520 pieces of mail in one year.
So, for 12 months, 8,520/12 = 710.
To deliver in 2 months, 710 x 2 = 1,420

### Share and Show – Page No. 81

Use compatible numbers to find two estimates.

Question 1.
22)$$\overline { 154 }$$
140 ÷ 20 = _____
160 ÷ 20 = _____
Estimate: _____ ; _____

140 ÷ 20 = 7
160 ÷ 20 = 8
Estimate: 7 ; 8

Explanation:
Two sets of compatible numbers to find two different estimates are
140 ÷ 20
14 ÷ 2 = 7
140 ÷ 20 = 7
160 ÷ 20
16 ÷ 2 = 8
160 ÷ 20  = 8

Question 2.
68)$$\overline { 503 }$$
Estimate: _____ ; _____

476 ÷ 68= 7
544 ÷ 68 = 8
Estimate: 7 ; 8

Explanation:
Multiples of 68:
68 136 204 272 340 408 476 544
Find multiples that are close to the dividend. Use either or both numbers to estimate the quotient.
476/68 = 7
544/68 = 8
The quotient is between 7 and 8.

Question 3.
81)$$\overline { 7,052 }$$
Estimate: _____ ; _____

6400 ÷ 80 = 80
7200 ÷ 80 = 90
Estimate: 80 ; 90

Explanation:
6400/80
64/8 = 8
640 / 80 = 8
6400/80 = 800
7200/80
72/8 = 9
720/80 =9
7200/80 = 90
Estimate: 80, 90

Question 4.
33)$$\overline { 291 }$$
Estimate: _____ ; _____

240 ÷ 30= 8
270 ÷ 30 = 9
Estimate: 8 ; 9

Explanation:
240/30
24/3 = 8
240/30 = 8
270/30
27/3 = 9
270/30 = 9
Estimate: 8, 9

Question 5.
58)$$\overline { 2,365 }$$
Estimate: _____ ;

2400 ÷ 60= 40
3000 ÷ 60 = 50
Estimate: 40 ; 50

Explanation:
2400/60
24/6 = 4
240/60 = 4
2400/60 = 40
3000/60
30/6 = 5
300/60 = 5
3000/60 = 50
Estimate: 40, 50

Question 6.
19)$$\overline { 5,312 }$$
Estimate: _____ ; _____

5300 ÷ 20= 7
5320 ÷ 20 = 8
Estimate: 265 ; 266

Explanation:
5300/20
5300/20 = 265
5320/20
5320/20 = 266

Use compatible numbers to find two estimates.

Question 7.
42)$$\overline { 396 }$$
Estimate: _____ ; _____

360 ÷ 40 = 9
400 ÷ 40 = 10
Estimate: 9 ; 10

Explanation:
360/40 = 9
400/40 = 10
Estimate: 9,10

Question 8.
59)$$\overline { 413 }$$
Estimate: _____ ; _____

420 ÷ 60= 7
480 ÷ 60 = 8
Estimate: 7 ; 8

Explanation:
420/60 = 7
480/60 = 8

Question 9.
28)$$\overline { 232 }$$
Estimate: _____ ; _____

240 ÷ 30 = 8
270÷ 30 = 9
Estimate: 8 ; 9

Explanation:
240/30 = 8
270/30 = 9
Estimate: 8 ; 9

How To Divide 5th Grade Lesson 2.3 Question 10.
22)$$\overline { 368 }$$
Estimate: _____ ; _____

320 ÷ 20= 16
340 ÷ 20 = 17
Estimate: 16 ; 17

Explanation:
320/20 = 16
340/20 = 17
Estimate: 16 ; 17

Question 11.
78)$$\overline { 375 }$$
Estimate: _____ ; _____

320 ÷ 80 = 4
400 ÷ 80 = 5
Estimate: 4 ; 5

Explanation:
320/80 = 4
400/80 = 5
Estimate: 16 ; 17

Question 12.
88)$$\overline { 6,080 }$$
Estimate: _____ ; _____

6210÷ 90= 69
6300 ÷ 90 = 70
Estimate: 69 ; 70

Explanation:
6210/90 = 69
6300/90 = 70

Question 13.
5,821 ÷ 71
Estimate: _____ ; _____

5180 ÷ 70 = 74
5250÷ 70 = 75
Estimate: 74 ; 75

Explanation:
5180/70 = 74
5250/70 = 75
Estimate: 74 ; 75

Question 14.
1,565 ÷ 67
Estimate: _____ ; _____

1610 ÷ 70 = 23
1680 ÷ 70 = 24
Estimate: 23 ; 24

Explanation:
1610/70 = 23
1680/70 = 24
Estimate: 23 ; 24

Question 15.
7,973 ÷ 91
Estimate: _____ ; _____

476 ÷ 90 = 87
544 ÷ 90 = 88
Estimate: 87 ; 88

Explanation:
6960/90 = 87
7920/90 = 88
Estimate: 87 ; 88

Use compatible numbers to estimate the quotient.

Question 16.
19)$$\overline { 228 }$$
Estimate: _____

240 ÷ 20 = 12
260 ÷ 20 = 13
Estimate: 12 ; 13

Explanation:
240/20 = 12
260/20 = 13
Estimate: 12 ; 13

Question 17.
25)$$\overline { 595 }$$
Estimate: $_____ Answer: 575 ÷ 25 = 23 600 ÷ 25 = 24 Estimate: 23 ; 24 Explanation: 575/25 = 23 600/25 = 24 Estimate: 23 ; 24 Question 18. 86)$$\overline { 7,130 }$$ Estimate: _____ Answer: 7380 ÷ 90 = 82 7470 ÷ 90 = 83 Estimate: 82 ; 83 Explanation: 7380/90 = 82 7470/90 = 83 Estimate: 82 ; 83 Question 19. 83)$$\overline { 462 }$$ Estimate: _____ Answer: 400 ÷ 80 = 5 480 ÷ 80 = 6 Estimate: 5 ; 6 Explanation: 400/80 = 5 480/80 = 6 Estimate: 5 ; 6 Question 20. 27)$$\overline { 9,144 }$$ Estimate: _____ Answer: 10,140 ÷ 30 = 338 10,170 ÷ 30 = 339 Estimate: 338 ; 339 Explanation: 10,140/30 = 338 10,170/30 = 339 Estimate: 338 ; 339 Question 21. 68)$$\overline { 710 }$$ Estimate: _____ Answer: 700 ÷ 70 = 10 770 ÷ 70 = 11 Estimate: 10 ; 11 Explanation: 700/70 = 10 770/70 = 11 Estimate: 10 ; 11 Question 22. 707 ÷ 36 Estimate: _____ Answer: 760 ÷ 40 = 19 800 ÷ 40 = 20 Estimate: 19 ; 20 Explanation: 760/40 = 19 800/40 = 20 Estimate: 19 ; 20 Question 23. 1,198 ÷ 41 Estimate: _____ Answer: 1160 ÷ 40 = 29 1200 ÷ 40 = 30 Estimate: 29 ; 30 Explanation: 1160/40 = 29 1200/40 = 30 Estimate: 29 ; 30 Question 24. 5,581 ÷ 72 Estimate: _____ Answer: 5390 ÷ 70 = 77 5460 ÷ 70 = 78 Estimate: 77 ; 78 Explanation: 5390/70 = 77 5460/70 = 78 Estimate: 77 ; 78 ### Problem Solving – Page No. 82 Use the picture to solve 25–26. Question 25. About how many meters tall is each floor of the Williams Tower? _____ m Answer: 4.29 meters Explanation: Williams Tower has 275 meters and 64 floors. 275/64 = 4.29 meters Question 26. About how many meters tall is each floor of the Chrysler Building? _____ m Answer: 4.142 m Explanation: Chrysler Building has 319 meters and 77 floors 319/77 = 4.142 Question 27. Eli needs to save$235. To earn money, he plans to mow lawns and charge $21 for each. Write two estimates Eli could use to determine the number of lawns he needs to mow. Decide which estimate you think is the better one for Eli to use. Explain your reasoning. Type below: __________ Answer: 220/20 = 11 Explanation: Calculate$235/$21 210/21 = 10 220/20 = 11 number 220 is closer to 235. So, the better estimate is 220/20 = 11. Question 28. Explain how you know whether the quotient of 298 ÷ 31 is closer to 9 or to 10. Type below: __________ Answer: 270/30 = 9 310/31 = 10 298 is closer to 270. So, the quotient is closer to 9 than 10. Question 29. Test Prep Anik built a tower of cubes. It was 594 millimeters tall. The height of each cube was 17 millimeters. About how many cubes did Anik use? Options: a. 10 b. 16 c. 30 d. 300 Answer: c. 30 Explanation: 594/17 540/18 = 30 600/15 = 40 So, Anik use 30 cubes ### Share and Show – Page No. 85 Divide. Check your answer. Question 1. 28)$$\overline { 620 }$$ _____ R _____ Answer: 22 R 4 Explanation: Divide integers 62/28 = 2 Multiply 28 x 2 = 56; Subtract 62 – 56 = 6 Write down 60 and divide integers 60/28 = 2. Multiply 28 x 2 = 56. Subtract 60 – 56 = 4. The remainder is 4. So, 22 R 4. Check: 22 x 28 = 616; 616 + 4 = 620 620 = 620 Question 2. 64)$$\overline { 842 }$$ _____ R _____ Answer: 13 R 10 Explanation: Divide integers 84/64 = 1 Multiply 64 x 1 = 64; Subtract 84 – 64 = 20 Write down 202 and divide integers 202/64 = 3. Multiply 64 x 3 = 192. Subtract 202 – 192 = 10. The remainder is 10. So, 13 R 10. Check: 64 x 13 = 832; 832 + 10 = 842 842 = 842 Go Math Grade 5 Lesson 2.4 Answer Key Question 3. 53)$$\overline { 2,340 }$$ _____ R _____ Answer: 44 R 8 Explanation: Divide integers 234/53 = 4 Multiply 53 x 4 = 212; Subtract 234 – 212 = 22 Write down 220 and divide integers 220/53 = 4. Multiply 53 x 4 = 212. Subtract 220 – 212 = 8. The remainder is 8. So, 44 R 8. Check: 53 x 44 = 2332; 2332 + 8 = 2340 2340 = 2340 Question 4. 723 ÷ 31 _____ R _____ Answer: 23 R 10 Explanation: Divide integers 72/31 = 2 Multiply 31 x 2 = 62; Subtract 72 – 62 = 10 Write down 103 and divide integers 103/31 = 3. Multiply 31 x 3 = 93. Subtract 103 – 93 = 10. The remainder is 10. So, 23 R 10. Check: 31 x 23 = 713; 713 + 10 = 723 723 = 723 Question 5. 1,359 ÷ 45 _____ R _____ Answer: 30 R 9 Explanation: Divide integers 135/45 = 3 Multiply 45 x 3 = 62; Subtract 135 – 135 = 0 Write down 9; 9<45 The remainder is 9. So, 30 R 9. Check: 45 x 30 = 1350; 1350 + 9 = 1359 1359 = 1359 Question 6. 7,925 ÷ 72 _____ R _____ Answer: 110 R 5 Explanation: Divide integers 79/72 = 1 Multiply 72 x 1 = 72; Subtract 79 – 72 = 7 Write down 72 and divide integers 72/72= 1. Multiply 72 x 1 = 72; Subtract 72 – 72 = 0 Write down 5; 5<72 The remainder is 5. So, 110 R 5. Check: 72 x 110 = 7920; 7920 + 5 = 7925 7925 = 7925 On Your Own Divide. Check your answer. Question 7. 16)$$\overline { 346 }$$ _____ R _____ Answer: Explanation: Divide integers 34/16 = 2 Multiply 16 x 2 = 32; Subtract 34 – 32 = 2 Write down 26 and divide integers 26/16= 1. Multiply 16 x 1 = 16; Subtract 26 – 16 = 10 The remainder is 10. So, 21 R 10. Check: 16 x 21 = 336; 336 + 10 = 346 346 = 346 Question 8. 34)$$\overline { 241 }$$ _____ R _____ Answer: 7 R 3 Explanation: Divide integers 241/34 = 7 Multiply 34 x 7 = 238; Subtract 241 – 238= 3 The remainder is 3. So, 7 R 3 Check: 34 x 7 = 238; 238 + 3 = 241 241 = 241 Question 9. 77)$$\overline { 851 }$$ _____ R _____ Answer: 11 R 4 Explanation: Divide integers 85/77 = 1 Multiply 77 x 1 = 77; Subtract 85 – 77 = 8 Write down 81 and divide integers 81/77= 1. Multiply 77 x 1 = 77; Subtract 81 – 77 = 4 The remainder is 4. So, 11 R 4. Check: 77 x 11 = 847; 847 + 4 = 851 851 = 851 Question 10. 21)$$\overline { 1,098 }$$ _____ R _____ Answer: 52 R 6 Explanation: Divide integers 109/21 = 5 Multiply 21 x 5 = 105; Subtract 109 – 105= 4 Write down 48 and divide integers 48/21 = 2. Multiply 21 x 2 = 42; Subtract 48 – 42 = 6 The remainder is 6. So, 52 R 6. Check: 21 x 52 = 1092; 1092 + 6 = 1098 1098 = 1098 Question 11. 32)$$\overline { 6,466 }$$ _____ R _____ Answer: 202 R 2 Explanation: Divide integers 64/32= 2 Multiply 32 x 2 = 64; Subtract 64 – 64 = 0 Write down 66 and divide integers 66/32 = 2. Multiply 32 x 2 = 64; Subtract 66 – 64 = 2 The remainder is 2. So, 202 R 2. Check: 32 x 202 = 6464; 6464 + 2 = 6466 6466 = 6466 Question 12. 45)$$\overline { 9,500 }$$ _____ R _____ Answer: 211 R 5 Explanation: Divide integers 95/45 = 2 Multiply 45 x 2 = 90; Subtract 95 – 90 = 5 Write down 50 and divide integers 50/45 = 1. Multiply 45 x 1 = 45; Subtract 50 – 45 = 5 Write down 50 and divide integers 50/45 = 1. Multiply 45 x 1 = 45; Subtract 50 – 45 = 5 The remainder is 5. So, 211 R 5. Check: 45 x 211 = 9495; 9495 + 5 = 9500 9500 = 9500 Question 13. 483 ÷ 21 _____ Answer: 23 Explanation: Divide integers 48/21 = 2 Multiply 21 x 2 = 42; Subtract 48 – 42 = 6 Write down 63 and divide integers 63/21 = 3. Multiply 21 x 3 = 63; Subtract 63 – 63 = 0 The remainder is 0. So, 23 R 0. Check: 23 x 21 = 483; 483 = 483 Question 14. 2,292 ÷ 19 _____ R _____ Answer: 120 R 12 Explanation: Divide integers 22/19 = 1 Multiply 19 x 1 = 19; Subtract 22 – 19 = 3 Write down 39 and divide integers 39/19 = 2. Multiply 19 x 2 = 38; Subtract 39 – 38 = 1 Write down 12; 12<19 The remainder is 12. So, 120 R 12. Check: 19 x 120 = 2280; 2280 + 12 = 2,292 2,292 = 2,292 Question 15. 4,255 ÷ 30 _____ R _____ Answer: 141 R 25 Explanation: Divide integers 42/30 = 1 Multiply 30 x 1 = 30; Subtract 42 – 30 = 12 Write down 125 and divide integers 125/30 = 4. Multiply 30 x 4 = 120; Subtract 125 – 120 = 5 Write down 55 and divide integers 55/30 = 1. Multiply 30 x 1 = 30; Subtract 55 – 30 = 25 The remainder is 25. So, 141 R 25. Check: 30 x 141 = 4230; 4230 + 25 = 4,255 4,255 = 4,255 Practice: Copy and Solve Divide. Check your answer. Question 16. 775 ÷ 35 _____ R _____ Answer: 22 R 5 Explanation: Divide integers 77/35 = 2 Multiply 35 x 2 = 70; Subtract 77 – 70 = 7 Write down 75 and divide integers 75/35 = 2. Multiply 35 x 2 = 70; Subtract 75 – 70 = 5 The remainder is 5. So, 22 R 5. Check: 22 x 35 = 770; 770 + 5 = 775 775 = 775 Go Math Grade 5 Student Edition Question 17. 820 ÷ 41 _____ Answer: 20 Explanation: Divide integers 82/41 = 2 Multiply 41 x 2 = 82; Subtract 82 – 82= 0 The remainder is 0. So, 20 R 0. Check: 41 x 20 = 820; 820 = 820 Question 18. 805 ÷ 24 _____ R _____ Answer: 33 R 13 Explanation: Divide integers 80/24 = 3 Multiply 24 x 3 = 72; Subtract 80 – 72 = 8 Write down 85 and divide integers 85/24 = 3. Multiply 24 x 3 = 72; Subtract 85 – 72 = 13 The remainder is 13. So, 33 R 13. Check: 24 x 33 = 792; 792 + 13 = 805 805 = 805 Question 19. 1,166 ÷ 53 _____ R _____ Answer: 22 R 0 Explanation: Divide integers 116/53 = 2 Multiply 53 x 2 = 106; Subtract 116 – 106= 10 Write down 106 and divide integers 106/53 = 2. Multiply 53 x 2 = 106; Subtract 106 – 106= 0 The remainder is 0. So, 22 R 0. Check: 53 x 22 = 1166; 1166 = 1166 Question 20. 1,989 ÷ 15 _____ R _____ Answer: 132 R 9 Explanation: Divide integers 19/15 = 1 Multiply 15 x 1 = 15; Subtract 19 – 15 = 4 Write down 48 and divide integers 48/15 = 3. Multiply 15 x 3 = 45; Subtract 48 – 45 = 3 Write down 39 and divide integers 39/15 = 2. Multiply 15 x 2 = 30; Subtract 39 – 30= 9 The remainder is 9. So, 132 R 9. Check: 15 x 132 = 1980; 1980 + 9 = 1989 1989 = 1989 Question 21. 3,927 ÷ 35 _____ R _____ Answer: 112 R 7 Explanation: Divide integers 39/35 = 1 Multiply 35 x 1 = 35; Subtract 39 – 35 = 4 Write down 42 and divide integers 42/35 = 1. Multiply 35 x 1 = 35; Subtract 42 – 35 = 7 Write down 77 and divide integers 77/35 = 2. Multiply 35 x 2 = 70; Subtract 77 – 70 = 7 The remainder is 7. So, 112 R 7. Check: 35 x 112 = 3920; 3920 + 7 = 3927 3927 = 3927 ### Problem Solving – Page No. 86 Use the list at the right to solve 22–24. Question 22. A smoothie shop receives a delivery of 980 ounces of grape juice. How many Royal Purple smoothies can be made with the grape juice? _____ smoothies Answer: 45 smoothies Explanation: A smoothie shop receives a delivery of 980 ounces of grape juice. 980 ounces of grape juice/22 ounces of grape juice = 45 Question 23. The shop has 1,260 ounces of cranberry juice and 650 ounces of passion fruit juice. If the juices are used to make Crazy Cranberry smoothies, which juice will run out first? How much of the other juice will be left over? Type below: _________ Answer: The shop has 1,260 ounces of cranberry juice and 650 ounces of passion fruit juice. If the juices are used to make Crazy Cranberry smoothies, passion fruit juice will run out first. Because 650<1,260. So, passion fruit juice will run out first. 1,260 – 650 =610 Crazy Cranberry juice will be left over. Question 24. In the refrigerator, there are 680 ounces of orange juice and 410 ounces of mango juice. How many Orange Tango smoothies can be made? Explain your reasoning. _____ smoothies Answer: In the refrigerator, there are 680 ounces of orange juice and 410 ounces of mango juice. So, 410 Orange Tango smoothies can be made. Because there are 410 ounces of mango juices available. Question 25. Test Prep James has 870 action figures. He decides to divide them equally among 23 boxes. How many action figures will James have left over? Options: a. 19 b. 23 c. 31 d. 37 Answer: d. 37 Explanation: James has 870 action figures. He decides to divide them equally among 23 boxes. 870/23 = 37 ### Share and Show – Page No. 89 Interpret the remainder to solve. Question 1. Erika and Bradley want to hike the Big Cypress Trail. They will hike a total of 75 miles. If Erika and Bradley plan to hike for 12 days, how many miles will they hike each day? a. Divide to find the quotient and remainder. _____ R _____ Answer: 6 R 3 Explanation: 75/12 = 6 The remainder is 3 6 R 3 Question 1. b. Decide how to use the quotient and remainder to answer the question. Type below: _________ Answer: 75/12 = 6 1/4 So, Each day they will hike 6$$\frac{1}{4}$$ miles. Question 2. What if Erika and Bradley want to hike 14 miles each day? How many days will they hike exactly 14 miles? _____ days Answer: 196 days Explanation: If Erika and Bradley want to hike 14 miles each day, 14 x 14 = 196 days Question 3. Dylan’s hiking club is planning to stay overnight at a camping lodge. Each large room can hold 15 hikers. There are 154 hikers. How many rooms will they need? _____ rooms Answer: 11 rooms Explanation: Dylan’s hiking club is planning to stay overnight at a camping lodge. Each large room can hold 15 hikers. There are 154 hikers. So, 154/15 = 10 and the remainder is 4. Dylan’s hiking club require 10 rooms for 150 hikers and other room for 4 hikers. So, in total they need 10 + 1 = 11 rooms. On Your Own Interpret the remainder to solve. Question 4. The students in a class of 24 share 84 cookies equally among them. How many cookies did each student eat? _____ $$\frac{□}{□}$$ cookies Answer: 3$$\frac{1}{2}$$ cookies Explanation: The students in a class of 24 share 84 cookies equally among them. So, 84/24 = 3$$\frac{12}{24}$$ = 3$$\frac{1}{2}$$ Question 5. A campground has cabins that can each hold 28 campers. There are 148 campers visiting the campground. How many cabins are full if 28 campers are in each cabin? _____ cabins Answer: 5$$\frac{1}{7}$$ cabins Explanation: A campground has cabins that can each hold 28 campers. There are 148 campers visiting the campground. 184/28 = 5$$\frac{1}{7}$$ Question 6. A total of 123 fifth-grade students are going to Fort Verde State Historic Park. Each bus holds 38 students. All of the buses are full except one. How many students will be in the bus that is not full? _____ students Answer: 9 students Explanation: A total of 123 fifth-grade students are going to Fort Verde State Historic Park. Each bus holds 38 students. 123/38 = 3 and the remainder is 9. 3 x 38 = 114 students. 1 bus is not full. So, 9 students will be in the bus that is not full Question 7. What’s the Error? Sheila is going to divide a 36-inch piece of ribbon into 5 equal pieces. She says each piece will be 7 inches long. Type below: _________ Answer: Sheila is going to divide a 36-inch piece of ribbon into 5 equal pieces. 36/5 = 7$$\frac{1}{5}$$. She said each piece will be 7 inches long and forgot about $$\frac{1}{5}$$ part. ### UNLOCK the Problem – Page No. 90 Question 8. Maureen has 243 ounces of trail mix. She puts an equal number of ounces in each of 15 bags. How many ounces of trail mix does Maureen have left over? a. What do you need to find? Answer: We need to find how many ounces of trail mix does Maureen have left over? Question 8. b. How will you use division to find how many ounces of trail mix are left over? Type below: _________ Answer: The division is 243/15 Question 8. c. Show the steps you use to solve the problem. Type below: _________ Answer: 243/15 Divide integers 24/15 = 1 Multiply 15 x 1 = 15; Subtract 24 – 15 = 9 Write down 93 and divide integers 93/3 = 6. Multiply 15 x 6 = 90. Subtract 93 – 90 = 3. The remainder is 3. So, 16 R 3. Question 8. d. Complete the sentences. Maureen has _______ ounces of trail mix. She puts an equal number in each of _______ bags. Each bag has _______ ounces. Maureen has _______ ounces of trail mix left over. Type below: _________ Answer: Maureen has 243 ounces of trail mix. She puts an equal number in each of 15 bags. Each bag has 16 ounces. Maureen has 3 ounces of trail mix left over. Question 8. e. Fill in the bubble completely to show your answer. Options: a. 3 ounces b. 15 ounces c. 16 ounces d. 17 ounces Answer: c. 16 ounces Question 9. Mr. Field wants to give each of his 72 campers a certificate for completing an obstacle course. If there are 16 certificates in one package, how many packages will Mr. Field need? Options: a. 4 b. 5 c. 16 d. 17 Answer: b. 5 Explanation: Mr. Field wants to give each of his 72 campers a certificate for completing an obstacle course. If there are 16 certificates in one package, 72/16 = 4.5 Question 10. James has 884 feet of rope. There are 12 teams of hikers. If James gives an equal amount of rope to each team, how much rope will each team receive? Options: a. 12 b. 73 c. 73 $$\frac{2}{3}$$ d. 74 Answer: b. 73 Explanation: James has 884 feet of rope. There are 12 teams of hikers. If James gives an equal amount of rope to each team, 884/12 = 73 ### Share and Show – Page No. 92 Adjust the estimated digit in the quotient, if needed. Then divide. Question 1. 4 41)$$\overline { 1,546 }$$ _____ R _____ Answer: 37 R 29 Explanation: 41 x 4 = 164; Subtract: 154 – 164 the estimate too high. Change the quotient to 3 41 x 3 = 123; Subtract: 154 – 123 = 31 Write down 316 and divide integers 316/41 41 x 7 = 287; Subtract: 316 – 287 = 29 37 R 29 Question 2. 2 16)$$\overline { 416 }$$ _____ Answer: 26 Explanation: 16 x 2 = 32; Subtract: 41 – 32 = 9 Write down 96 and divide integers 96/16 16 x 6 = 96; Subtract: 96 – 96 = 0 26 Question 3. 9 34)$$\overline { 2,831 }$$ _____ R _____ Answer: 83 R 9 Explanation: 34 x 9 = 306; Subtract: 283 – 306 the estimate too high. Change the quotient to 8 34 x 8 = 272; Subtract: 283 – 272 = 11 Write down 111 and divide integers 111/34 34 x 3 = 102; Subtract: 111 – 102 = 9 83 R 9 Divide. Question 4. 19)$$\overline { 915 }$$ _____ R _____ Answer: 48 R 3 Explanation: 900/18 = 50 19 x 5 = 95; Subtract: 91 – 95 the estimate too high. Change the quotient to 4 19 x 4 = 76; Subtract: 91 – 76 = 15 Write down 155 and divide integers 155/19 19 x 7 = 133; Subtract: 155 – 133 = 22 22 > 19; So Change the quotient to 8 19 x 8 = 152; Subtract: 155 – 152 = 3 48 R 3 Question 5. 28)$$\overline { 1,825 }$$ _____ R _____ Answer: Explanation: 1800/30 = 60 28 x 6 = 168; Subtract: 182 – 168 = 14 Write down 145 and divide integers 145/28 28 x 5 = 140; Subtract: 145 – 140 = 5 65 R 5 Question 6. 45)$$\overline { 3,518 }$$ _____ R _____ Answer: Explanation: 3600/40 = 90 45 x 9 = 405; Subtract: 351 – 405 the estimate too high. Change the quotient to 7 45 x 7 = 315; Subtract: 351 – 315 = 36 Write down 368 and divide integers 368/45 45 x 8 = 360; Subtract: 368 – 315 = 8 78 R 8 ### On Your Own – Page No. 93 Adjust the estimated digit in the quotient, if needed. Then divide. Question 7. 2 26)$$\overline { 541 }$$ _____ R _____ Answer: 20 R 21 Explanation: 500/25 = 2 26 x 2 = 52; Subtract: 54 – 52 = 2 Write down 21 and divide integers 21/26 20 R 21 Question 8. 1 43)$$\overline { 688 }$$ _____ Answer: 16 Explanation: 800/40 = 20 43 x 2 = 86; Subtract: 68 – 86 the estimate is too high. Change the quotient to 1 43 x 1 = 43; Subtract: 68 – 43 = 25 Write down 258 and divide integers 258/43 43 x 6 = 258; Subtract: 258 – 258 = 0 So, 16 Question 9. 6 67)$$\overline { 4,873 }$$ _____ R _____ Answer: 72 R 49 Explanation: 4800/70 = 60 67 x 6 = 402; Subtract: 487 – 402 = 85 the estimate is too low. Change the quotient to 7 67 x 7 = 469; Subtract: 487 – 469 = 18 Write down 183 and divide integers 183/67 67 x 2 = 134; Subtract: 183 – 134 = 49 72 R 49 Question 10. 15)$$\overline { 975 }$$ _____ Answer: 65 Explanation: 15 x 6 = 90; Subtract 97 – 90 = 7 Write down 75 and divide integers 75/15 15 x 5 = 75; Subtract: 75 – 75 = 0 So, 65 Question 11. 37)$$\overline { 264 }$$ _____ R _____ Answer: 7 R 5 Explanation: 240/40 = 6 37 x 6 = 222; Subtract: 264 – 222 = 42 The estimate is too low. Change the quotient to 7 37 x 7 = 259; Subtract: 264 – 259 = 5 7 R 5 Question 12. 22)$$\overline { 6,837 }$$ _____ R _____ Answer: 310 R 17 Explanation: 6300/20 = 325 22 x 3 = 66; Subtract: 68 – 66 = 2 Write down 23 and divide integers 23/22 22 x 1 = 22; Subtract: 23 – 22 = 1 Write down 17; 17 < 22 310 R 17 Practice: Copy and Solve Divide. Question 13. 452 ÷ 31 _____ $$\frac{□}{□}$$ Answer: 14$$\frac{18}{31}$$ Explanation: Divide integers 45/31 = 1 Multiply 31 x 1 = 31; Subtract 45 – 31 = 14 Write down 142 and divide integers 142/31 = 4. Multiply 31 x 4 = 124. Subtract 142 – 124 = 18. The remainder is 18. So, 14 R 18. 14$$\frac{18}{31}$$ Question 14. 592 ÷ 74 _____ Answer: 8 Explanation: Divide integers 592/74 = 8 So, 8. Question 15. 785 ÷ 14 _____ R _____ Answer: 56$$\frac{1}{14}$$ Explanation: Divide integers 78/14 = 5 Multiply 14 x 5 = 70; Subtract 78 – 70 = 8 Write down 85 and divide integers 85/14 = 6. Multiply 14 x 6 = 84. Subtract 85 – 84 = 1. The remainder is 1. So, 56 R 1. 56$$\frac{1}{14}$$ Question 16. 601 ÷ 66 _____ R _____ Answer: 9 R 7 Explanation: Divide integers 601/66 = 9 Multiply 66 x 9 = 594 ; Subtract 601 – 594= 7 The remainder is 7. So, 9 R 7. 9$$\frac{7}{66}$$ Question 17. 1,067 ÷ 97 _____ Answer: 11 Explanation: Divide integers 106/97 = 1 Multiply 97 x 1 = 97; Subtract 106 – 97 = 9 Write down 97 and divide integers 97/97 = 1 Multiply 97 x 1 = 97; Subtract 97 – 97 = 0 The remainder is 0. So, 11 is the answer. Question 18. 2,693 ÷ 56 _____ R _____ Answer: 48 R 5 Explanation: Divide integers 269/56 = 4 Multiply 56 x 4 = 224; Subtract 269 – 224 = 45 Write down 453 and divide integers 453/56 = 8 Multiply 56 x 8 = 448. Subtract 453 – 448 = 5. The remainder is 5. So, 48 R 5. Question 19. 1,488 ÷ 78 _____ R _____ Answer: 19 R 6 Explanation: Divide integers 148/78 = 1 Multiply 78 x 1 = 78; Subtract 148 – 78 = 70 Write down 708 and divide integers 708/78 = 9. Multiply 78 x 9 = 702. Subtract 708 – 702 = 6. The remainder is 6. So, 19 R 6. Question 20. 2,230 ÷ 42 _____ R _____ Answer: 53 R 4 Explanation: Divide integers 223/42 = 5 Multiply 42 x 5 = 210; Subtract 223 – 210 = 13 Write down 130 and divide integers 130/42 = 3. Multiply 42 x 3 = 126. Subtract 130 – 126 = 4. The remainder is 4. So, 53 R 4. Question 21. 4,295 ÷ 66 _____ R _____ Answer: 65 R 5 Explanation: Divide integers 429/66 = 6 Multiply 66 x 6 = 396; Subtract 429 – 396 = 33 Write down 335 and divide integers 335/66 = 5. Multiply 66 x 5 = 330. Subtract 335 – 330 = 5. The remainder is 5 So, 65 R 5 Algebra Write the unknown number for each ■. Question 22. ■ ÷ 33 = 11 ■ = _____ Answer: 363 Explanation: n ÷ 33 = 11 n = 11 x 33 = 363 Question 23. 1,092 ÷ 52 = ■ ■ = _____ Answer: 21 Explanation: 1,092 ÷ 52 = 21 Question 24. 429 ÷ ■ = 33 ■ = _____ Answer: 13 Explanation: 429 ÷ n = 33 n = 429 ÷ 33 n = 13 ### UNLOCK the Problem – Page No. 94 Question 25. A banquet hall serves 2,394 pounds of turkey during a 3-week period. If the same amount is served each day, how many pounds of turkey does the banquet hall serve each day? a. What do you need to find? Type below: _________ Answer: How many Lbs at turkey do they serve each day? Question 25. b. What information are you given? Type below: _________ Answer: Every 3 weeks, serves 2,394 lbs. Question 25. c. What other information will you use? Type below: _________ Answer: Same each day, 3 weeks = 21 days Question 25. d. Find how many days there are in 3 weeks. There are ______ days in 3 weeks. Type below: _________ Answer: There are ______ days in 3 weeks Explanation: 1 week = 7 days. 3 x 7 = 21 days Question 25. e. Divide to solve the problem. Type below: _________ Answer: 2394/3 = t t = 798 798/7 = 114 pounds Question 25. f. Fill in the bubble for the correct answer choice. Options: a. 50,274 pounds b. 798 pounds c. 342 pounds d. 114 pounds Answer: d. 114 pounds Adjust Quotients Lesson 2.8 Go Math Grade 5 Partial Quotients Question 26. Marcos mixes 624 ounces of lemonade. He wants to fill the 52 cups he has with equal amounts of lemonade. How much lemonade should he put in each cup? Options: a. 8 ounces b. 12 ounces c. 18 ounces d. 20 ounces Answer: b. 12 ounces Explanation: Marcos mixes 624 ounces of lemonade. He wants to fill the 52 cups he has with equal amounts of lemonade. 624/52 = 12 ounces. 12 ounces should he put in each cup Question 27. The Box of Sox company packs 18 pairs of socks in a box. How many boxes will the company need to pack 810 pairs of socks? Options: a. 40 b. 45 c. 55 d. 56 Answer: b. 45 Explanation: The Box of Sox company packs 18 pairs of socks in a box. So, for 810 pairs of socks, 810/18 = 45 ### Share and Show – Page No. 97 Question 1. Paula caught a tarpon with a weight that was 10 times as great as the weight of a permit fish she caught. The total weight of the two fish was 132 pounds. How much did each fish weigh? First, draw one box to represent the weight of the permit fish and ten boxes to represent the weight of the tarpon. Next, divide the total weight of the two fish by the total number of boxes you drew. Place the quotient in each box. Last, find the weight of each fish. The permit fish weighed _____ pounds. The tarpon weighed _____ pounds. Type below: _________ Answer: The permit fish weighed 12 pounds. The tarpon weighed 120 pounds. Explanation: Let S be the weight of a permit fish Paula caught. The weight of the tarpon is 10 times as great as the weight of a permit fish she caught = 10 S The total weight of the two fish was 132 pounds. S + 10S = 132 11S = 132 S = 132/11 = 12 So, Paula caught a fish with the weight of 12 pounds. The tarpon weighted 120 pounds. Question 2. What if the weight of the tarpon was 11 times the weight of the permit fish, and the total weight of the two fish was 132 pounds? How much would each fish weigh? permit fish: _________ pounds tarpon: _________ pounds Answer: permit fish: 11 pounds tarpon: 11 x 11 = 121 pounds Explanation: Let S be the weight of a permit fish Paula caught. The weight of the tarpon is 11 times as great as the weight of a permit fish she caught = 11S Total weight is 132 11S + S = 132 12S = 132 S = 132/12 = 11. permit fish: 11 pounds tarpon: 11 x 11 = 121 pounds Question 3. Jon caught four fish that weighed a total of 252 pounds. The kingfish weighed twice as much as the amberjack and the white marlin weighed twice as much as the kingfish. The weight of the tarpon was 5 times the weight of the amberjack. How much did each fish weigh? amberjack: _________ pounds kingfish: _________ pounds marlin: _________ pounds tarpon: _________ pounds Answer: amberjack: 21 pounds kingfish: 42 pounds marlin: 84 pounds tarpon: 105 pounds Explanation: Let S be the weight of the amberjack. The kingfish weighed twice as much as the amberjack = 2S The white marlin weighed twice as much as the kingfish = 2 X 2S = 4S The weight of the tarpon was 5 times the weight of the amberjack = 5S Total weight = 252 pounds. 2S + 4S + 5S + S = 252 12S = 252 S = 252/12 S = 21. The kingfish weighed twice as much as the amberjack = 2S = 2 x 21 = 42 pounds. The white marlin weighed twice as much as the kingfish = 2 X 2S = 4S = 4 x 21 = 84 pounds. The weight of the tarpon was 5 times the weight of the amberjack = 5S = 5 x 21 = 105 pounds. ### On Your Own – Page No. 98 Use the table to solve 4–7. Question 4. Kevin is starting a saltwater aquarium with 36 fish. He wants to start with 11 times as many damselfish as clown fish. How many of each fish will Kevin buy? How much will he pay for the fish? Type below: _________ Answer: Kevin is starting a saltwater aquarium with 36 fish. He uses 1 damselfish and 11 clown fish. So, three groups form for 36 fishes. 1 damselfish and 11 clown fish =$7 + (11 x $20) = 7 + 220 = 227 He buys 3 damselfish and 33 clown fish. 3 x 7 = 21$ for damselfish and 33 x 20 = 660 for clown fish.
Each fish = 681/36 = 19

Kevin used a store coupon to buy a 40-gallon tank, an aquarium light, and a filtration system. He paid a total of $240. How much money did Kevin save by using the coupon?$ _____

$25 Explanation: 40-gallon tank =$170
aquarium light = $30 filtration system =$65
170 + 30 + 65 = 265
He paid a total of $240; 265 -240 =$25
Kevin save by using the coupon $25. Question 6. Kevin bought 3 bags of gravel to cover the bottom of his fish tank. He has 8 pounds of gravel left over. How much gravel did Kevin use to cover the bottom of the tank? _____ pounds Answer: 37 pounds. Explanation: 15lb bag of gravel =$13.
3 bags of gravel = 45lb.
He has 8 pounds of gravel left over = 45 – 8 = 37
Kevin use 37 pounds of gravel to cover the bottom of the tank

Question 7.
Pose a Problem Look back at Problem 6. Write a similar problem by changing the number of bags of gravel and the amount of gravel left.
Type below:
_________

If he bought 5 bags of gravel to cover the bottom of his fish tank. He has 10 pounds of gravel left over.
5 bags of gravel = 15 x 5 = 75lbs
He has 10 pounds of gravel left over = 75 – 10 lbs = 65 lbs
65lbs

Explanation:

Question 8.
Test Prep Captain James offers a deep-sea fishing tour. He charges $2,940 for a 14-hour trip. How much does each hour of the tour cost? Options: a.$138
b. $201 c.$210
d. $294 Answer: c.$210

Explanation:
Captain James offers a deep-sea fishing tour. He charges $2,940 for a 14-hour trip. Each hour =$2940/14 = 210

### Chapter Review/Test – Vocabulary – Page No. 99

Choose the best term from the box.

Question 1.
You can to estimate quotients because they are easy
use _________ to compute with mentally

Compatible Numbers

Question 2.
To decide where to place the first digit in the
quotient, you can estimate or use _________

Place Value

Concepts and Skills

Use compatible numbers to estimate the quotient.

Question 3.
522 ÷ 6 = _____

90

Explanation:
522 is close to 540. 540 ÷ 6 = 90

Question 4.
1,285 ÷ 32 = _____

40

Explanation:
1,280 ÷ 32 = 40

Question 5.
6,285 ÷ 89 = _____

70

Explanation:
6,300 ÷ 90 = 70

Question 6.
2)$$\overline { 554 }$$ = _____

277

Explanation:
Divide integers 5/2 = 2
Multiply 2 x 2 = 4; Subtract 5 – 4 = 1
Write down 15 and divide integers 15/2 = 7.
Multiply 2 x 7 = 14. Subtract 15 – 14 = 1
Write down 14 and divide integers 14/2 = 7.
Multiply 2 x 7 = 14. Subtract 14 – 14 = 0
The remainder is 0.

Question 7.
8)$$\overline { 680 }$$ = _____

85

Explanation:
Divide integers 68/8 = 8
Multiply 8 x 8 = 64; Subtract 68 – 64 = 4
Write down 40 and divide integers 40/8 = 5.
Multiply 8 x 5 = 40. Subtract 40 – 40 = 0
The remainder is 0.

Question 8.
5)$$\overline { 462 }$$ = _____ R _____

92 R 2

Explanation:
Divide integers 46/5 = 9
Multiply 5 x 9 = 45; Subtract 46 – 45 = 1
Write down 12 and divide integers 12/5 = 2.
Multiply 5 x 2 = 10. Subtract 12 – 10 = 2
The remainder is 2.
So, 92 R 2
Check:
(92 x 5) + 2 = 460 + 2 = 462

Question 9.
522 ÷ 18 = _____

29

Explanation:
Divide integers 52/18 = 2
Multiply 18 x 2 = 36; Subtract 52 – 36 = 16
Write down 162 and divide integers 162/8 = 9.
Multiply 8 x 9 = 162. Subtract 162 – 162 = 0
The remainder is 0

Question 10.
529 ÷ 37 = _____ R _____

14 R 11

Explanation:
Divide integers 52/37 = 1
Multiply 37 x 1 = 37; Subtract 52 – 37 = 15
Write down 159 and divide integers 159/37 = 4.
Multiply 37 x 4 = 148. Subtract 159 – 148 = 11
The remainder is 11.
So, 14 R 11
Check:
(14 x 37) + 11 = 518 + 11 = 529

Question 11.
987 ÷ 15 = _____ R _____

65 R 12

Explanation:
Divide integers 98/15 = 6
Multiply 15 x 6 = 90; Subtract 98 – 90 = 8
Write down 87 and divide integers 87/15 = 5.
Multiply 15 x 5 = 75. Subtract 87 – 75 = 12
The remainder is 12.
So, 65 R 12
Check:
(15 x 65) + 12 = 975 + 12 = 987

Question 12.
1,248 ÷ 24 = _____

52

Explanation:
Divide integers 124/24 = 5
Multiply 24 x 5 = 120; Subtract 124 – 120 = 4
Write down 48 and divide integers 48/24 = 2.
Multiply 24 x 2 = 48. Subtract 48 – 48 = 0
The remainder is 0

Question 13.
5,210 ÷ 17 = _____ R _____

306 R 8

Explanation:
Divide integers 52/17 = 3
Multiply 17 x 3 = 51; Subtract 52 – 51 = 1
Write down 110 and divide integers 110/17 = 6.
Multiply 17 x 6 = 102. Subtract 110 – 102 = 8
The remainder is 8.
So, 306 R 8
Check:
(306 x 17) + 8 = 5202 + 8 = 5210

Question 14.
8,808 ÷ 42 = _____ R _____

209 R 30

Explanation:
Divide integers 88/42 = 2
Multiply 42 x 2 = 84; Subtract 88 – 84 = 4
Write down 408 and divide integers 408/42 = 9.
Multiply 42 x 9 = 378. Subtract 408 – 378 = 30
The remainder is 30.
So, 209 R 30
Check:
(209 x 42) + 30 = 8778 + 30 = 8808

### Chapter Review/Test – Page No. 100

Question 15.
Samira bought 156 ounces of trail mix. She wants to divide the amount equally into 24 portions. How many ounces of trail mix will be in each portion?
Options:
A. 6 ounces
B. 6 $$\frac{1}{2}$$ ounces
C. 7 ounces
D. 12 ounces

B. 6 $$\frac{1}{2}$$ ounces

Explanation:
Samira bought 156 ounces of trail mix. She wants to divide the amount equally into 24 portions.156/24 = 6.5 = 6 $$\frac{1}{2}$$ ounces

Question 16.
A school band performed 6 concerts. Every seat for each performance was sold. If a total of 1,248 seats were sold for all 6 concerts, how many seats were sold for each performance?
Options:
A. 28
B. 200
C. 206
D. 208

D. 208

Explanation:
A school band performed 6 concerts. Every seat for each performance was sold. If a total of 1,248 seats were sold for all 6 concerts, then 1,248/6 = 208.

Question 17.
Dylan’s dog weighs 12 times as much as his pet rabbit. The dog and rabbit weigh 104 pounds altogether. How much does Dylan’s dog weigh?
Options:
A. 104 pounds
B. 96 pounds
C. 88 pounds
D. 8 pounds

D. 8 pounds

Explanation:
Dylan’s dog weighs 12 times as much as his pet rabbit. The dog and rabbit weigh 104 pounds altogether.
rabbit weight = S
dog weighs = 12S
S + 12S = 104; 13S = 104; S = 104/13 =8.

Question 18.
Jamie is sewing 14 identical costumes for the school play. She needs 210 buttons to complete all of the costumes. How many buttons will she sew onto each costume?
Options:
A. 15
B. 14
C. 11
D. 9

A. 15

Explanation:
Jamie is sewing 14 identical costumes for the school play. She needs 210 buttons to complete all of the costumes. 210/14 = 15

### Chapter Review/Test – Page No. 101

Question 19.
A book publishing company is shipping an order of 300 books. The books are packaged in boxes that each can hold 24 books. How many boxes are needed to ship the order of books?
Options:
A. 10
B. 11
C. 12
D. 13

D. 13

Explanation:
A book publishing company is shipping an order of 300 books. The books are packaged in boxes that each can hold 24 books.
300/24 = 12.5. That is 12 and above boxes. So, the answer is 13

Question 20.
Richard is planning a trip to Italy. He thinks he will need $2,750 for the trip. If the trip is 40 weeks away, which is the best estimate of how much money Richard needs to save each week? Options: A.$60
B. $70 C.$600
D. $700 Answer: B.$70

Explanation:
Richard is planning a trip to Italy. He thinks he will need $2,750 for the trip. If the trip is 40 weeks away,$2,750/40 = $68.75. That is equal to$70

Question 21.
A school club raises $506 to spend on a field trip. There are 23 people going on the trip. How much money did the club raise for each person going? Options: A.$27
B. $22 C.$18
D. $12 Answer: B.$22

Explanation:
A school club raises $506 to spend on a field trip. There are 23 people going on the trip.$506/23 = $22. Question 22. A local orange grower processes 2,330 oranges from his grove this year. The oranges are packaged in crates that each hold 96 oranges. All but one crate is full. How many oranges are in this last crate? Options: A. 24 B. 25 C. 26 D. 27 Answer: C. 26 Explanation: 2330 oranges / 96 orange/crate = 24.2708333 crates the decimal portion is the fraction of 96 in the last crate= 96 x .2708333 = 26 oranges in the last crate. ### Chapter Review/Test – Page No. 102 Constructed Response Question 23. On Monday, 1,900 bottles of perfume are delivered to a warehouse. The bottles are packed in boxes. Each box can hold 32 bottles. How many boxes were delivered? Explain how you found your answer. _____ boxes Answer: I need to divide 1,900 by 32, which is 59 r12. That means the bottles will completely fill 59 boxes. But there will be 12 bottles left over. These would be packed in another box, which makes a total of 60 boxes. Performance Task Question 24. Quincy needs 322 yards of ribbon to decorate quilts for a craft fair.The ribbon comes in rolls of 15 yards. A. How many rolls of ribbon should Quincy buy? Explain your answer. _____ rolls Answer: I need to divide 322 by 15. The answer is 21 R 7. Since he can’t buy a part of a roll, I need to add 1 to the quotient. So, the final answer is 22. Question 24. B. Alice needs twice as many yards of ribbon as Quincy. How many rolls of ribbon does Alice need? Explain your answer. _____ rolls Answer: Twice the length of 322 yards is 644 yards. If I divide 644 by 15, the answer is 42 R 14. Alice needs to buy 43 rolls of ribbon. The remainder doubled is still less than the amount In 1 roll. Question 24. C Elena needs yellow, red, and blue ribbon. She needs 285 yards of the three colors combined. Suggest numbers of rolls of each color that would give her enough ribbon. (HINT: Break apart the 285 yards into any combination of 3 groups that total this amount.) Type below: _________ Answer: Sample 1: If Elena wants the same amounts, she will need 95 yards of each color. 95 divided by 15 is 6 R 5, so she will need 7 rolls of each color. Sample 2: If she wants 109 yards of yellow, 100 yards of red, and 85 yards of blue, she will need 7 rolls of yellow, 7 rolls of red, and 6 rolls of blue. ### Conclusion: Go Math Grade 5 Answer Key Chapter 2 Divide Whole Numbers PDF for download. Get the explanation for every problem along with practice questions. Students can easily solve any math questions in minutes with the help of Go Math Grade 5 Chapter 2 Divide Whole Numbers Solution Key. ## Go Math Grade 8 Answer Key Chapter 13 Volume Gather all the Go Math Grade 8 Questions and answers along with the explanations are provided for all the students. The best math practice will come with the Go Math Grade 8 Answer Key Chapter 13 Volume. Everyday learning is easy with the practice of the Go Math Grade 8 Chapter 13 Volume Solution Key. Get a free pdf of Go Math Grade 8 Answer Key now to practice maths offline. Be the first to grab your HMH Go Math Grade 8 Answer Key and read all the questions of maths. ## Go Math Grade 8 Chapter 13 Volume Answer Key Refer to Go Math Grade 8 Answer Key Chapter 13 Volume for answers and explanations. It is very easy to get good marks in the exam by practicing with the help of Go Math Grade 8 Solution Key. Top-ranked student’s first choice is Go Math Grade 8 Answer Key Chapter 13 Volume. Learn and practice the maths in the best way using Go Math Grade 8 Answer Key. Lesson 1: Volume of Cylinders Lesson 2: Volume of Cones Lesson 3: Volume of Spheres Model Quiz : Review : ### Guided Practice – Volume of Cylinders – Page No. 402 Question 1. Vocabulary Describe the bases of a cylinder. Type below: ____________ Answer: The ends of a cylinder are the bases of the cylinder of the two flat surfaces. Question 2. Figure 1 shows a view from above of inch cubes on the bottom of a cylinder. Figure 2 shows the highest stack of cubes that will fit inside the cylinder. Estimate the volume of the cylinder. Explain your reasoning. ________ in3 Answer: 427in³ Explanation: Number of inch cubes that fit in the base of the cylinder = 61 Number of inch cubes that fit in the length of the cylinder = 7 The volume of cylinder = base area x height V= 61 x 7 V = 427 cubic units. Volume of each cube = 1 in³ Volume of cylinder = 427in³ Lesson 13.1 Volume of Cylinders Practice and Problem Solving a/b Question 3. Find the volume of the cylinder to the nearest tenth. Use 3.14 for π. The volume of the cylinder is approximately _____ m3. ________ m3 Answer: The volume of the cylinder is approximately 1695.6 m3. 1695.6m³ Explanation: V = πr²h V = π . 6² . 15 V = 3.14 × 36 × 15 V = 1695.6m³ Question 4. A Japanese odaiko is a very large drum that is made by hollowing out a section of a tree trunk. A museum in Takayama City has three odaikos of similar size carved from a single tree trunk. The largest measures about 2.7 meters in both diameter and length, and weighs about 4.5 metric tons. Using the volume formula for a cylinder, approximate the volume of the drum to the nearest tenth. The radius of the drum is about _____ m. The volume of the drum is about _____ m3. The radius of the drum is about ___________ m The volume of the drum is about ___________ m3 Answer: The radius of the drum is about 1.35 m. The volume of the drum is about 15.5 m3. Explanation: Diameter of base of drum = 2.7 m The radius of the base of the drum = 2.7/2 R = 1.35 m The volume of cylinder = πr²h Height (h) = 2.7 m Radius (R) = 1.35 m Volume = 3.14 × (1.35) × 2.7 V = 15.4511 m³ V = 15.5 m³ ESSENTIAL QUESTION CHECK-IN Question 5. How do you find the volume of a cylinder? Describe which measurements of a cylinder you need to know. Type below: ____________ Answer: The volume of the cylinder is = πr²h Explanation: We need to find the radius of the base, r, and the height of the cylinder, h. The volume of the cylinder is = πr²h ### 13.1 Independent Practice – Volume of Cylinders – Page No. 403 Find the volume of each figure. Round your answers to the nearest tenth if necessary. Use 3.14 for π. Question 6. _________ cm3 Answer: 569.9 cm³ Explanation: Radius of base = 11 cm Height of cylinder = 1.5 cm The volume of the cylinder = πr²h V = 3.14 × (11)² × 1.5 V = 569.91 V = 569.9 cm³ Question 7. _________ in3 Answer: 1205.8 in³ Explanation: Radius of base = 4 in Height of cylinder = 24 in The volume of cylinder = πr²h V = 3.14 × (4)² × 24 V = 1205.76 V = 1205.8 in³ 8th Grade Review for Volume of Cylinders, Cones, and Spheres Answer Key Question 8. _________ m3 Answer: 1256 m³ Explanation: Radius of base = 5 m Height of cylinder = 16 m The volume of the cylinder = πr²h V = 3.14 × (5)² × 16 V = 1256 V = 1256 m³ Question 9. _________ in3 Answer: 942 in³ Explanation: Diameter of base = 10 in Radius of base = 5 in Height of cylinder = 12 in The volume of the cylinder = πr²h V = 3.14 × (5)² × 12 V = 942 in³ Question 10. A cylinder has a radius of 4 centimeters and a height of 40 centimeters. _________ cm3 Answer: 2009.6 cm³ Explanation: Radius of base = 4 cm Height of cylinder = 40 cm The volume of cylinder = πr²h V = 3.14 × (4)² × 40 V = 2009.6 cm³ Question 11. A cylinder has a radius of 8 meters and a height of 4 meters. _________ m3 Answer: 803.8 m³ Explanation: The radius of base = 8 m Height of cylinder = 4 m The volume of the cylinder = πr²h V = 3.14 × (8)² × 4 V = 803.84 m³ V = 803.8 m³ Round your answer to the nearest tenth, if necessary. Use 3.14 for π. Question 12. The cylindrical Giant Ocean Tank at the New England Aquarium in Boston is 24 feet deep and has a radius of 18.8 feet. Find the volume of the tank. _________ ft3 Answer: 26635.2 ft³ Explanation: The base radius of the tank = 18.8 ft Depth of the tank in the ocean = 24 ft The volume of the cylinder = πr²h V = 3.14 × (18.8)² × 24 V = 3.14 × 354.44 × 24 V = 26635.2384 ft³ V = 26635.2 ft³ Question 13. A standard-size bass drum has a diameter of 22 inches and is 18 inches deep. Find the volume of this drum. _________ in3 Answer: 6838.9 in³ Explanation: The base diameter of the drum = 22 in Base radius of the drum = 22/2 = 11 in Depth of the bass drum = 18 in The volume of the bass drum = πr²h V = 3.14 × (11)² × 18 V = 3.14 × 121 × 18 V = 6838.92 in³ V = 6838.9 in³ Question 14. Grain is stored in cylindrical structures called silos. Find the volume of a silo with a diameter of 11.1 feet and a height of 20 feet. _________ ft3 Answer: 1934.4 ft³ Explanation: Base diameter of silo = 11.1 ft Base radius of the silo = 11.1/2 = 5.55 ft Depth of the silo = 20 ft Volume of the silo = πr²h V = 3.14 × (5.55)² × 18 V = 3.14 × 30.8025 × 18 V = 1934.397 ft³ V = 1934.4 ft³ Question 15. The Frank Erwin Center, or “The Drum,” at the University of Texas in Austin can be approximated by a cylinder that is 120 meters in diameter and 30 meters in height. Find its volume. _________ m3 Answer: 339120 m³ Explanation: Base diameter of the drum = 120 m Base radius of the drum = 120/2 = 60 m Height of the drum = 30 m Volume of the drum = πr²h V = 3.14 × (60)² × 30 V = 3.14 × 3600 × 30 V = 339120 m³ ### Volume of Cylinders – Page No. 404 Question 16. A barrel of crude oil contains about 5.61 cubic feet of oil. How many barrels of oil are contained in 1 mile (5280 feet) of a pipeline that has an inside diameter of 6 inches and is completely filled with oil? How much is “1 mile” of oil in this pipeline worth at a price of$100 per barrel?
__________ barrels
$__________ Answer: 184.7 barrels$18470

Explanation:
Volume of barrel = 5.61 cubic feet
Length of the pipe = 1 mile = 5280 feet
Diameter of the pipe = 6 inches = 0.5 feet
Radius of the pipe = 6/2 inches = 3 inches = 0.25 feet
Volume of oil in the pipe = πr²h = 3.14 × (0.25)² × 5280 = 1036.2 cubic feet
Number of barrels in the pipe = 1036.2/5.61 = 184.7 barrels
Cost of one barrel = $100 Cost of 184.7 barrels =184.7 ×$100 = $18470 Question 17. A pan for baking French bread is shaped like half a cylinder. It is 12 inches long and 3.5 inches in diameter. What is the volume of uncooked dough that would fill this pan? _________ in3 Answer: 57.697 in³ Explanation: The length of the pan = 12 in The diameter of the pan = 3.5 in Radius = 3.5/2 = 1.75 in The volume of uncooked dough = Half the volume of the full cylinder of the above dimensions. = (πr²h)/2 = (3.14 × (1.75)² × 12)/2 = 115.395/2 = 57.697 in³ FOCUS ON HIGHER ORDER THINKING Question 18. Explain the Error A student said the volume of a cylinder with a 3-inch diameter is two times the volume of a cylinder with the same height and a 1.5-inch radius. What is the error? Type below: _______________ Answer: The volume of the cylinder of 3 in is four times the volume of the new cylinder of radius 1.5 in Explanation: The volume of a cylinder is directly proportional to the square of the radius of the cylinder. The volume does not depend on the radius linearly. Volume = πr²h V1 = π(3)²h V2 = π(1.5)²h V1/V2 = (π(3)²h)/(π(1.5)²h) V1/V2 = 4 V1 = 4V2 Volume of Cylinders and Cones Mini Quiz Answer Key Question 19. Communicate Mathematical Ideas Explain how you can find the height of a cylinder if you know the diameter and the volume. Include an example with your explanation. Type below: _______________ Answer: Let the diameter be D. Radius r = D/2 Volume = πr²h Volume = π(D/2)²h V = π((D)²/4)h h = 4V/π(D)² To find the height of a cylinder with diameter D = 2 m Let the volume be 10 m³ h = 4V/π(D)² h = (4 × 10)/(3.14 × 2²) h = 3.18 m³ Question 20. Analyze Relationships Cylinder A has a radius of 6 centimeters. Cylinder B has the same height and a radius half as long as cylinder A. What fraction of the volume of cylinder A is the volume of cylinder B? Explain. Fraction: $$\frac{□}{□}$$ Answer: $$\frac{VA}{4}$$ Explanation: rA = 6 cm rB = half of the radius of cylinder A = 3 cm hA = hB VA = πrA²h VB = πrB²h VA/VB = (πrA²h)/(πrB²h) VA/VB = 6²/3² = 36/9 = 4 Thus VB = VA/4 ### Guided Practice – Volume of Cones – Page No. 408 Question 1. The area of the base of a cylinder is 45 square inches and its height is 10 inches. A cone has the same area for its base and the same height. What is the volume of the cone? The volume of the cone is _____ in3. _________ in3 Answer: 150 in³ Explanation: In the question, the area of the base of the cylinder, B = 45 in² Height of the cylinder, h = 10 inch Volume of the cylinder, V cylinder = B × h = 45 × 10 = 450 inch³ Volume of the cone, V Cone = 1/3 V cylinder =1/3(450 inch) = 150 inch³ So, the volume of the cone is Vcone = 150 in³ Volume of Cylinders and Cones Mini Quiz Answer Key Question 2. A cone and a cylinder have congruent heights and bases. The volume of the cone is 18 m3. What is the volume of the cylinder? Explain. _________ m3 Answer: 54 m3 Explanation: The volume of the cone is 18 m3. Vcone = 1/3 Vcylinder Vcylinder = 3Vcone Vcylinder = 3.18 Vcylinder = 54 m3 Find the volume of each cone. Round your answer to the nearest tenth if necessary. Use 3.14 for π. Question 3. _________ ft3 Answer: 65.94 ft³ Explanation: the diameter of the cone is 6ft. so, the radius of the cone is 3ft. the height of the cone is 7ft. the volume of the cone = 1/3 × πr²h = 1/3 × 3.14 × 3² × 7 = 65.94 ft³ Question 4. _________ in3 Answer: 113982in³ Explanation: The radius is 33inch and the height is 100 inch Volume of the cone = 1/3 × πr²h = 1/3 × π(33)²100 = 113982in³ Question 5. Gretchen made a paper cone to hold a gift for a friend. The paper cone was 15 inches high and had a radius of 3 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π. _________ in3 Answer: 141.3in³ Explanation: the radius of the cone is 3inch and the height of the cone is 15inch. Volume of the cone = 1/3 × πr²h = 1/3 × π(3)² × 15 = 141.3in³ Question 6. A cone-shaped building is commonly used to store sand. What would be the volume of a cone-shaped building with a diameter of 50 meters and a height of 20 meters? Round your answer to the nearest tenth. Use 3.14 for π. _________ m3 Answer: 13083.33 m³ Explanation: The diameter of the cone is 50 meters. So, the radius of the cone is 25 meters. The height of the cone is 20 meters. Volume of the cone = 1/3 × πr²h = 1/3 × π(25)² × 20 = 13083.33 m³ ESSENTIAL QUESTION CHECK-IN Question 7. How do you find the volume of a cone? Type below: ____________ Answer: V cone = 1/3 V cylinder V cone = 1/3 πr²h ### 13.2 Independent Practice – Volume of Cones – Page No. 409 Find the volume of each cone. Round your answers to the nearest tenth if necessary. Use 3.14 for π. Question 8. _________ mm3 Answer: 410.3 mm³ Explanation: Radius r = 7 mm height = 8 mm Volume of cone = 1/3 πr²h Volume = 1/3(3.14)(7)²(8) Volume = 410.29 mm³ Volume = 410.3 mm³ Question 9. _________ in3 Answer: 25.1 in3 Explanation: Radius r = 2 in Height = 6 in Volume of cone = 1/3 πr²h Volume = 1/3(3.14)(2)²(6) Volume = 25.12 in3 Volume = 25.1 in3 Lesson 2 Extra Practice Volume of Cones Answers Key Question 10. A cone has a diameter of 6 centimeters and a height of 11.5 centimeters. _________ cm3 Answer: 108.3 cm3 Explanation: Diameter of base = 6 cm Radius = 6/2 cm = 3 cm Height = 11.5 cm Volume of cone = 1/3 πr²h Volume = 1/3(3.14)(3)² (11.5) Volume = 108.33 cm3 Volume = 108.3 cm3 Question 11. A cone has a radius of 3 meters and a height of 10 meters. _________ m3 Answer: 94.2 m3 Explanation: Radius r = 3 m Height = 10 m Volume of cone = 1/3 πr²h Volume = 1/3(3.14)(3)²(10) Volume = 94.2 m3 Round your answers to the nearest tenth if necessary. Use 3.14 for π. Question 12. Antonio is making mini waffle cones. Each waffle cone is 3 inches high and has a radius of $$\frac{3}{4}$$ inch. What is the volume of a waffle cone? _________ in3 Answer: 1.8 in3 Explanation: Radius = 3/4 in Radius r = 0.75 in Height = 3 in Volume of each waffle cone = 1/3 πr²h Volume = 1/3 (3.14) (0.75)² (3) Volume = 1.76625 in3 Volume = 1.8 in3 Question 13. A snack bar sells popcorn in cone-shaped containers. One container has a diameter of 8 inches and a height of 10 inches. How many cubic inches of popcorn does the container hold? _________ in3 Answer: 167.5 in3 Explanation: Diameter of base = 8 in Radius = 8/2 in = 4 in Height = 10 in Volume of cone = 1/3 πr²h Volume = 1/3 (3.14) (4)² (10) Volume = 167.466 in3 Volume = 167.5 in3 Question 14. A volcanic cone has a diameter of 300 meters and a height of 150 meters. What is the volume of the cone? _________ m3 Answer: 3534291.7 m3 Explanation: Diameter of base = 300 m Radius = 300/2 m = 150 m Height = 150 m Volume of cone = 1/3 πr²h Volume = 1/3 (3.14) (150)² (150) Volume = 3534291.735 m3 Volume = 3534291.7 m3 The volume of Cones Answers Key Question 15. Multistep Orange traffic cones come in a variety of sizes. Approximate the volume, in cubic inches, of a traffic cone that has a height of 2 feet and a diameter of 10 inches. Use 3.14 for π. _________ in3 Answer: 628 in³ Explanation: The radius of the cone is Diameter/2 = 10/2 = 5 The height of the cone is 2 ft = 2 . 12 = 24 in Vcone = 1/3 πr²h Vcone = 1/3 (3.14) (5)² (24) Vcone = 628 in³ Find the missing measure for each cone. Round your answers to the nearest tenth if necessary. Use 3.14 for π. Question 16. radius = _______ height = 6 in. volume = 100.48 in3 _________ in. Answer: radius = 4 in. 4 in. Explanation: Let radius be R. Height = 6 in Volume = 100.4 in Volume of cone = 1/3 πr²h √(3v/hπ) = R √((3 × 100.48)/(18.84)) = R √(301.44/18.84) = R R = √(16) R = 4 in Question 17. diameter = 6 cm height = _______ volume = 56.52 cm3 _______ cm Answer: height = 6 cm h = 6 cm Explanation: Let height be h Diameter = 6 cm Radius = 6/2 = 3 cm Volume = 56.52 cm Volume of cone = 1/3 πr²h (3V/r²h) = h (3 × 56.52)/(3² × 3.14) = h 169.56/28.26 = h h = 6 cm Question 18. The diameter of a cone-shaped container is 4 inches, and its height is 6 inches. How much greater is the volume of a cylinder-shaped container with the same diameter and height? Round your answer to the nearest hundredth. Use 3.14 for π. Type below: ____________ Answer: The volume of the cylinder is 50.24 in³ greater than the volume of the cone. Explanation: The diameter of a cone, d = 4 inch radius of a cone, r = d/2 = 4/2 = 2 inches height of a cone, h = 6 inches. So, the volume of a cone, V cone = 1/3 πr²h = 1/3 (3.14) (2)² (6) = 25.12 in³ And the volume of a cylinder with the same diameter and height, V cylinder = πr²h = (3.14) (2)² (6) = 75.36 in³ The volume of the cylinder is 50.24 in³ greater than the volume of the cone. ### FOCUS ON HIGHER ORDER THINKING – Volume of Cones – Page No. 410 Question 19. Alex wants to know the volume of sand in an hourglass. When all the sand is in the bottom, he stands a ruler up beside the hourglass and estimates the height of the cone of sand. a. What else does he need to measure to find the volume of sand? ____________ Answer: To find the volume of the sand, he needs to measure the radius of the base of the hourglass. Question 19. b. Make a Conjecture If the volume of sand is increasing at a constant rate, is the height increasing at a constant rate? Explain. ____________ Answer: The volume of the cone is linearly proportional to the height of the cone. Therefore, if the volume is increasing at a constant rate, the height is also increasing at a constant rate. Question 20. Problem Solving The diameter of a cone is x cm, the height is 18 cm, and the volume is 301.44 cm3. What is x? Use 3.14 for π. ________ cm Answer: 8 cm Explanation: V cone = 1/3 πr²h 301.44 = 1/3 . 3.14 . r² . 18 r² = 904.32/56.52 r² = 16 r = 4 cm The diameter of the circle is twice its radius, therefore x = 2 . r x = 2 . 4 x = 8 cm Question 21. Analyze Relationships A cone has a radius of 1 foot and a height of 2 feet. How many cones of liquid would it take to fill a cylinder with a diameter of 2 feet and a height of 2 feet? Explain. ________ cones Answer: 3 cones Explanation: The diameter of the base of the cylinder is 2 feet, which means that its radius is 1 foot. Its height is 2 feet. The volume of this cylinder is V cylinder = πr²h V cylinder = (3.14) (1)² (2) V cylinder = 6.28 The radius of the cone is 1 foot and the height of the cone is 2 feet. The volume of the cone is: V cone = 1/3 πr²h V cone = 1/3 (3.14) (1)² (2) V cone = 1/3 × 6.28 V cone = 1/3 . V cylinder V cone = 2.09 It would take 3 cones of liquid to fill the cylinder. Question 22. Critique Reasoning Herb knows that the volume of a cone is one third that of a cylinder with the same base and height. He reasons that a cone with the same height as a given cylinder but 3 times the radius should therefore have the same volume as the cylinder, since $$\frac{1}{3}$$ ⋅ 3 = 1. Is Herb correct? Explain. ____________ Answer: The volume of the given cylinder is V cylinder = πr²h The volume of the cone with the same height h as a given cylinder but 3 times the radius r is V cone = 1/3 π(3r)²h V cone = 3 πr²h V cone = 3 V cylinder As we can see, Herb is not correct. The volume of the cone is not equal to the volume of the cylinder. But it is three times the volume of the cylinder. ### Guided Practice – Volume of Spheres – Page No. 414 Question 1. Vocabulary A sphere is a three-dimensional figure with all points _____ from the center. Type below: ____________ Answer: A sphere is a three-dimensional figure with all points at equal distances from the center. Lesson 13.2 Volume of Cones Practice and Problem Solving a/b Answers Question 2. Vocabulary The _____ is the distance from the center of a sphere to a point on the sphere. Type below: ____________ Answer: radius Explanation: The radius is the distance from the center f the sphere to a point on the sphere Find the volume of each sphere. Round your answers to the nearest tenth if necessary. Use 3.14 for π. Question 3. _______ in3 Answer: 4.12 in3 Explanation: V = 4/3πr³ V = 4/3 (3.14) (1)³ V = 4.12 in3 Question 4. _______ cm3 Answer: 4186.7 cm³ Explanation: Diameter = 20 cm Radius r = 20/2 = 10 cm Volume of sphere = 4/3πr³ Volume = 4/3 (3.14) (10)³ Volume = 4186.66 cm³ Volume = 4186.7 cm³ Question 5. A sphere has a radius of 1.5 feet. _______ ft3 Answer: 14.1 ft³ Explanation: Radius r = 1.5 ft The volume of the sphere = 4/3πr³ Volume = 4/3 (3.14) (1.5)³ Volume = 14.13 ft³ Volume = 14.1 ft³ Question 6. A sphere has a diameter of 2 yards. _______ yd3 Answer: 4.2 yd³ Explanation: Diameter = 2 yards Radius r = 2/2 yards Radius r = 1 yd Volume of sphere = 4/3πr³ Volume = 4/3 (3.14) (1)³ Volume = 4.1866 yd³ Volume = 4.2 yd³ Question 7. A baseball has a diameter of 2.9 inches. Find the volume of the baseball. Round your answer to the nearest tenth if necessary. Use 3.14 for π. _______ in3 Answer: 12.8 in³ Explanation: Diameter of baseball = 2.9 in Radius r = 2.9/2 in Radius of baseball = 1.45 in The volume of the sphere = 4/3πr³ Volume = 4/3 (3.14) (1.45)³ Volume = 12.763 in³ Volume = 12.8 in³ Lesson 13.3 Volume of Spheres Practice and Problem Solving a/b Question 8. A basketball has a radius of 4.7 inches. What is its volume to the nearest cubic inch? Use 3.14 for π. _______ in3 Answer: 1304 in³ Explanation: Radius of baseball = 4.7 in The volume of the sphere = 4/3πr³ Volume = 4/3 (3.14) (4.7)³ Volume = 1304.0168 in³ Volume = 1304 in³ Question 9. A company is deciding whether to package a ball in a cubic box or a cylindrical box. In either case, the ball will touch the bottom, top, and sides. a. What portion of the space inside the cylindrical box is empty? Explain. Type below: _______________ Answer: The volume of the cylinder is V cylinder = πr²h Since the ball touches the bottom, top, and sides, then the height of the cylinder will be equal to 2r. V cylinder = πr²(2r) = 2πr³ On the other hand, the volume of the sphere is V sphere = 4/3 πr³ The volume of the empty space inside the cylindrical box is found by subtracting the volume of the sphere from the volume of the cylinder V cylinder – V sphere = 2πr³ – 4/3 πr³ = (2 – 4/3)πr³ = 2/3πr³ Question 9. b. Find an expression for the volume of the cubic box. Type below: _______________ Answer: The volume of a cube with side a is V cube = a³ Since the ball touches the bottom, top, and sides, then the side of the cube will be equal to 2r. V cube = (2r)³ V cube = 8r³ Question 9. c. About what portion of the space inside the cubic box is empty? Explain Type below: _______________ Answer: The volume of the empty space inside the cubical box is found by subtracting the volume of the sphere from the volume of the cube: V cube – V sphere = 8r³ – 4/3 πr³ = (8 – 4/3π)r³ = (8 – 4.2)r³ = 3.8r³ ESSENTIAL QUESTION CHECK-IN Question 10. Explain the steps you use to find the volume of a sphere. Type below: _______________ Answer: Step 1: The radius of the sphere is found out. Step 2: The volume of the sphere is 4/3 πr³; where R is the radius. Step 3: Put the value of radius in the equation of volume. Step 4: Calculate the volume. ### 13.3 Independent Practice – Volume of Spheres – Page No. 415 Find the volume of each sphere. Round your answers to the nearest tenth if necessary. Use 3.14 for π. Question 11. radius of 3.1 meters _______ m3 Answer: 124.7 m³ Explanation: The volume of the sphere with a radius of 3.1 meter is 4/3 πr³ V = 4/3 . (3.14) . (3.1)³ V = 124.7 m³ Question 12. diameter of 18 inches _______ in3 Answer: 3052.1 in³ Explanation: The diameter of the sphere is 18 inches, which means that its radius is 9 inches. The volume of the sphere is V = 4/3 πr³ V = 4/3 . (3.14) . (9)³ V = 3052.08 in³ V = 3052.1 in³ Volume of Cylinders Cones and Spheres Iready Answers Question 13. r = 6 in. _______ in3 Answer: 904.3 in³ Explanation: The volume of the sphere with a radius of 6 inches is V = 4/3 πr³ V = 4/3 (3.14) (6)³ V = 904.32 V = 904.3 in³ Question 14. d = 36 m _______ m3 Answer: 24416.6 m³ Explanation: d = 36 m radius r = 36/2 = 18 m Volume = 4/3 πr³ = 4/3 (3.14) (18)³ = 24416.64 Volume = 24416.6 m³ Question 15. _______ cm3 Answer: 5572.5 cm³ Explanation: The volume of the sphere with a radius of 11 centimeters is V = 4/3 πr³ V = 4/3 (3.14) (11)³ V = 5572.5 cm³ Question 16. _______ ft3 Answer: 8.2 feet³ Explanation: The diameter of the sphere is 2.5 feet, which means that its radius is 1.25 feet. The volume of the sphere is V = 4/3 πr³ V = 4/3 . (3.14) . (1.25)³ V = 8.2 feet³ The eggs of birds and other animals come in many different shapes and sizes. Eggs often have a shape that is nearly spherical. When this is true, you can use the formula for a sphere to find their volume. Question 17. The green turtle lays eggs that are approximately spherical with an average diameter of 4.5 centimeters. Each turtle lays an average of 113 eggs at one time. Find the total volume of these eggs, to the nearest cubic centimeter. _______ cm3 Answer: 5389 cm³ Explanation: The diameter of an egg (sphere) is 4.5 centimeters, which means that its radius is 2.25 centimeters. The volume of a single egg is V = 4/3 πr³ V = 4/3 (3.14) (2.25)³ V = 47.68875 cm³ Therefore, the total volume of 113 eggs is 113 . V = 113(47.68875) = 5388.82875 = 5389 cm³ Question 18. Hummingbirds lay eggs that are nearly spherical and about 1 centimeter in diameter. Find the volume of an egg. Round your answer to the nearest tenth. _______ cm3 Answer: 0.5 cm³ Explanation: The diameter of an egg (sphere) is 1 centimeter, which means that its radius is 0.5 centimeters. The volume of a single egg is V = 4/3 πr³ V = 4/3 (3.14) (0.5)³ V = 0.5 cm³ Question 19. Fossilized spherical eggs of dinosaurs called titanosaurid sauropods were found in Patagonia. These eggs were 15 centimeters in diameter. Find the volume of an egg. Round your answer to the nearest tenth. _______ cm3 Answer: 1766.25 cm³ Explanation: Diameter of an egg = 15 cm Its radius = 15/2 = 7.5 cm Volume = 4/3 πr³ V = 4/3 (3.14) (7.5)³ V = 1766.25 cm³ Volume and Surface Area of Spheres Question 20. Persevere in Problem Solving An ostrich egg has about the same volume as a sphere with a diameter of 5 inches. If the eggshell is about $$\frac{1}{12}$$ inch thick, find the volume of just the shell, not including the interior of the egg. Round your answer to the nearest tenth. _______ in3 Answer: 6.8 in³ Explanation: Diameter including the eggshell = 5 + (2 . 1/2) = (5 + 1/6) in = 5.166 in Radius including eggshell = 5.166/2 = 2.5833 in Volume = 4/3 πr³ Volume = 4/3 (3.14) (2.5833)³ =72.176 in³ Volume with shell = 72.2 in³ Radius excluding shell = 5/2 = 2.5 in Volume = 4/3 (3.14) (2.5)³ = 65.416 in³ Volume (without shell) = 65.4 in³ Volume of shell = Total volume – Inner Volume = 72.2 – 65.4 = 6.8 in³ Question 21. Multistep Write the steps you would use to find a formula for the volume of the figure at right. Then write the formula. Type below: _____________ Answer: 5/3πr³ Explanation: The radius of the hemisphere = r The radius of cylinder = r Height of cylinder = r Step 1: Find the formula for the volume of a hemisphere The volume of hemisphere = 4/3 π/2 r³ = 2/3πr³ Step 2: Find the formula for the volume of a cylinder The volume of the cylinder = πr²h =πr³ Step 3: Add both the volume expressions: Total volume = 2/3πr³ + πr³ = 5/3πr³ ### Volume of Spheres – Page No. 416 Question 22. Critical Thinking Explain what happens to the volume of a sphere if you double the radius. Type below: _____________ Answer: Let Radius = r Volume V1 = 4/3πr³ Radius = 2r Volume V2 = 4/3π(2r)³ = 8 . 4/3πr³ = 8 V1 = 8(initial volume) By doubling the radius of the sphere we make the volume 8 times the initial value. Question 23. Multistep A cylindrical can of tennis balls holds a stack of three balls so that they touch the can at the top, bottom, and sides. The radius of each ball is 1.25 inches. Find the volume inside the can that is not taken up by the three tennis balls. _______ in3 Answer: 12.3 in³ Explanation: Radius of the ball = 1.25 inch Height of the cylinder = (2 × 1.25) × 3 = (2.5) × 3 = 7.5 in radius of base of cylinder = 1.25 in. Volume of cylinder = πr²h = (3.14) (1.25)² (7.5) = 36.7968 = 36.8 in³ Volume of a ball (all three) = 3 × 4/3πr³ = 4 (3.14) (1.25)³ = 24.53125 in³ = 24.5 in³ Volume of empty space = Volume of cylinder – Volume of ball = 36.8 – 24.5 = 12.3 in³ FOCUS ON HIGHER ORDER THINKING Question 24. Critique Reasoning A sphere has a radius of 4 inches, and a cube-shaped box has an edge length of 7.5 inches. J.D. says the box has a greater volume, so the sphere will fit in the box. Is he correct? Explain. _____________ Answer: The volume of sphere = 4/3πr³ = 4/3 (3.14) (4)³ = 267.9466 = 268 The volume of cube = (7.5)³ = 421.875 =421.9 The volume of cube > Volume of a sphere But the base of the cube has an area of (7.5 × 7.5) = 56.25 while the cross-action area of the sphere. πr² = (3.14) (4)² = 50.24 The cross-section area of the cube is less than that of a sphere. thus J.D. is wrong and the ball (sphere) will not fit in the cube. Question 25. Critical Thinking Which would hold the most water: a bowl in the shape of a hemisphere with radius r, a cylindrical glass with radius r and height r, or a cone-shaped drinking cup with radius r and height r? Explain. _____________ Answer: The volume of a sphere with radius r is V sphere = 4/3πr³ Therefore, the volume of a hemisphere is V hemisphere = V sphere/2 V hemisphere = 2/3πr³ The volume of a cylinder with radius r and height r is V cylinder = πr²h V cylinder = πr³ The volume of a cone with radius r and height r is V cone = 1/3πr²h V cone = 1/3πr³ V cone < V hemisphere < V cylinder Therefore, the cylindrical glass with radius r and height r will hold the most water. 8th Grade Review for Volume of Cylinders, Cones, and Spheres Answer Key Question 26. Analyze Relationships Hari has models of a sphere, a cylinder, and a cone. The sphere’s diameter and the cylinder’s height are the same, 2r. The cylinder has radius r. The cone has diameter 2r and height 2r. Compare the volumes of the cone and the sphere to the volume of the cylinder. Type below: _____________ Answer: Radius of sphere = 2r/2 = r Volume of sphere = 4/3πr³ The radius of cylinder = r Height of cylinder = 2r volume of cylinder = πr²(2r) V cylinder = 2πr³ Radius of cone = 2r/2 = r Height of cone = 2r Volume of cone = 1/3 πr²(2r) V cone = 2/3πr³ Volume of cylinder > Volume of sphere > Volume of cone 2πr³ > 4/3πr³ > 2/3πr³ Question 27. A spherical helium balloon that is 8 feet in diameter can lift about 17 pounds. What does the diameter of a balloon need to be to lift a person who weighs 136 pounds? Explain. _______ feet Answer: Diameter of ballon = 8 ft Weight it could lift = 17 pound Volume = 4/3 π(8/2)³ = 4³(4π/3) 4³/x(4π/3) = 17/36 1/x = 1/8 × 3/4π × 1/48 x = 4π/3 . 4³ . 2³ x = 4/3. π . 8³ The volume of ballon which can lift 136 pounds is equal to 4/3. π . 8³ The radius of that ballon = 8ft Diameter = 8 . 2 = 16 ft ### Ready to Go On ? – Model Quiz – Page No. 417 13.1 Volume of Cylinders Find the volume of each cylinder. Round your answers to the nearest tenth if necessary. Use 3.14 for π. Question 1. _______ ft3 Answer: 904.8 ft³ Explanation: Radius of base = 6 ft Height of cylinder = 8 ft The volume of cylinder = πr²h Volume = (3.14) (6)² (8) Volume = 904.77 ft³ Volume = 904.8 ft³ Volume of Cylinders, Cones, and Spheres Iready Answers Question 2. A can of juice has a radius of 4 inches and a height of 7 inches. What is the volume of the can? _______ in3 Answer: 351.7 in³ Explanation: Radius if cylindrical can = 4 in Height of cylindrical can = 7 in The volume of cylinder = πr²h Volume = (3.14) (4)² (7) Volume = 351.68 in³ Volume = 351.7 in³ 13.2 Volume of Cones Find the volume of each cone. Round your answers to the nearest tenth if necessary. Use 3.14 for π. Question 3. _______ cm3 Answer: 565.2 cm³ Explanation: Radius of base of cone = 6 cm Height of cone = 15 cm Volume of cone = 1/3πr²h Volume = 1/3 (3.14) (4)² (7) Volume = 565.2 cm³ Question 4. _______ in3 Answer: 3014.4 in³ Explanation: The radius of the base of cone = 12 in Height of cone = 20 in The volume of cone = 1/3πr²h Volume = 1/3 (3.14) (12)² (20) Volume = 3014.4 in³ 13.3 Volume of Spheres Find the volume of each sphere. Round your answers to the nearest tenth if necessary. Use 3.14 for π. Question 5. _______ in3 Answer: 113 in³ Explanation: Radius of sphere = 3 ft Volume of sphere = 4/3πr³ Volume = 4/3 (3.14) (3)³ Volume = 113.04 ft³ Volume = 113 in³ Volume of Cylinders Cones and Spheres Iready Quiz Answers Question 6. _______ cm3 Answer: 1149.8 cm³ Explanation: Diameter = 13 cm Radius = 13/2 cm = 6.5 cm Volume of sphere = 4/3πr³ Volume = 4/3 (3.14) (6.5)³ Volume = 1149.7633 cm³ Volume = 1149.8 cm³ ESSENTIAL QUESTION Question 7. What measurements do you need to know to find the volume of a cylinder? a cone? a sphere? Type below: ___________ Answer: Sphere: To find the volume of the sphere, the radius is to be measured. Cylinder: To measure the volume of the cylinder, we need to find out the base radius of the base of the cylinder along with the height of the cylinder. Cone: To calculate the volume of the cone, we need to calculate the base radius of the base of the cone along with the height of the cone. Explanation: The volume of sphere = 4/3 πr³ Sphere: For finding the volume of the sphere, the radius is to be measured The volume of Cylinder = πr²h Cylinder: To calculate the volume of the cylinder, we need to find out the base radius of the base of the cylinder along with the height of the cylinder The volume of Cone = 1/3 πr²h Cone: To calculate the volume of the cone, we need to measure the base radius of the base of the cone along with the height of the cone ### Selected Response – Mixed Review – Page No. 418 Question 1. The bed of a pickup truck measures 4 feet by 8 feet. To the nearest inch, what is the length of the longest thin metal bar that will lie flat in the bed? Options: a. 11 ft 3 in. b. 10 ft 0 in. c. 8 ft 11 in. d. 8 ft 9 in. Answer: d. 8 ft 9 in. Explanation: The length of the longest thin metal bar that will lie flat in the bed’s equal to the length of the bed’s hypotenuse. Let a = 4 and b = 8. Using the Pythagorean Theorem a² + b² = c² 4² + 8² = c² 16 + 64 = c² 80 = c² Rounding the length of the hypotenuse to the nearest tenth of a foot c = 8.9 ft Therefore, the length of the longest thin metal bar that will lie flat in the bed is 8 ft. 9 in. Question 2. Using 3.14 for π, what is the volume of the cylinder below to the nearest tenth? Options: a. 102 cubic yards b. 347.6 cubic yards c. 1,091.6 cubic yards d. 4,366.4 cubic yards Answer: c. 1,091.6 cubic yards Explanation: Diameter of the base of the cylinder = 11.4 yd Radius = 11.4/2 yd = 5.7 yd Height = 10.7 ys Volume of cylinder = πr²h Volume = (3.14) (5.7)² (10.7) Volume = 1091.599 yd³ Volume = 1091.6 yd³ Question 3. Rhett made mini waffle cones for a birthday party. Each waffle cone was 3.5 inches high and had a radius of 0.8 inches. What is the volume of each cone to the nearest hundredth? Options: a. 1.70 cubic inches b. 2.24 cubic inches c. 2.34 cubic inches d. 8.79 cubic inches Answer: c. 2.34 cubic inches Explanation: Height of each waffle cone = 3.5 in Radius of base = 0.8 in Volume of cone = 1/3 πr²h Volume = 1/3 (3.14) (0.8)² (3.5) Volume = 2.344533 in³ Volume = 2.34 in³ Question 4. What is the volume of a cone that has a height of 17 meters and a base with a radius of 6 meters? Use 3.14 for π and round to the nearest tenth. Options: a. 204 cubic meters b. 640.6 cubic meters c. 2,562.2 cubic meters d. 10,249 cubic meters Answer: b. 640.6 cubic meters Explanation: Height of the cone = 17 m Radius of base = 6 m Volume of cone = 1/3 πr²h Volume = 1/3 (3.14) (6)² (17) Volume = 640.56 m³ Volume = 640.6 m³ Lesson 13.3 Volume of Spheres Question 5. Using 3.14 for π, what is the volume of the sphere to the nearest tenth? Options: a. 4,180 cubic centimeters b. 5,572.5 cubic centimeters c. 33,434.7 cubic centimeters d. 44,579.6 cubic centimeters Answer: b. 5,572.5 cubic centimeters Explanation: Diameter of the base of the sphere = 22 cm Radius = 22/2 yd = 11 cm Volume of sphere = 4/3 πr³ Volume = 4/3 (3.14) (11)³ Volume = 5572.4533 cm³ Volume = 5572.5 cm³ Mini-Task Question 6. A diagram of a deodorant container is shown. It is made up of a cylinder and half of a sphere. Use 3.14 for π and round answers to the nearest tenth. a. What is the volume of the half sphere? _______ cm3 Answer: 8.574 cm³ Explanation: The radius of the cylinder as well as the hemisphere = 1.6 cm Height = 6.2 cm the volume of the hemisphere = 2/3 πr³ the volume of the hemisphere = 2/3 (3.14) (1.6)³ the volume of the hemisphere = 8.574 cm³ Question 6. b. What is the volume of the cylinder? _______ cm3 Answer: 49.838 cm³ Explanation: The volume of cylinder = πr²h = (3.14) (1.6)² (6.2) = 49.838 cm³ Question 6. c. What is the volume of the whole figure? _______ cm3 Answer: 58.4 cm³ Explanation: Total volume = Volume of cylinder + volume of a hemisphere Total volume = 8.574 cm³ + 49.838 cm³ Total volume = 58.4 cm³ ### Conclusion: Download Go Math Grade 8 Answer Key Chapter 13 Volume for free of cost. Self-study is also possible with the help of HMH Go Math Grade 8 Solution Key. Begin your practice now by referring to Go Math Grade 8 Chapter 13 Volume Solution Key. Every student love to practice maths with the help of the Go Math Grade 8 Solution Key. Each and every problem is explained in a detailed way to help the students to practice in the best way. ## Go Math Grade 3 Answer Key Chapter 12 Two-Dimensional Shapes Extra Practice Add extra skills for your students with Go Math Grade 3 Answer Key Chapter 12 Two-Dimensional Shapes Extra Practice. Elaborate your children thinking by solving every practice question on Go Math Grade 3 Chapter 12 Two-Dimensional Shapes Extra Practice. The Go Math Grade 3 Chapter 12 Two-Dimensional Shapes Extra Practice Answer Key is given for the guidance. See the creative approach to solve the math problems. HMH Go Math Grade 3 introducing a new way of problem-solving and providing the new path for the students to solve problems. ## Go Math Grade 3 Chapter 12 Two-Dimensional Shapes Extra Practice Answer Key Download Go Math Grade 3 Answer Key Chapter 12 Two-Dimensional Shapes Extra Practice PDF and use it whenever you want. Solve all the problems with easy techniques and grab knowledge. Expert opinion is included to solve the problems of Grade 3 Chapter 12 Two-Dimensional Shapes Extra Practice. Follow the explanation and Go Math Grade 3 Chapter 12 Two-Dimensional Shapes Extra Practice Answer Key. The methodology implemented to solve problems is clear and easy. ### Common Core – Page No. 257000 Chapter 12 Extra Practice Lessons 12.1–12.3 Name the polygon. Question 1. _________ Answer: quadrilateral Explanation: 4 sides; 4 angles; quadrilateral Question 2. _________ Answer: decagon Explanation: 10 sides; 10 angles; decagon Question 3. _________ Answer: hexagon Explanation: 6 sides; 6 angles; hexagon Question 4. _________ Answer: triangle Explanation: 3 sides; 3 angles; triangle Question 5. _________ Answer: octagon Explanation: 8 sides; 8 angles; octagon Question 6. _________ Answer: pentagon Explanation: 5 sides; 5 angles; pentagon Lesson 12.4 Look at the dashed sides of the polygon. Tell if they appear to be intersecting, perpendicular, or parallel. Write all the words that describe the sides. Question 7. _________ _________ Answer: perpendicular lines Explanation: The dashed sides are meeting to form a right angle. So, they are perpendicular lines. Question 8. _________ Answer: parallel lines Explanation: The dashed sides are not intersecting with each other. So, the given lines are parallel lines. Question 9. _________ Answer: intersecting lines Explanation: The dashed line segments meet and form an angle. So, they are intersecting lines. Lesson 12.5 Circle all the words that describe the quadrilateral. Question 10. Options: a. rhombus b. trapezoid c. rectangle Answer: c. rectangle Explanation: The given shape has two pairs opposite with the same length. Also, all the angles are right angles. The given shape is a rectangle. Question 11. Options: a. square b. rhombus c. trapezoid Answer: a. square b. rhombus Explanation: The given shape has 4 sides with equal lengths. Also, all the angles are right angles. So, a possible answer is a square and rhombus. Question 12. Options: a. trapezoid b. rectangle c. rhombus Answer: a. trapezoid Explanation: Even though the given shape has four sides, they are not equal. Also, it has only two right angles. The given shape is a trapezoid. ### Common Core – Page No. 258000 Lesson 12.6 Draw a quadrilateral that does not belong. Then explain why. Question 1. Type below: _________ Answer: Explanation: The shape is a trapezoid. Even though the given shape has four sides, they are not equal. Also, the angles are not right angles. Lesson 12.7 Use the triangles for 1–2. Write A, B, or C. Then complete the sentences. Question 2. Triangle ____ has 1 angle greater than a right angle and appears to have ____ sides of equal length. Answer: Triangle C has 1 angle greater than a right angle and appears to have 0 sides of equal length. Question 3. Triangle____ has 1 right angle and appears to have ____ sides of equal length. Answer: Triangle A has 1 right angle and appears to have 2 sides of equal length. Lesson 12.8 Question 4. What label could you use to describe Circle A? Type below: _________ Answer: All sides of Equal Lengths Question 5. What label could you use to describe Circle B? Type below: _________ Answer: Right Angle Lesson 12.9 Draw lines to divide the shape into equal parts that show the fraction given. Question 6. $$\frac{1}{4}$$ Answer: Question 7. $$\frac{1}{3}$$ Answer: ### Conclusion Go Math Grade 3 Answer Key Chapter 12 Two-Dimensional Shapes Extra Practice for better practice. Download Go Math Grade 3 Answer Key PDF for easy understanding. Every problem is clearly explained with images and graphs. Follow Go Math Grade 3 Chapter 12 Two-Dimensional Shapes Extra Practice Answer Key and achieve the valuable knowledge. ## Go Math Grade 3 Answer Key Chapter 11 Perimeter and Area Extra Practice Go Math Grade 3 Answer Key Chapter 11Perimeter and Area Extra Practice will help to more number of students to get more knowledge on the perimeter and area of the different shapes. By following the Go Math Answer key, students can easily find out the Perimeter and Area of the different shapes like rectangle, square, and etc.. Go Math answer key will give you the perfect answers with a clear explanation to every question in an easy way. ## Go Math Grade 3 Chapter 11 Perimeter and Area Answer Key Follow the Go Math Grade 3 Chapter 11 Perimeter and Area Answer Key, get the step by step explanation to every question. Each and every student will easily gain the knowledge on Perimeter and Area topic by using the Go Math Grade 3 Chapter 11 Perimeter and Area Answer Key. ### Common Core – Page No. 235000 Chapter 11 Extra Practice Lessons 11.1, 11.3 Question 1. Find the perimeter of the shape. Each unit is 1 centimeter. ______ centimeters Answer: 18 centimeters Explanation: Each square in the grid is a 1 by 1-centimeter square. So, we have to do is add up the lengths of the dark segments right over the figure. Start the count from the box where 1 is placed. This parameter is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18 centimeters long. So, it is 18 centimeters. Question 2. The square has a perimeter of 28 inches. What is the length of each side of the square? ______ inches Answer: 7 inches Explanation: From the given data Perimeter of a square is = 28 inch Length of each side of the square is = a inch Perimeter of a square = a + a + a + a = 4a = 28 inch 4a= 28 Then, a = 28/4= 7 Therefore, length of each side of the square is = a = 7 inch Lesson 11.2 Use a centimeter ruler to find the perimeter. Question 3. ______ cm Answer: 11 cm Explanation: 1 + 4 + 1 + 2 + 3 = 11 cm Question 4. ______ cm Answer: 15 cm Explanation: 5 + 4 + 3 + 3 = 15 cm Lessons 11.4–11.6 Find the area of the shape. Each unit square is 1 square inch. Question 5. Area = ______ square inches Answer: Area = 15 square inches Explanation: As per the given data, Each unit square is 1 square inch Then, the area of the shape is = 15 square inches Question 6. Area = ______ square inches Answer: Area = 20 Square inches Explanation: From the given data, Each unit square is 1 square inch Then, the area of the shape = 5 x 4 = 20 Square inches ### Common Core – Page No. 236000 Lesson 11.7 Use the rectangles for 1–2. Question 1. How do the length and width change from Rectangle A to Rectangle B? Type below: __________ Answer: 22 centimeters Explanation: Rectangle A: Length = 2 ft; Width = 2 ft. Rectangle B: Length = 3 ft; Width = 2 ft. The Width from Rectangle A to Rectangle B is the same. The Length is increased 1 ft from Rectangle A to Rectangle B. Question 2. How do the areas change from Rectangle A to Rectangle B to Rectangle C? Rectangle A: ______ sq. ft. Rectangle B: ______ sq. ft. Rectangle C: ______ sq. ft. Answer: 22 centimeters Explanation: Area of Rectangle A: 2 x 2 = 4 sq. ft Area of Rectangle B: 2 x 3 = 6 sq. ft Area of Rectangle C: 2 x 4 = 8 sq. ft Then, areas change from Rectangle A to Rectangle B to Rectangle C is 2 sq. ft Lesson 11.8 Draw a line to break apart the shape into rectangles. Find the area of the shape. Question 3. ______ square units Answer: 23 square units Explanation: 2 x 7= 14 Sq. units; 3 x 3= 9 Sq. units 14 + 9 = 23 Sq. units Area of the shape is = 23 Sq. units Question 4. ______ square units Answer: 26 square units Explanation: 4 x 5 = 20 Sq. units; 2 x 3 = 6 Sq. units 20 + 6 = 26 Sq. units Then, the area of the shape is = 26 Sq. units Lessons 11.9–11.10 Find the perimeter and area of each rectangle. Use your results to answer questions 5–6. Question 5. Which two rectangles have the same perimeter? Rectangles ______ and ______ Answer: Rectangles A and C Explanation: Rectangle A: Permiter = 4 + 4 + 4 + 4 = 16 Units. Rectangle B: Permiter = 3 + 4 + 3 + 4 = 14 Units. Rectangle C: Permiter = 6 + 2 + 6 + 2 = 16 Units. Rectangle A and Rectangle C have the same perimeter Question 6. Which two rectangles have the same area? Rectangles ______ and ______ Answer: Rectangles B and C Explanation: Rectangle A: Area = 4 x 4 = 16 Sq. Units Rectangle B: Area = 4 x 3 = 12 Sq. Units Rectangle C: Area = 6 x 2 = 12 Sq. Units Rectangle B and Rectangle C have the same area. ### Conclusion In this Chapter, Go Math explained clearly about Perimeter and Area of different Shapes by using images, indicating images with arrows, and numbers. Every student has a chance to know how to find out the perimeter of shapes and how to find out the area of shapes with the Go Math Grade 3 Perimeter and Area answer key. Get quick knowledge with the Go Math solutions and find out the Perimeter and Area of shapes very quickly. By following the Go Math Grade 3 solutions, students can quickly find the perimeter and area of shapes within a few minutes. Do not move to anywhere, stay on Go Math, and follow them each and every question of Perimeter and Area with explanation and strengthen your knowledge. ## Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Extra Practice Get the source of Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Extra Practice. All the problems are solved and included with answers and explanations. Refer Go Math Grade 3 Chapter 3 Understand Multiplication Extra Practice Answer Key for an easy process of learning. Students can easily familiar with the types of questions and solving processes with extra practice. Score high marks by solving HMH Go Math Grade 3 practice questions. 100% free resources with an excellent explanation is available on Go Math Grade 3 Extra Practice Answer Key. ## Go Math Grade 3 Chapter 3 Understand Multiplication Extra Practice Answer Key The series of math problems and solutions will real solve practice to gain good grades. Every problem is explained with real term examples. Refer our Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Extra Practice and be on top to get a good score. ### Common Core – Page No. 63000 Lesson 3.1 Draw equal groups. Skip count to find how many. Question 1. 2 groups of 4 ______ Answer: 8 Explanation: Draw 4 counters in each group. There are 2 equal groups. skip count by 4 until you say 2 numbers. There are 2 equal groups with 4 counters in each group. So, there are 8 counters in all. Question 2. 4 groups of 3 ______ Answer: 12 Explanation: Draw 3 counters in each group. There are 4 equal groups. skip count by 3 until you say 4 numbers. There are 4 equal groups with 3 counters in each group. So, there are 12 counters in all. Lesson 3.2 Draw a quick picture to show the equal groups. Then write related addition and multiplication sentences. Question 3. 2 groups of 5 ______ + ______ = ______ ______ × ______ = ______ Answer: 5 + 5 = 10 2 x 5 = 10 Explanation: Addition Sentence Draw 5 counters in each group. There are a total of 2 groups. Now, the addition sentence is 5 + 5 = 10. Multiplication sentence Draw 5 counters in each circle or group. Since there is the same number of counters in each group, multiply counters and groups to find how many there are altogether. 2 x 5 = 10. factor x factor = product Question 4. 3 groups of 2 ______ + ______ + ______ = ______ ______ × ______ = ______ Answer: 2 + 2 + 2 = 6 3 x 2 = 6 Explanation: Addition Sentence Draw 2 counters in each group. There are a total of 3 groups. Now, the addition sentence is 2 + 2 + 2 = 6 Multiplication sentence Draw 2 counters in each circle or group. Since there is the same number of counters in each group, multiply groups and counters to find how many there are altogether. 3 x 2 = 6. factor x factor = product Lesson 3.3 1. Draw jumps on the number line to show 3 groups of 6. Find the product. Question 5. 3 × 6 = ______ Answer: Explanation: 3 x 6 = 18 Write the multiplication sentence the number line shows. Question 6. ______ × ______ = ______ Answer: 4 x 3 = 12 Explanation: 1 jump on the number is considered as 1 group. There are 3 jumps on a number line. So, there are 3 groups. The length of each jump is 4. Begin at 0. Skip count by 3’s. Multiply 4 x 3 = 12. ### Common Core – Page No. 64000 Lesson 3.4 Question 1. Destiny placed her hair ribbons in 3 groups of 5 on her dresser. How many hair ribbons in all does Destiny have? Draw a diagram to solve. ______ hair ribbons Answer: 15 hair ribbons Explanation: 3 groups of 5 Draw 3 counters (hair ribbons) in each group. There are 5 equal groups (dresser). We skip count by 3’s until you say 5 numbers (3,6,9,12,15) There are 15 hair ribbons in all. Lesson 3.5 Draw an array to find the product. Question 2. 2 × 7 = ______ Answer: 2 x 7 = 14 Explanation: 2 x 7 = 14 Question 3. 2 × 6 = ______ Answer: 2 x 6 = 12 Explanation: 2 x 6 = 12 Lesson 3.6 Write a multiplication sentence for the model. Then use the Commutative Property of Multiplication to write a related multiplication sentence. Question 4. □□□□□ □□□□□ □□□□□ □□□□□ ______ × ______ = ______ ______ × ______ = ______ Answer: 4 x 5 = 20 5 x 4 = 20 Explanation: The given image has 4 rows and 5 columns of square boxes. So, multiplication = 4 x 5. Using Commutative Property of Multiplication 4 x 5 = 5 x 4. Question 5. ______ × ______ = ______ ______ × ______ = ______ Answer: Explanation: Lesson 3.7 Find the product. Question 6. 6 × 0 = ______ Answer: 0 Explanation: The Zero Property of Multiplication states that the product of zero and any number is zero. So, 6 x 0 = 0. Question 7. 5 × 1 = ______ Answer: 5 Explanation: Use Commutative Property of Multiplication: 5 x 1 = 1 x 5. The Identity Property of Multiplication states that the product of any number and 1 is that number. 5 x 1 = 5. Question 8. 0 × 9 = ______ Answer: 0 Explanation: The Zero Property of Multiplication states that the product of zero and any number is zero. So, 0 x 9 = 0. Question 9. 1 × 8 = ______ Answer: 8 Explanation: The Identity Property of Multiplication states that the product of any number and 1 is that number. 1 x 8 = 8. Question 10. 1 × 4 = ______ Answer: 4 Explanation: The Identity Property of Multiplication states that the product of any number and 1 is that number. 1 x 4 = 4. Question 11. 9 × 1 = ______ Answer: 9 Explanation: Use Commutative Property of Multiplication: 9 x 1 = 1 x 9. The Identity Property of Multiplication states that the product of any number and 1 is that number. 9 x 1 = 9. Question 12. 1 × 0 = ______ Answer: 0 Explanation: The Zero Property of Multiplication states that the product of zero and any number is zero. So, 1 x 0 = 0. Question 13. 7 × 0 = ______ Answer: 0 Explanation: The Zero Property of Multiplication states that the product of zero and any number is zero. So, 7 x 0 = 0. ### Conclusion Go Math Grade 3 Answer Key Chapter 3 Understand Multiplication Extra Practice is intended to help the students to increase their solving ability. It is a great opportunity for students to learn the best way to solve questions. Go Math Grade 3 Chapter 3 Understand Multiplication Extra Practice Answer Key is the first priority who wants to achieve their top grades. Download HMH Go Math Grade 3 Answer Key for free. ## Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Extra Practice Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Extra Practice is the pocket maths help you to have extraordinary skills. The extra practice will help the ability to solve skills. The extra practice of Go Math Grade 3 Chapter 4 Multiplication Facts and Strategies Answer Key is provided with a clear explanation. If your students face problems or struck at some point, then say them to refer HMH Go Math Grade 3 Multiplication Facts and Strategies Answer key. They feel happy by solving Grade 3 Chapter 4 Multiplication Facts and Strategies along with having Answer Key with them. Add extra skills in their pocket using Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Extra Practice. ## Go Math Grade 3 Chapter 4 Multiplication Facts and Strategies Extra Practice Answer Key All concepts are covered in one place along with answers for Go Math Grade 3 Chapter 4 Extra Practice. Follow the steps of Go Math Grade 3 Multiplication Facts and Strategies explanation to learn the easy method to solve problems. ### Common Core – Page No. 87000 Lessons 4.1–4.2 Find the product. Question 1. 4 × 2 = ______ Answer: 4 × 2 = 8. Explanation: Double 2×2 to get 4×2. 2 x 2 = 4. Double: 4 + 4 = 8. 4 x 2 = 8. Question 2. 8 × 5 = ______ Answer: 8 x 5 = 40 Explanation: Factor 8 is an even number. 4+ 4 5 x 4 = 20. 20 doubled is 40. 8 x 5 = 40. Question 3. 10 × 7 = ______ Answer: 10 × 7 = 70 Explanation: A multiple of 10 is any product that has 10 as one of its factors. So, the multiplication of any number with 10 is 10’s of that particular number. The answer is 10 × 7 = 70. Question 4. 2 × 9 = ______ Answer: 2 x 9 = 18 Explanation: Double the given number 6 to get the final answer. The answer is 9 + 9 = 18. 2 x 9 = 18. Question 5. 6 × 1 0 ——- ______ Answer: 6 x 10 = 60 Explanation: Using doubles, we can find a 6 x 10 value. First, multiply the factor with half of 6. So, now we can do 3 x 10 = 30. Now, we can double the value of 3 x 10. That is 30 + 30 = 60. So, the answer for 6 x 10 = 60. Question 6. 5 × 7 ——- ______ Answer: 5 x 7 = 35. Explanation: Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35. Question 7. 2 × 1 0 ——- ______ Answer: 2 x 10 = 20. Explanation: Double 10 to get the answer of 2 x 10. 10 + 10 = 20. 2 x 10 = 20. Question 8. 4 × 5 ——- ______ Answer: 4 x 5 =20 Explanation: Multiply 2×5 to get the answer for 4×5. Double the answer of 2×5 to get the final answer. 2 x 5 =10. Double: 10 + 10 = 20. 4 x 5 =20. Lessons 4.3–4.5 Find the product. Question 9. 6 × 2 ——- ______ Answer: 6 x 2 = 12. Explanation: Use doubles to find the answer of 6 x 2. Multiply 3 x 2 = 6. Double: 6 + 6 = 12. The answer for 6 x 2 is 12. Question 10. 3 × 9 ——- ______ Answer: 3 x 9 = 27. Explanation: Skip count by 3’s until you say 9 numbers. Write like 3, 6, 9, 12, 15, 18, 21, 24, 27. The answer for 3 x 9 is 27. Question 11. 7 × 3 ——- ______ Answer: 7 x 3 = 21 Explanation: Write 7 x 3 as 3 x 7 according to the Commutative Law of Multiplication. Skip count by 3’s until you say 7 numbers. Write like 3, 6, 9, 12, 15, 18, 21. The answer for 3 x 7 is 21. So, 7 x 3 = 21. Question 12. 8 × 6 ——- ______ Answer: 8 × 6 = 48 Explanation: 8 × 6 = (2 x 4) x 6 Use the Associative Property. 8 × 6 = 2 x (4 x 6) Multiply. 4 × 6 8 × 6 = 2 x 24 Double the product. 8 × 6 = 24 + 24 8 × 6 = 48. Write one way to break apart the array. Then find the product. Question 13. Type below: __________ Answer: 36 Explanation: Draw a line to seperate the columns. Divide the columns with 4 and 5 factors. The array is 4 x 9 = 4 x (5 + 4) (4 x 5) + (4 x 4) = 20 + 16 = 36. Find the product. Question 14. 5 × 7 = ______ Answer: 5 x 7 = 35 Explanation: Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35. Question 15. 2 × 6 = ______ Answer: 2 x 6 = 12 Explanation: Double 6 to get the answer. 6 + 6 = 12. 2 x 6 = 12. Question 16. 4 × 7 = ______ Answer: Double 2 x 7 to find 4 x 7. 2 x 7 = 14. Double: 14 + 14 = 28. 4 x 7 = 28. Explanation: Question 17. 8 × 3 = ______ Answer: 8 × 3 = 24 Explanation: 8 × 3 = (2 x 4) x 3 Use the Associative Property. 8 × 3 = 2 x (4 x 3) Multiply. 4 × 3 8 × 3 = 2 x 12 Double the product. 8 × 3 = 12 + 12 8 × 3 = 24. Question 18. Abby has 5 stacks of cards with 7 cards in each stack. How many cards does she have in all? ______ cards Answer: 35 cards Explanation: 5 x 7 = 35. Abby has 35 cards. Question 18. Noah has 3 sisters. He gave 6 balloons to each sister. How many balloons did Noah give away in all? ______ balloons Answer: 18 balloons Explanation: 3 x 6 = 18. Noah gave 18 balloons to his sisters. ### Common Core – Page No. 88000 Lesson 4.6 Write another way to group the factors. Then find the product. Question 1. (3 × 2) × 5 = ______ Explain: __________ Answer: 3 × (2 × 5) 30 Explanation: Using Associative Property of Multiplication, we can write (3 × 2) × 5 = 3 × (2 × 5). Find (3 × 2) × 5. Multiply 3 x 2 = 6. Then, multiply 6 x 5 = 30. Find 3 x (2 x 5). Multiply 2 x 5 = 10. Then, multiply 3 x 10 = 30. So, (3 × 2) × 5 = 3 × (2 × 5). The product value is 30. Question 2. 2 × (5 × 3) = ______ Explain: __________ Answer: (2 x 5) x 3 30 Explanation: Using the Associative Property of Multiplication, we can write 2 × (5 × 3) = (2 x 5) x 3. Find 2 × (5 × 3). Multiply 5 x 3 = 15. Then, multiply 2 x 15 = 30. Find (2 x 5) x 3. Multiply 2 x 5 = 10. Then, multiply 10 x 3 = 30. So, 2 × (5 × 3) = (2 x 5) x 3. The product value is 30. Question 3. (1 × 4) × 2 = ______ Explain: __________ Answer: 1 x (4 x 2) Explanation: Using the Associative Property of Multiplication, we can write (1 × 4) × 2 = 1 x (4 x 2). Find 1 × (4 × 2). Multiply 4 x 2 = 8. Then, multiply 1 x 8 = 8. Find (1 x 4) x 2. Multiply 1 x 4 = 4. Then, multiply 4 x 2 = 8. So, (1 × 4) × 2 = 1 x (4 x 2). The product value is 8. Lesson 4.7 Is the product even or odd? Write even or odd. Question 4. 6 × 6 ______ Answer: Even Explanation: 6 x 6 = 36. The numbers end with 0, 2, 4, 6, 8 are even numbers. So, 36 is even number. The 6 x 6 is an even number. Question 5. 2 × 3 ______ Answer: even Explanation: Products with 2 as a factor are even. Question 6. 3 × 9 ______ Answer: odd Explanation: The product of two odd numbers is an odd number. The answer is odd. So, 3 x 9 = 27. Lessons 4.8–4.9 Find the product. Question 7. 8 × 2 = ______ Answer: 16 Explanation: Factor 8 is an even number. 4+ 4 2 x 4 = 8. 8 doubled is 16. 8 x 2 = 16. Question 8. 5 × 9 = ______ Answer: 5 × 9 = 45 Explanation: The multiplication of 5 × 9 is calculated as Skip-count by 5’s 9 times. You can write as 5, 10, 15, 20, 25, 30, 35, 40, 45. The final answer for 5 × 9 is 45. Question 9. ______ = 3 × 9 Answer: 27 = 3 x 9 Explanation: Skip count by 3’s until you say 9 numbers. Write like 3, 6, 9, 12, 15, 18, 21, 24, 27. The answer for 3 x 9 is 27. Question 10. 4 × 8 = ______ Answer: 2 × 5 = 10 Explanation: Double 2×8 to get 4×8. 2 x 8 = 16. 16 + 16 = 32. 4 x 8 = 32. Question 11. ______ = 9 × 4 Answer: 36 Explanation: 9 = 3 + 6 9 × 4 = (3 + 6) x 4 Multiply each addend by 4. 9 × 4 = (3 x 4) + (6 x 4) Add the products. 9 × 4 = 12 + 24 9 × 4 = 36. Question 12. 6 × 8 = ______ Answer: 48 Explanation: Use doubles to find the answer of 6 x 8. Firstly, multiply 3 x 8 = 24. Then, double the value of 3 x 8. 24 + 24 = 48. The answer for 6 x 8 is 48. Lesson 4.10 Question 13. Leo has a total of 45¢. He has some dimes and pennies. How many different combinations of dimes and pennies could Leo have? Make a table to solve. Leo could have ______ combinations of 45¢. Answer: Leo could have 4 combinations of 45¢. Explanation: 1 dime 35 pennies 2 dimes 25 pennies 3 dimes 15 pennies 4 dimes 5 pennies. Question 13.  Number of Dimes ____1_____ _____2____ ___3______ _____4____ Number of Pennies ____35_____ _____25____ ___15______ ______5___ Total Value 45¢ 45¢ 45¢ 45¢ ### Conclusion Here is the comprehensive collection of math solutions for Grade 3 Chapter 4 Multiplication Facts and Strategies. Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Extra Practice is the source for students to learn easy maths. Follow the methods of solving problems mentioned on this page and get the Go Math Grade 3 Chapter 4 Multiplication Facts and Strategies Extra Practice Answer Key. ## Go Math Grade 3 Chapter 11 Answer Key Pdf Perimeter and Area Go Math Grade 3 Chapter 11 Answer Key Pdf: Go Math Grade 3 Answer Key Chapter 11 Perimeter and Area is an essential study material for students. Basic concepts of Perimeter and Area are clearly explained to score high marks for students. Also, in-depth knowledge of Chapter 11 Perimeter and Area Go Math Grade 3 Answer Key mentioned with a clear explanation. Furthermore, Go Math Grade 3 Perimeter and Area is very convenient for students who are struggling and want to do extra practice in small groups. Every problem is solved and mentioned with a detailed explanation to support the students while their practice. The quiz, homework, formative assessment, or just extra practice whatever you wish to solve can easily do using Go Math Grade 3 Answer Key Chapter 11 Perimeter and Area Answer Key. ## Perimeter and Area Go Math Grade 3 Chapter 11 Answer Key Pdf For the bright future of students, following Go Math Grade 3 Chapter 11 Answer Key Perimeter and Area is mandatory. Improve problem-solving capacity by using HMH Go Math Grade 3 Answer Key. Lesson 1: Model Perimeter Lesson 2: Find Perimeter Lesson 3: Find Unknown Side Lengths Lesson 4: Understand Area Lesson 5: Measure Area Lesson 6: Use Area Models Mid -Chapter Checkpoint Lesson 7: Problem Solving Area of Rectangles Lesson 8: Area of Combined Rectangles Lesson 9: Same Perimeter, Different Areas Review/Test ### Model Perimeter – Page No. 629 Find the perimeter of the shape. Each unit is 1 centimeter. Question 1. 22 centimeters Answer: 22 centimeters Explanation: Each square in the grid is a 1 by 1-centimeter square. So, we have to do is add up the lengths of the dark segments right over the figure. Start the count from the box where 1 is placed. This parameter is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22 centimeters long. So, it is 22 centimeters. Question 2. __________ centimeters Answer: 22 centimeters Explanation: Look at the length of each side. Then, add the length of each side to get the perimeter of the given shape. The lengths of the sides are 6 + 5 + 6 + 5 = 22 centimeters. Go Math Grade 3 Practice Book Pdf Lesson 11.1 Answer Key Question 3. __________ centimeters Answer: 26 centimeters Explanation: Given that each unit is 1 centimeter. Count the lengths of each box from number 1. So, this parameter is 26 centimeters long. or 6 + 5 + 2 + 2 + 2 + 2 + 2 + 5 = 26. Question 4. __________ centimeters Answer: 30 centimeters Explanation: Look at the length of each side. Then, add the length of each side to get the perimeter of the given shape. The lengths of the sides are 2 + 3 + 3+ 3 + 2 + 5 + 7 + 5 = 30 centimeters long. Problem Solving Use the drawing for 5–6. Each unit is 1 centimeter. Question 5. What is the perimeter of Patrick’s shape? __________ centimeters Answer: 20 centimeters Explanation: The perimeter of Patrick’s shape = 5 + 5 + 5 + 5 =20 centimeters. Question 6. How much greater is the perimeter of Jillian’s shape than the perimeter of Patrick’s shape? __________ centimeters Answer: 2 centimeters Explanation: First, the perimeter of Jillian’s shape = 8 + 1 + 4 + 2 + 4 + 3 = 22 centimeters. Difference = 22 – 20 = 2 centimeters. The perimeter of Jillian’s shape is 2 centimeters greater than the perimeter of Patrick’s shape. ### Model Perimeter – Page No. 630 Lesson Check Question 1. Find the perimeter of the shape. Each unit is 1 centimeter. Options: a. 14 centimeters b. 16 centimeters c. 18 centimeters d. 20 centimeters Answer: d. 20 centimeters Explanation: Given that each unit is 1 centimeter. Count the lengths of each box of the dark lines from number 1. So, this parameter is 20 centimeters long. Grade 3 Assessment Test Pdf Chapter 11 Answers Question 2. Find the perimeter of the shape. Each unit is 1 centimeter. Options: a. 19 centimeters b. 26 centimeters c. 33 centimeters d. 55 centimeters Answer: b. 26 centimeters Explanation: Find the length of each box and add them to find the perimeter of the given shape. The perimeter of the given shape is 8 + 4 +3 + 1 + 4 + 4 + 1 + 1 = 26 centimeters. Spiral Review Question 3. Which lists the fractions in order from least to greatest? $$\frac{2}{4}, \frac{2}{3}, \frac{2}{6}$$ Options: a. $$\frac{2}{3}, \frac{2}{4}, \frac{2}{6}$$ b. $$\frac{2}{6}, \frac{2}{4}, \frac{2}{3}$$ c. $$\frac{2}{4}, \frac{2}{3}, \frac{2}{6}$$ d. $$\frac{2}{3}, \frac{2}{6}, \frac{2}{4}$$ Answer: b. $$\frac{2}{6}, \frac{2}{4}, \frac{2}{3}$$ Explanation: The numerator of the given factors is the same. So, look at the denominators to compare the size of the pieces. As the denominator gets smaller, the fraction gets larger. In the given problem, 3 is the smaller denominator compared to 4 and 6. Then, 4 is the next smaller denominator. So, the fractions in order from least to greatest are 2/6, 2/4, 2/3. Question 4. Kasey’s school starts at the time shown on the clock. What time does Kasey’s school start? Options: a. 6:40 b. 8:06 c. 8:30 d. 9:30 Answer: c. 8:30 Explanation: In the figure, hour-hand is indicating number 8. So, we say it is 8 hours. The minute hand is on 6. To find the minutes, multiply 6 x 5 = 30. So, it indicates 30 minutes. The time is 8 hours 30 minutes. Question 5. Michael and Dex are comparing fraction strips. Which statement is NOT correct? Options: a. $$\frac{1}{2}<\frac{2}{2}$$ b. $$\frac{2}{3}>\frac{1}{3}$$ c. $$\frac{4}{8}<\frac{3}{8}$$ d. $$\frac{4}{6}>\frac{2}{6}$$ Answer: c. $$\frac{4}{8}<\frac{3}{8}$$ Explanation: The denominators of the given fractions are the same. So, look at the numerators to compare the numbers. 1 < 2 is correct. 2 > 1 is correct. 4 < 3 is not correct. So, 4/8 < 3/8 is not correct. Question 6. Aiden wants to find the mass of a bowling ball. Which unit should he use? Options: a. liter b. inch c. gram d. kilogram Answer: d. kilogram Explanation: The kilogram is used to find the mass of a bowling ball. ### Find Perimeter – Page No. 635 Use a ruler to find the perimeter. (Note: on mobile devices like smart phones or tablets, the measurements will not be accurate.) Question 1. 12 centimeters Answer: 12 cm Explanation: Add the lengths of the sides measured to the perimeter. 4 + 3 + 2 + 3 = 12 cm. Question 2. _________ centimeters Answer: 13 centimeters Explanation: Use a centimeter ruler to measure the length of each side. Record and add the lengths of the sides measured to the nearest centimeter. 5 cm + 1 cm + 1 cm + 2 cm + 4 cm = 13 centimeters. Question 3. _________ inches Answer: 8 inches Explanation: Use an inch ruler to measure the length of each side to the nearest inch. Record and add the lengths of the sides measured to the nearest inch. 2 in + 2 in + 2 in + 2 in =8 inches. Third Grade Go Math How to Find The Perimeter and Area Question 4. _________ inches Answer: 6 inches Explanation: Use an inch ruler to measure the length of each side. Record and add the lengths of the sides measured to the nearest inch. 2 in + 2 in + 2 in = 6 inches. Problem Solving Draw a picture to solve 5–6. Question 5. Evan has a square sticker that measures 5 inches on each side. What is the perimeter of the sticker? _________ inches Answer: 20 inches Explanation: The square has equal sides. Each side has 5 inches. So, the perimeter of the sticker is 5 x 4 = 20 inches. Question 6. Sophie draws a shape that has 6 sides. Each side is 3 centimeters. What is the perimeter of the shape? _________ centimeters Answer: 18 centimeters Explanation: The perimeter of the shape is = Addition of all sides. Given that Sophie draws a shape that has 6 sides with 3 centimeters. So, the perimeter of the shape = 3 + 3 + 3 + 3 + 3 + 3 = 18 centimeters ### Find Perimeter – Page No. 636 Lesson Check Use an inch ruler for 1–2. Question 1. Ty cut a label the size of the shape shown. What is the perimeter, in inches, of Ty’s label? Options: a. 4 inches b. 5 inches c. 6 inches d. 7 inches Answer: c. 6 inches Explanation: By using an inch ruler, Ty can measure the length of each side of the given shape. Now, find the lengths of each side. 1 in + 2 in + 1 in + 2 in = 6 inches. Question 2. Julie drew the shape shown below. What is the perimeter, in inches, of the shape? Options: a. 2 inches b. 4 inches c. 6 inches d. 8 inches Answer: d. 8 inches Explanation: Julie can use an inch ruler to measure the length of each side of the shape. Now, find the lengths of each side. Each side has 2 inches. So, the perimeter of the shape is 2 in + 2 in + 2 in + 2 in = 8 inches. Spiral Review Question 3. What is the perimeter of the shape below? Options: a. 8 units b. 10 units c. 20 units d. 22 units Answer: c. 20 units Explanation: From the figure, each unit is 1 centimeter. Count the lengths of each box from number 1. So, this parameter is 20 units long. Go Math 3rd Grade Pdf Chapter 11 Measurement Answers Question 4. Vince arrives for his trumpet lesson after school at the time shown on the clock. What time does Vince arrive for his trumpet lesson? Options: a. 3:26 A.M. b. 4:26 A.M. c. 3:26 P.M. d. 4:26 P.M. Answer: c. 3:26 P.M. Explanation: Given that Vince arrives for his trumpet lesson after school at the time shown on the clock. As it is mentioned after school time, it is Noon. The times afternoon and before midnight are written with P.M. The hour hand is indicating the number 3. So, the answer is 3:26 P.M. Question 5. Matthew’s small fish tank holds 12 liters. His large fish tank holds 25 liters. How many more liters does his large fish tank hold? Options: a. 12 liters b. 13 liters c. 25 liters d. 37 liters Answer: b. 13 liters Explanation: To get the more liters, do subtraction of large fish tank liters to small fish tank liters. So, The large fish tank is 25 liters – 12 liters = 13 liters more than Matthew’s small fish tank. Question 6. Cecila and Sasha are comparing fraction strips. Which statement is correct? Options: a. $$\frac{1}{2}<\frac{1}{3}$$ b. $$\frac{1}{8}>\frac{1}{6}$$ c. $$\frac{1}{4}>\frac{1}{2}$$ d. $$\frac{1}{6}<\frac{1}{4}$$ Answer: d. $$\frac{1}{6}<\frac{1}{4}$$ Explanation: Cecila and Sasha are comparing fraction strips. In the given fractions, the numerators are same. So, compare the denominators to find the largest fraction. As the denominator gets smaller, the fraction gets larger. 2 < 3 wrong. 8 > 6 wrong. 4 > 2 wrong. 6 < 4 correct. So, 1/6 < 1/4 is the correct answer. ### Find Unknown Side Lengths – Page No. 641 Find the unknown side lengths. Question 1. Perimeter = 33 centimeters 5 + 8 + 7 + 4 + x = 33 24 + x = 33 x = 9 x = ____ 9 _____ centimeters Answer: 9 centimeters Explanation: If I knew the length x, I would add all the side lengths to find the perimeter. Given Perimeter = 33 centimeters. Add the lengths of the given sides. 5 + 8 + 7 + 4 + x = 33. 24 + x = 33. x = 33 – 24 =9. x = 9 centimeters. Question 2. Perimeter = 14 feet r = ____ feet Answer: 3 feet Explanation: Given Perimeter = 14 feet. Add the lengths of the given sides to find r. 4 ft + 4 ft + r + r = 14 feet. If r =1 -> 4 + 4 + 1 + 1 = 10 not equal to 14. If r = 2 -> 4 + 4 + 2 + 2 = 12 not equal to 14. If r = 3 -> 4 + 4 + 3 + 3 = 14 equal to 14. So, r = 3 feet. 3rd Grade Go Math Topic 11 Lesson 11.3 Answer Key Question 3. Perimeter = 37 meters s = ____ meters Answer: 11 meters Explanation: Given that Perimeter = 37 meters. Add the lengths of the given sides to find s. 8 + 11 + 5 + 2 + s = 37. 26 + s = 37. s = 37 – 26 = 11. s = 11 meters. Question 4. Perimeter = 92 inches t = ____ inches Answer: 15 inches Explanation: Given that Perimeter = 92 inches. Add the lengths of the given sides to find t. 7 + 23 + 12 + 12 +23 + t = 92 77 + t = 92. s = 92 – 77 = 15. s = 15 inches. Problem Solving Question 5. Steven has a rectangular rug with a perimeter of 16 feet. The width of the rug is 5 feet. What is the length of the rug? ____ feet Answer: 3 feet Explanation: Given that Steven has a rectangular rug with a perimeter of 16 feet. Rectangular has 4 sides with two pairs of opposite sides that are equal in length. Let the length will be x. If x = 1 feet -> 5 + x + 5 + x = 5 + 1 + 5 + 1 = 12 feet not equal to 16. If x = 2 feet -> 5 + x + 5 + x = 5 + 2 + 5 + 2 = 14 feet not equal to 16. If x = 3 feet -> 5 + x + 5 + x = 5 + 3 + 5 + 3 = 16 feet equal to 16. So, the length of the blanket is 3 feet. Question 6. Kerstin has a square tile. The perimeter of the tile is 32 inches. What is the length of each side of the tile? ____ inches Answer: 8 inches Explanation: A square has four sides that are equal in length. So, 4 x s = 32 4 x 8 = 32. So, the length of each side of the square is 8 inches. ### Find Unknown Side Lengths – Page No. 642 Lesson Check Question 1. Jesse is putting a ribbon around a square frame. He uses 24 inches of ribbon. How long is each side of the frame? Options: a. 4 inches b. 5 inches c. 6 inches d. 8 inches Answer: c. 6 inches Explanation: Jesse is putting a ribbon around a square frame. A square has four sides that are equal in length. So, 4 x k = 24 inches. 4 x 6 = 24 inches. Each side of the frame 6 inches. Question 2. Davia draws a shape with 5 sides. Two sides are each 5 inches long. Two other sides are each 4 inches long. The perimeter of the shape is 27 inches. What is the length of the fifth side? Options: a. 9 inches b. 13 inches c. 14 inches d. 18 inches Answer: a. 9 inches Explanation: . From the given information, Davia draws a shape with 5 sides. 2 sides = each 5 inches long. 2 sides = each 4 inches long. Let the other side is k. The perimeter of the shape = 5 + 5 + 4 + 4 + k = 27 inches. 18 + k = 27 inches. k = 27 – 18 inches. k = 9 inches. Spiral Review Question 3. Which of the following represents 7 + 7 + 7 + 7? Options: a. 4 × 4 b. 4 × 7 c. 6 × 7 d. 7 × 7 Answer: b. 4 × 7 Explanation: 7 + 7 + 7 + 7 = 28. 4 x 4 = 16 not equal to 28. 4 x 7 = 28 equal to 28. 7 + 7 + 7 + 7 = 4 × 7. Go Math Grade 3 Chapter 11 Review/Test Answer Key Question 4. Bob bought 3 packs of model cars. He gave 4 cars to Ann. Bob has 11 cars left. How many model cars were in each pack? Options: a. 18 b. 11 c. 7 d. 5 Answer: d. 5 Explanation: If Bob has 11 cars left after he gave 4 to Ann, that means he had 15 cars in total. If Bob had 15 cars in total, and these 15 cars were divided into 3 packs, that means each pack contained 5 cars. The answer is 5 cars in each pack. Question 5. Randy looked at his watch when he started and finished reading. How long did Randy read? Options: a. 55 minutes b. 45 minutes c. 35 minutes d. 15 minutes Answer: b. 45 minutes Explanation: Randy started reading at 4:10. Randy finished reading at 4:55. Subtract to find the Randy read time. 4:55 – 4:10 = 45 minutes So, Randy read 45 minutes. Question 6. Which statement does the model represent? Options: a. $$\frac{4}{4}$$ = 1 b. $$\frac{3}{4}$$ = 1 c. $$\frac{2}{4}$$ = 1 d. $$\frac{1}{4}$$ = 1 Answer: a. $$\frac{4}{4}$$ = 1 Explanation: The first image represents the whole circle divided into 4 equal parts. So, each part is $$\frac{1}{4}$$. Together, all 4 parts represent $$\frac{4}{4}$$ or one whole circle. The second image represents one whole circle. $$\frac{4}{4}$$ = 1. ### Understand Area – Page No. 647 Count to find the area for the shape. Question 1. Area = 6 square units Answer: 6 square units Explanation: The area is the measure of the number of unit squares needed to cover a flat surface. A unit square is a square with a side length of 1 unit. It has an area of 1 square unit (sq un). Count the number of Squares to get the answers. 1, 2, 3, 4, 5, 6. Area = 6 square units. Question 2. Area = ______ square units Answer: 4 square units Explanation: Count the number of Squares to get the answers. 1, 2, 3, 4. Area = 4 square units. Question 3. Area = ______ square units Answer: 5 square units Explanation: Count the number of Squares to get the answers. 1, 2, 3, 4, 5. Area = 5 square units. Question 4. Area = ______ square units Answer: 7 square units Explanation: Count the number of Squares to get the answers. 1, 2, 3, 4, 5, 6, 7. Area = 7 square units. Question 5. Area = ______ square units Answer: 8 square units Explanation: Count the number of Squares to get the answers. 1, 2, 3, 4, 5, 6, 7, 8. Area = 8 square units. Question 6. Area = ______ square units Answer: 13 square units Explanation: Count the number of Squares to get the answers. 1, 2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12, 13. Area = 13 square units. Write area or perimeter for each situation. Question 7. carpeting a floor _________ Answer: Area Question 8. fencing a garden _________ Answer: 2. Perimeter Problem Solving Use the diagram for 9–10. Answer: 12 square units Explanation: Count the number of Squares to get the answers. 1, 2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12. Area = 12 square units. Question 9. Rober to is building a platform for his model railroad. What is the area of the platform? Area = ______ square units Answer: 12 square units Explanation: The area of the platform = Count the total number of Squares to get the answers. 1, 2, 3, 4, 5, 6, 7, 8,9, 10, 11, 12. Area = 12 square units. Question 10. Rober to will put a border around the edges of the platform. How much border will he need? Border = ______ units Answer: 16 units Explanation: To know the edges of the platform, we need to calculate the perimeter of the given shape. So, we need to add the length of all sides. 2 + 4 + 3 + 2 + 1 + 1 + 2 + 1 = 16 units. ### Understand Area – Page No. 648 Lesson Check Question 1. Josh used rubber bands to make the shape below on his geoboard. What is the area of the shape? Options: a. 3 square units b. 4 square units c. 5 square units d. 6 square units Answer: a. 3 square units Explanation: If Josh used rubber bands to make the shape below on his geoboard, he can divide the shape into 2 smaller regular shapes. The shape 1 marked as square = 1 square unit. The shape 2 marked as rectangle = 2 square units. The total area = Shape 1 + Shape 2 = 1 + 2 = 3 square units. Go Math Grade 3 Pdf Chapter 11 Review/Test Question 2. Wilma drew the shape below on dot paper. What is the area of the shape she drew? Options: a. 4 square units b. 5 square units c. 6 square units d. 7 square units Answer: b. 5 square units Explanation: Wilma drew the shape below on dot paper. The area of the shape = number of unite square boxes = 1 + 1 + 1 + 1 + 1 = 5 square units. Spiral Review Question 3. Leonardo knows it is 42 days until summer break. How many weeks is it until Leonardo’s summer break? (Hint: There are 7 days in a week.) Options: a. 5 weeks b. 6 weeks c. 7 weeks d. 8 weeks Answer: b. 6 weeks Explanation: Leonardo knows it is 42 days until summer break. There are 7 days in a week. So, by dividing 42 with 7 Leonardo can find summer break in weeks. 42/7 = 6 weeks. Question 4. Nan cut a submarine sandwich into 4 equal parts and ate one part. What fraction represents the part of the sandwich Nan ate? Options: a. $$\frac{1}{4}$$ b. $$\frac{1}{3}$$ c. $$\frac{4}{4}$$ d. $$\frac{4}{1}$$ Answer: a. $$\frac{1}{4}$$ Explanation: Nan cut a submarine sandwich into 4 equal parts and ate one part. So, remaining parts are 3. The fraction of the sandwich Nan ate = $$\frac{1}{4}$$. Question 5. Wanda is eating breakfast. Which is a reasonable time for Wanda to be eating breakfast? Options: a. 7:45 A.M. b. 7:45 P.M. c. 2:15 P.M. d. 2:15 A.M. Answer: a. 7:45 A.M. Explanation: The reasonable time for Wanda to eat breakfast is 7:45 A.M. Because breakfast will eat in the morning i.e, A.M. Question 6. Dick has 2 bags of dog food. Each bag contains 5 kilograms of food. How many kilograms of food does Dick have in all? Options: a. 3 kilograms b. 5 kilograms c. 7 kilograms d. 10 kilograms Answer: d. 10 kilograms Explanation: Dick has 2 x 5 = 10 kilograms of food in total. ### Measure Area – Page No. 653 Count to find the area of the shape. Each unit square is 1 square centimeter. Question 1. Area 14 square centimeters. Answer: 14 square centimeters Explanation: The number of unit square in the given figure is 14. So, the area of the shape = 14 square centimeters. Question 2. Area = ________ square centimeters Answer: 16 square centimeters Explanation: The area of the shape = 16 square centimeters. Go Math 3rd Grade Chapter 11 Test Question 3. Area = ________ square centimeters Answer: 11 square centimeters Explanation: The area of the shape = 11 square centimeters. Question 4. Area = ________ square centimeters Answer: 22 square centimeters Explanation: The area of the shape = 22 square centimeters. Problem Solving Alan is painting his deck gray. Use the diagram at the right for 5–6. Each unit square is 1 square meter. Question 5. What is the area of the deck that Alan has already painted gray? _______ square meters Answer: 16 square meters Explanation: The area of the deck that Alan has already painted gray is 16 square meters. Question 6. What is the area of the deck that Alan has left to paint? _______ square meters Answer: 19 square meters Explanation: The area of the deck that Alan has left to paint is 19 square meters. ### Measure Area – Page No. 654 Lesson Check Each unit square in the diagram is 1 square foot. Question 1. How many square feet are shaded? Options: a. 19 square feet b. 21 square feet c. 23 square feet d. 25 square feet Answer: c. 23 square feet Explanation: Question 2. What is the area that has NOT been shaded? Options: a. 19 square feet b. 21 square feet c. 23 square feet d. 25 square feet Answer: a. 19 square feet Explanation: Spiral Review Question 3. Sonya buys 6 packages of rolls. There are 6 rolls in each package. How many rolls does Sonya buy? Options: a. 42 b. 36 c. 24 d. 12 Answer: b. 36 Explanation: 6 x 6 = 36. Sonya buys 36 rolls. Go Math Grade 3 Chapter 11 Test Answer Key Question 4. Charlie mixed 6 liters of juice with 2 liters of soda to make fruit punch. How many liters of fruit punch did Charlie make? Options: a. 3 liters b. 4 liters c. 8 liters d. 12 liters Answer: c. 8 liters Explanation: 6 + 2 = 8 liters. Charlie can make 8 liters of fruit punch. Question 5. Which drawing shows $$\frac{2}{3}$$ of the circle shaded? Options: a. b. c. d. Answer: d. Explanation: Option d is the correct answer. 2/3 means the whole circle has 3 parts. 2 of the parts are shaded. Question 6. Use the models to name a fraction that is equivalent to $$\frac{1}{2}$$. Options: a. $$\frac{2}{1}$$ b. $$\frac{2}{2}$$ c. $$\frac{2}{4}$$ d. $$\frac{4}{4}$$ Answer: c. $$\frac{2}{4}$$ Explanation: $$\frac{2}{4}$$ = $$\frac{1}{2}$$. So, the answer is $$\frac{2}{4}$$ ### Use Area Models – Page No. 659 Find the area of each shape. Each unit square is 1 square foot. Question 1. Answer: 24 square feet Explanation: There are 3 rows of 8 unit squares. 3 x 8 = 24. Question 2. _________ square feet Find the area of each shape. Each unit square is 1 square meter. Answer: 16 square feet Explanation: There are 4 rows of 4 unit squares. 4 x 4 = 16 square feet. Question 3. _________ square meters Answer: 12 square meters Explanation: There are 2 rows of 6 unit squares. 2 x 6 = 12 square meters. Question 4. _________ square meters Answer: 24 square meters Explanation: There are 4 rows of 6 unit squares. 4 x 6 = 24 square meters. Question 5. _________ square meters Answer: 15 square meters Explanation: There are 5 rows of 3 unit squares. 5 x 3 = 15 square meters. Problem Solving Question 6. Landon made a rug for the hallway. Each unit square is 1 square foot. What is the area of the rug? _________ square feet Answer: 20 square feet Explanation: Count the number of unit square boxes = 20 square feet. Or, there are 2 rows of 10 unit squares. 2 x 10 = 20 square feet. Go Math 3rd Grade Chapter 11 Review Test Answer Key Question 7. Eva makes a border at the top of a picture frame. Each unit square is 1 square inch. What is the area of the border? _________ square feet Answer: 8 square feet Explanation: Count the number of unit square boxes = 20 square feet. Or, there are 1 rows of 8 unit squares. 1 x 8 = 8 square feet. ### Use Area Models – Page No. 660 Lesson Check Question 1. The entrance to an office has a tiled floor. Each square tile is 1 square meter. What is the area of the floor? Options: a. 8 square meters b. 9 square meters c. 10 square meters d. 12 square meters Answer: b. 9 square meters Explanation: There are 9 square boxes available. So, the area of the floor = 9 square meters. Question 2. Ms. Burns buys a new rug. Each unit square is 1 square foot. What is the area of the rug? Options: a. 5 square feet b. 7 square feet c. 10 square feet d. 12 square feet Answer: c. 10 square feet Explanation: The area of the rug = 10 square feet. Spiral Review Question 3. Ann and Bill are comparing fraction strips. Which statement is correct? Options: a. $$\frac{3}{8}>\frac{5}{8}$$ b. $$\frac{3}{4}<\frac{1}{4}$$ c. $$\frac{3}{6}>\frac{4}{6}$$ d. $$\frac{1}{3}<\frac{2}{3}$$ Answer: d. $$\frac{1}{3}<\frac{2}{3}$$ Explanation: The denominator of the given fractions are same. So, compare the numerators to find the correct answer. 3 > 5 wrong. 3 < 1 wrong. 3 > 4 wrong. 1 < 2 correct. The answer is $$\frac{1}{3}<\frac{2}{3}$$. Question 4. Claire bought 6 packs of baseball cards. Each pack had the same number of cards. If Claire bought 48 baseball cards in all, how many cards were in each pack? Options: a. 54 b. 42 c. 8 d. 6 Answer: c. 8 Explanation: 6 x k = 48. So, k = 48/6 = 8. 8 cards were in each pack. Question 5. Austin left for school at 7:35 A.M.. He arrived at school 15 minutes later. What time did Austin arrive at school? Options: a. 7:40 A.M. b. 7:50 A.M. c. 7:55 A.M. d. 8:00 A.M. Answer: b. 7:50 A.M. Explanation: 7:35 A.M. + 15 minutes = 7:50 A.M Question 6. Wyatt’s room is a rectangle with a perimeter of 40 feet. The width of the room is 8 feet. What is the length of the room? Options: a. 5 feet b. 12 feet c. 16 feet d. 32 feet Answer: b. 12 feet Explanation: The perimeter of rectangle = 40 feet. The width of the room is 8 feet. 8 + k + 8 + k = 40. If k = 10 -> 8 + 10 + 8 + 10 = 36. If k = 11 -> 8 + 11 + 8 + 11 = 38. If k = 12 -> 8 + 12 + 8 + 12 = 40. So, the length of the room = 12 feet. ### Mid -Chapter Checkpoint – Page No. 661 Vocabulary Choose the best term from the box. Question 1. The distance around a figure is the _____________ . _____________ Answer: Perimeter Question 2. The measure of the number of unit squares needed to cover a figure with no gaps or overlaps is the _____________ . _____________ Answer: Area Concepts and Skills Find the perimeter of the figure. Each unit is 1 centimeter. Question 3. _______ centimeters Answer: 16 centimeters Explanation: 5 + 2 + 2 + 1 + 2 + 1 + 1 + 2 = 16 centimeters. Question 4. _______ centimeters Answer: 14 cm Explanation: 4 + 3 + 4 + 3 = 14 cm. Find the unknown side lengths. Question 5. Perimeter = 33 centimeters g = ______ centimeters Answer: 3 centimeters Explanation: Given that Perimeter = 33 centimeters. 10 + 6 + 10 + g + 4 = 33 centimeters. 30 + g = 33 centimeters. g= 33 – 30 centimeters. g = 3 centimeters. Go Math Chapter 11 Grade 3 Answer Key Question 6. Perimeter = 32 feet k = ______ feet Answer: 4 feet Explanation: Perimeter = 32 feet. 12 ft + k + 12 ft + k = 32 feet. If k = 1 then 12 + 1 + 12 + 1 = 26 feet not equal to 32 feet. If k = 2 then 12 + 2 + 12 + 2 = 28 feet not equal to 32 feet. If k = 3 then 12 + 3 + 12 + 3 = 30 feet not equal to 32 feet. If k = 4 then 12 + 4 + 12 + 4 = 32 feet equal to 32 feet. So, k = 4 feet. Find the area of the figure. Each unit square is 1 square meter. Question 7. ______ square meters Answer: 14 square meters Explanation: Question 8. ______ square meters Answer: 30 square meters Explanation: 10 x 3 = 30 square meters. ### Mid -Chapter Checkpoint – Page No. 662 Question 9. Ramona is making a lid for her rectangular jewelry box. The jewelry box has side lengths of 6 centimeters and 4 centimeters. What is the area of the lid Ramona is making? ______ square meters Answer: 24 square meters. Explanation: The area of the lid = 4 cm x 6 cm = 24 cm. Ramona making 24 cm lid for her rectangular jewelry box. Question 10. Adrienne is decorating a square picture frame. She glued 36 inches of ribbon around the edge of the frame. What is the length of each side of the picture frame? a = ______ inches Answer: 9 inches Explanation: A square has the same lengths. The length of each side 4 x a = 36 inches. a = 36/4 = 9 inches. Question 11. Margo will sweep a room. A diagram of the floor that she needs to sweep is shown at the right. What is the area of the floor? ______ square units Answer: 27 square units Explanation: 27 square units Question 12. Jeff is making a poster for a car wash for the Campout Club. What is the perimeter of the poster? ______ feet Answer: 8 ft Explanation: Perimeter = 3 + 1 + 3 + 1 = 8 ft. Question 13. A rectangle has two side lengths of 8 inches and two side lengths of 10 inches. What is the perimeter of the rectangle? What is the area of the rectangle? Perimeter ______ inches Area = ______ square inches Answer: Perimeter = 36 inches. Area = 80 square inches. Explanation: The perimeter of the rectangle = 8 + 10 + 8 + 10 = 36. Area = 10 x 8 = 80 square inches. ### Problem Solving Area of Rectangles – Page No. 667 Use the information for 1–3. An artist makes rectangular murals in different sizes. Below are the available sizes. Each unit square is 1 square meter. Question 1. Complete the table to find the area of each mural.  Mural Length (in meters) Width (in meters) Area (in square meters) A 2 1 2 B 2 2 4 C 2 __4_______ __8_______ D 2 ____8_____ ___16______ Question 2. Find and describe a pattern of how the length changes and how the width changes for murals A through D. Type below: _____________ Answer: For each mural, the width doubles and the length stays the same. Question 3. How do the areas of the murals change when the width changes? Type below: _____________ Answer: For each mural, the area doubles. Question 4. Dan built a deck that is 5 feet long and 5 feet wide. He built another deck that is 5 feet long and 7 feet wide. He built a third deck that is 5 feet long and 9 feet wide. How do the areas change? Type below: _____________ Answer: The area of each deck is increased by 10 square feet. Explanation: 1st deck area = 5 x 5 = 25 feet. 2nd deck area = 5 x 7 = 35 feet. 3rd deck area = 5 x 9 = 45 feet. The area of each deck is increased by 10 square feet. ### Problem Solving Area of Rectangles – Page No. 668 Lesson Check Question 1. Lauren drew the designs below. Each unit square is 1 square centimeter. If the pattern continues, what will be the area of the fourth shape? Options: a. 10 square centimeters b. 12 square centimeters c. 14 square centimeters d. 16 square centimeters Answer: b. 12 square centimeters Explanation: 4 x 3 = 12 cm. The area of the fourth shape is 12 square centimeters. Question 2. Henry built one garden that is 3 feet wide and 3 feet long. He also built a garden that is 3 feet wide and 6 feet long, and a garden that is 3 feet wide and 9 feet long. How do the areas change? Options: a. The areas do not change. b. The areas double. c. The areas increase by 3 square feet. d. The areas increase by 9 square feet. Answer: d. The areas increase by 9 square feet. Explanation: 1st garden = 3 x 3 = 9 feet. 2nd garden = 3 x 6 = 18 feet. 3rd garden = 3 x 9 = 27 feet. The areas increase by 9 square feet. Spiral Review Question 3. Joe, Jim, and Jack share 27 football cards equally. How many cards does each boy get? Options: a. 7 b. 8 c. 9 d. 10 Answer: c. 9 Explanation: x + x + x = 27. 3x = 27. x = 27/3 = 9. Each boy gets 9 football cards. Question 4. Nita uses $$\frac{1}{3}$$ of a carton of 12 eggs. How many eggs does she use? Options: a. 3 b. 4 c. 6 d. 9 Answer: b. 4 Explanation: $$\frac{1}{3}$$ of a carton of 12 eggs = $$\frac{1}{3}$$ x 12 = 4. Nita uses 4 eggs. Question 5. Brenda made 8 necklaces. Each necklace has 10 large beads. How many large beads did Brenda use to make the necklaces? Options: a. 80 b. 85 c. 90 d. 100 Answer: a. 80 Explanation: 8 x 10 = 80 beads. Brenda uses 80 beads to make the necklaces 3rd Grade Math Book Answers How to Find Area and Perimeter Question 6. Neal is tiling his kitchen floor. Each square tile is 1 square foot. Neal uses 6 rows of tiles with 9 tiles in each row. What is the area of the floor? Options: a. 15 square feet b. 52 square feet c. 54 square feet d. 57 square feet Answer: c. 54 square feet Explanation: The area of the floor = 6 x 9 = 54 square feet. ### Area of Combined Rectangles – Page No. 673 Use the Distributive Property to find the area. Show your multiplication and addition equations. Question 1. Answer: 28 Square Units Explanation: Question 2. _______ square units Answer: 27 square units Explanation: 3 x 3 = 9; 3 x 6 = 18. 9 + 18 = 27 27 square units. Draw a line to break apart the shape into rectangles. Find the area of the shape. Question 3. Type below: _____________ Answer: 31 square units Explanation: 5 x 5 = 25; 2 x 3 = 6 25 + 6 = 31 31 square units Question 4. Type below: _____________ Answer: 32 square units Explanation: 4 x 4 = 16; 2 x 8 = 16. 16 + 16 = 32. 32 square units Problem Solving A diagram of Frank’s room is at right. Each unit square is 1 square foot. Question 5. Draw a line to divide the shape of Frank’s room into rectangles. Answer: Question 6. What is the total area of Frank’s room? _______ square feet Answer: 75 square feet Explanation: 6 x 5 = 30; 5 x 9 = 45 30 + 45 = 75. 75 square feet ### Area of Combined Rectangles – Page No. 674 Lesson Check Question 1. The diagram shows Ben’s backyard. Each unit square is 1 square yard. What is the area of Ben’s backyard? Options: a. 12 square yards b. 16 square yards c. 18 square yards d. 24 square yards Answer: b. 16 square yards Explanation: 6 x 3 = 18 square yards Question 2. The diagram shows a room in an art gallery. Each unit square is 1 square meter. What is the area of the room? Options: a. 24 square meters b. 30 square meters c. 36 square meters d. 40 square meters Answer: b. 30 square meters Explanation: 3 x 5 = 15; 3 x 5 = 15 15 + 15 = 30 square meters Spiral Review Question 3. Naomi needs to solve 28 ÷ 7 = ■. What related multiplication fact can she use to find the unknown number? Options: a. 3 × 7 = 21 b. 4 × 7 = 28 c. 5 × 7 = 35 d. 6 × 7 = 42 Answer: b. 4 × 7 = 28 Explanation: 28 ÷ 7 = 4. So, 4 x 7 = 28 is the answer. Go Math Workbook Grade 3 Pdf Perimeter Answer Key Question 4. Karen drew a triangle with side lengths of 3 centimeters, 4 centimeters, and 5 centimeters. What is the perimeter of the triangle? Options: a. 7 centimeters b. 9 centimeters c. 11 centimeters d. 12 centimeters Answer: d. 12 centimeters Explanation: Perimeter = 3 centimeters + 4 centimeters + 5 centimeters = 12 centimeters. Question 5. The rectangle is divided into equal parts. What is the name of the equal parts? Options: a. half b. third c. fourth d. sixth Answer: c. fourth Question 6. Use an inch ruler. To the nearest half inch, how long is this line segment? Options: a. 1 b. 1 $$\frac{1}{2}$$ c. 2 d. 2 $$\frac{1}{2}$$ Answer: c. 2 Explanation: The line segment = 2 inches. ### Same Perimeter, Different Areas – Page No. 679 Find the perimeter and the area. Tell which rectangle has a greater area. Question 1. A: Perimeter = 12 ; Area = 9 square units B: Perimeter = ______ units; Area = ______ square units; Rectangle ______ has a greater area. Answer: Rectangle A has a greater area. Explanation: A: Perimeter = 12 ; Area = 9 square units B: Perimeter = 2 + 4 + 2 + 4 = 12 Area = 2 x 4 = 8 square units Rectangle A has a greater area. Question 2. A: Perimeter = ______ units; Area = ______ square units; B: Perimeter = ______ units; Area = ______ square units; Rectangle ______ has a greater area. Answer: Rectangle A has a greater area. Explanation: A: Perimeter = 4 + 1 + 4 + 1 = 10 Area = 4 x 1 = 4 square units B: Perimeter = 3 + 2 + 3 + 2 = 10 Area = 3 x 2 = 6 square units Rectangle B has a greater area. Problem Solving Question 3. Tara’s and Jody’s bedrooms are shaped like rectangles. Tara’s bedroom is 9 feet long and 8 feet wide. Jody’s bedroom is 7 feet long and 10 feet wide. Whose bedroom has the greater area? Explain. _________ ‘s bedrooms is greater. Answer: Tara’s bedroom has a greater area than Jody’s bedroom area. Explanation: Tara’s bedroom area = 9 x 8 = 72 feet. Jody’s bedroom area = 7 x 10 = 70 feet. 72 feet > 70 feet. Tara’s bedroom has a greater area than Jody’s bedroom area. Chapter 11 Mid Chapter Test Go Math Grade 3 Question 4. Mr. Sanchez has 16 feet of fencing to put around a rectangular garden. He wants the garden to have the greatest possible area. How long should the sides of the garden be? Width: ______ Length: ______ feet long Answer: All four sides should be 4 feet long. Explanation: Mr. Sanchez has 16 feet of fencing to put around a rectangular garden. Perimeter = 1 + 7 + 1 + 7 = 16 feet. Area = 1 x 7 = 7 feet. Perimeter = 2 + 6 + 2 + 6 = 16 feet. Area = 2 x 6 = 12 feet. Perimeter = 3 + 5 + 3 + 5 = 16 feet. Area = 3 x 5 = 15 feet. perimeter = 4 + 4 + 4 + 4 = 16 feet. Area = 4 x 4 = 16 feet. The area is maximum when all the four sides are 4 feet long. ### Same Perimeter, Different Areas – Page No. 680 Question 1. Which shape has a perimeter of 12 units and an area of 8 square units? Options: a. b. c. d. Answer: b Explanation: Perimeter = 2 + 4 + 2 + 4 = 12 units. Area = 2 x 4 = 8 square units Question 2. All four rectangles below have the same perimeter. Which rectangle has the greatest area? Options: a. b. c. d. Answer: d Explanation: a. Area = 2 x 10 = 20. b. Area = 3 x 9 = 27. c. Area = 4 x 8 = 32. d. Area = 5 x 7 = 35. d has the greatest area. Spiral Review Question 3. Kerrie covers a table with 8 rows of square tiles. There are 7 tiles in each row. What is the area that Kerrie covers in square units? Options: a. 15 square units b. 35 square units c. 42 square units d. 56 square units Answer: d. 56 square units Explanation: Area = 8 x 7 = 56. Kerrie covers 56 square units area. Question 4. Von has a rectangular workroom with a perimeter of 26 feet. The length of the workroom is 6 feet. What is the width of Von’s workroom? Options: a. 7 feet b. 13 feet c. 20 feet d. 26 feet Answer: a. 7 feet Explanation: Perimeter = 26 feet. Length = 6 feet. Given Von has a rectangular workroom. So, two lengths and two widths are the same for a rectangle. Perimeter of a rectangle = Length + Width + Length + Width = 6 + W + 6 + W = 26 feet. 12 + 2W = 26 feet. 2W = 26 – 12 = 14. W = 14/2 = 7 feet. ### Same Perimeter, Different Areas – Page No. 685 Find the perimeter and the area. Tell which rectangle has a greater perimeter. Question 1. A: Area = 8 square units ; Perimeter = 18 units ; B: Area = _______ square units; Perimeter = _______ units; Rectangle _______ has a greater perimeter. Answer: Rectangle A has a greater perimeter Explanation: A: Area = 8 square units ; Perimeter = 18 units ; B: Area = ___8____ square units; Perimeter = ____12___ units; Rectangle ___A____ has a greater perimeter. Question 2. A: Area = _______ square units; Perimeter = _______ units; Question 2. B: Area = _______ square units; Perimeter = _______ units; Rectangle _______ has a greater perimeter. Answer: Rectangle B has a greater perimeter Explanation: A: Area = 12 square units ; Perimeter = 14 units ; B: Area = ___12____ square units; Perimeter = ____16___ units; Rectangle ___B____ has a greater perimeter. Question 3. A: Area = _______ square units; Perimeter = _______ units; Question 3. B: Area = _______ square units; Perimeter = _______ units; Rectangle _______ has a greater perimeter. Answer: Rectangle B has a greater perimeter Explanation: A: Area = 16 square units ; Perimeter = 16 units ; B: Area = ___16____ square units; Perimeter = ____20___ units; Rectangle ___B____ has a greater perimeter. Problem Solving Use the tile designs for 4–5. Perimeter and Area Answer Key Go Math Florida Grade 3 Question 4. Compare the areas of Design A and Design B. The area of Design A ________ The area of Design B Answer: The area of Rectangle A and Rectangle B are equal. Explanation: A: Area = 20 square units ; B: Area = ___20____ square units; Question 5. Compare the perimeters. Which design has the greater perimeter? The perimeter of A ________ The perimeter of B Answer: The perimeter of A Greater than the perimeter of B Explanation: A: Perimeter = 24 units ; B: Perimeter = ____18___ units; ### Same Perimeter, Different Areas – Page No. 686 Lesson Check Question 1. Jake drew two rectangles. Which statement is true? Options: a. The perimeters are the same. b. The area of A is greater. c. The perimeter of A is greater. d. The perimeter of B is greater Answer: d. The perimeter of B is greater Explanation: A: Area = 6 square units ; Perimeter = 10 units ; B: Area = ___6____ square units; Perimeter = ____14___ units; The perimeter of B is greater. Question 2. Alyssa drew two rectangles. Which statement is true? Options: a. The perimeter of B is greater. b. The perimeter of A is greater. c. The area of B is greater. d. The perimeters are the same. Answer: b. The perimeter of A is greater. Explanation: A: Area = 18 square units ; Perimeter = 22 units ; B: Area = ___18____ square units; Perimeter = ____18___ units; The perimeter of A is greater. Spiral Review Question 3. Marsha was asked to find the value of 8 – 3 x 2. She wrote a wrong answer. Which is the correct answer? Options: a. 22 b. 10 c. 4 d. 2 Answer: d. 2 Explanation: 8 – (3 x 2) = 8 – 6 = 2 Go Math Grade 3 Chapter 11 Answer Key Pdf Question 4. What fraction names the point on the number line? Options: a. $$\frac{1}{4}$$ b. $$\frac{2}{3}$$ c. $$\frac{3}{4}$$ d. $$\frac{3}{1}$$ Answer: c. $$\frac{3}{4}$$ Explanation: From the given figure, we can write the fraction name the point on the number line = $$\frac{3}{4}$$ Question 5. Kyle drew three line segments with these lengths: $$\frac{2}{4}$$ inch, $$\frac{2}{3}$$ inch, and $$\frac{2}{6}$$ inch. Which list orders the fractions from least to greatest? Options: a. $$\frac{2}{6}, \frac{2}{4}, \frac{2}{3}$$ b. $$\frac{2}{3}, \frac{2}{4}, \frac{2}{6}$$ c. $$\frac{2}{4}, \frac{2}{3}, \frac{2}{6}$$ d. $$\frac{2}{6}, \frac{2}{3}, \frac{2}{4}$$ Answer: c. $$\frac{3}{4}$$ Explanation: Given fractions are $$\frac{2}{4}$$ inch, $$\frac{2}{3}$$ inch, and $$\frac{2}{6}$$ inch. All the fractions have the same numerator. The denominators should compare to find the answer. The smaller denominator represents the larger number. So, $$\frac{2}{6}, \frac{2}{4}, \frac{2}{3}$$ is the answer. Question 6. On Monday, $$\frac{3}{8}$$ inch of snow fell. On Tuesday, $$\frac{5}{8}$$ inch of snow fell. Which statement correctly compares the snow amounts? Options: a. $$\frac{3}{8}=\frac{5}{8}$$ b. $$\frac{3}{8}<\frac{5}{8}$$ c. $$\frac{5}{8}<\frac{3}{8}$$ d. $$\frac{3}{8}>\frac{5}{8}$$ Answer: b. $$\frac{3}{8}<\frac{5}{8}$$ Explanation: Given fractions are $$\frac{3}{8}$$ and $$\frac{5}{8}$$. The denominators are equal for given fractions. So, compare numerators to find the correct equation. 3 < 5. So, $$\frac{3}{8}<\frac{5}{8}$$ is the correct answer. ### Review/Test – Page No. 687 Question 1. Find the perimeter of each figure on the grid. Identify the figure that have a perimeter of 14 units. Mark all that apply. Options: a. b. c. d. Answer: a and c have a perimeter of 14 units. Explanation: a. The Perimeter of A = 14 units. b. The perimeter of B = 16 units. c. The perimeter of C = 14 units. d. The perimeter of D = 16 units Question 2. Kim wants to put trim around a picture she drew. How many centimeters of trim does Kim need for the perimeter of the picture? _________ centimeters Answer: 24 centimeters Explanation: Perimeter = 6 + 6 + 6+ 6 = 24 centimeters. Question 3. Sophia drew this rectangle on dot paper. What is the area of the rectangle? _________ square units Answer: 8 square units Explanation: 8 square units ### Review/Test – Page No. 688 Question 4. The drawing shows Seth’s plan for a fort in his backyard. Each unit square is 1 square foot. Which equations can Seth use to find the area of the fort? Mark all that apply. Options: a. 4 + 4 + 4 + 4 = 16 b. 7 + 4 + 7 + 4 = 22 c. 7 + 7 + 7 + 7 = 28 d. 4 × 4 = 16 e. 7 × 7 = 49 f. 4 × 7 = 28 Answer: b and f are correct. Explanation: Area = 4 × 7 = 28 Perimeter = 7 + 4 + 7 + 4 = 22. Question 5. Which rectangle has a number of square units for its area equal to the number of units of its perimeter? Options: a. b. c. d. Answer: B rectangle has a number of square units for its area equal to the number of units of its perimeter Explanation: a. Area = 1 x 7 = 7 units. Perimeter = 1 + 7 + 1 + 7 = 16 units. b. a. Area = 4 x 4 = 16 units. Perimeter = 4 + 4 + 4 + 4 = 16 units. c. a. Area = 2 x 6 = 12 units. Perimeter = 2 + 6 + 2 + 6 = 16 units. d. a. Area = 3 x 5 = 7 units. Perimeter = 3 + 5 + 3 + 5 = 16 units. Question 6. Vanessa uses a ruler to draw a square. The perimeter of the square is 12 centimeters. Select a number to complete the sentence. The square has a side length of centimeters. _________ centimeters Answer: 3 centimeters Explanation: Perimeter = s + s + s + s = 12 centimeters. 4s = 12 centimeters. s = 3 centimeters. ### Review/Test – Page No. 689 Question 7. Tomas drew two rectangles on grid paper. Circle the words that make the sentence true. Rectangle A has an area that is the area of Rectangle B, and a perimeter that is the perimeter of Rectangle B. Type below: _____________ Answer: Rectangle A has an area that is the same as the area of Rectangle B. A perimeter that is less than the perimeter of Rectangle B. Explanation: A: Area = 3 x 4 = 12 units. Perimeter = 3 + 4 + 3 + 4 = 14 units. B: Area = 2 x 6 = 12 units. Perimeter = 2 + 6 + 2 + 6 = 16 units. Question 8. Yuji drew this figure on grid paper. What is the perimeter of the figure? ________ units Answer: 18 units Explanation: Question 9. What is the area of the figure shown? Each unit square is 1 square meter. ________ square meters Answer: 13 square meters Explanation: ### Review/Test – Page No. 690 Question 10. Shawn drew a rectangle that was 2 units wide and 6 units long. Draw a different rectangle that has the same perimeter but a different area. Type below: _____________ Answer: Area = 2 x 6 = 12 Square Units. Area = 4 x 4 = 16 Square Units. Question 11. Mrs. Rios put a wallpaper border around the room shown below. She used 72 feet of wallpaper border. What is the unknown side length? Show your work. a = ________ ft Answer: 16 feet Explanation: 20 + a + 6 + 8 + 14 + 8 = 72 feet. a + 56 = 72 feet. a = 72 – 56 feet. a = 16 feet. Question 12. Elizabeth has two gardens in her yard. The first garden is 8 feet long and 6 feet wide. The second garden is half the length of the first garden. The area of the second garden is twice the area of the first garden. For numbers 12a–12d, select True or False. First garden = 8 x 6 = 48 feet. Second garden length = Half the length of the first garden = 4 feet. Second Garden Area = Twice the area of the first garden = 2 x 48 = 96. Second Garden Area Width = 4 x s = 96. s = 96/4 = 24 a. The area of the first garden is 48 square feet. i. True ii. False Answer: i. True Question 12. b. The area of the second garden is 24 square feet. i. True ii. False Answer: ii. False Question 12. c. The width of the second garden is 12 feet. i. True ii. False Answer: ii. False Explanation: Question 12. d. The width of the second garden is 24 feet. i. True ii. False Answer: i. True ### Review/Test – Page No. 691 Question 13. Marcus bought some postcards. Each postcard had a perimeter of 16 inches. Which could be one of the postcards Marcus bought? Mark all that apply. Options: a. b. c. d. Answer: a and d options are correct. Explanation: 3 + 5 + 3 + 5 = 16 inches 4 + 6 + 4 + 6 = 20 inches. 5 + 10 + 5 + 10 = 30 inches. 4 + 4 + 4 + 4 = 16 inches. Question 14. Anthony wants to make two different rectangular flowerbeds, each with an area of 24 square feet. He will build a wooden frame around each flowerbed. The flowerbeds will have side lengths that are whole numbers. Part A Each unit square on the grid below is 1 square foot. Draw two possible flowerbeds. Label each with a letter. Type below: __________ Answer: Question 14. Part B Which of the flowerbeds will take more wood to the frame? Explain how you know. Type below: __________ Answer: A Perimeter is greater than B Perimeter. Explanation: Area = 24. 3 x 8 = 24; 4 x 6 = 24. A Perimeter = 8 + 3 + 8 + 3 = 22 feet. B Perimeter = 4 + 6 + 4 + 6 = 20 feet. A Perimeter is greater than B Perimeter. ### Review/Test – Page No. 692 Question 15. Keisha draws a sketch of her living room on grid paper. Each unit square is 1 square meter. Write and solve a multiplication equation that can be used to find the area of the living room in square meters. Type below: __________ Answer: 40 meter. Explanation: 4 x 10 = 40 m. Question 16. Mr. Wicks designs houses. He uses grid paper to plan a new house design. The kitchen will have an area between 70 square feet and 85 square feet. The pantry will have an area between 4 square feet and 15 square feet. Draw and label a diagram to show what Mr. Wicks could design. Explain how to find the total area. Type below: __________ Answer: 78 square feet Explanation: Are of Kitchen = 8 x 9 = 72 square feet. (70 < 72 < 85) Area of Pantry = 3 x 2 = 6 square feet. (4 < 6 < 15) Total area of kitchen and pantry = 72 + 6 = 78 square feet. ### Conclusion Go Math Grade 3 Answer Key Chapter 11 Perimeter and Area is given with answers and explanations. Move with every step of solving the process to solve your problems easily. Also, you will be the topper with excessive skills if you follow Go Math Grade 3 Chapter 11 Perimeter and Area Answer Key. All chapters with explanations are available at go math answer key. Practice Go Math Grade 3 Answer Key Chapter 11 Perimeter and Area Extra Practice to grab more knowledge. ## Go Math Grade 3 Chapter 12 Answer Key Pdf Two-Dimensional Shapes Go Math Grade 3 Chapter 12 Answer Key Pdf: Follow the Go Math Grade 3 Answer Key Chapter 12 Two-Dimensional Shapes for Answers with an explanation. Additional practice problems with a detailed step-by-step explanation will help the students for a better understanding. Also, students can easily improve their problem-solving skills with the help of Go Math Grade 3 Answer Key. Quick learning is possible with the clear explanations of Grade 3 Chapter 12 Answer Key. So, instantly start your practicing now and strengthen the knowledge. Complete concepts are solved with simple steps included in the Go Math Answer Key for Grade 3 Chapter 12 Two-Dimensional Shapes. ## Two-Dimensional Shapes Go Math Grade 3 Chapter 12 Answer Key Pdf The practice is the only way to get knowledge. So, solving simple tricks and techniques will lead the students to get high grades. Go Math Grade 3 Answer Key Chapter 12 is a one-stop solution for learning problem-solving skills. Easy learning and fast solving will comes at the same place by using Go Math Grade 3 Answer Key Chapter 12 Two-Dimensional Shapes. ### Lesson 1: Describe Plane Shapes ### Lesson 2: Describe Angles in Plane Shapes ### Lesson 3: Identify Polygons ### Chapter: Unlock the Problem – Page No. 715 ### Lesson 4: Describe Sides of Polygons ### Mid -Chapter Checkpoint ### Lesson 5: Classify Quadrilaterals ### Lesson 6: Draw Quadrilaterals ### Lesson 7: Describe Triangles ### Lesson 8: Problem Solving Classify Plane Shapes ### Lesson 9: Relate Shapes, Fractions, and Area ### Review/Test ### Describe Plane Shapes – Page No. 701 Write how many line segments the shape has. Question 1. 4 line segments Answer: 4 line segments Explanation: Question 2. ________ line segments Answer: 6 line segments Explanation: Describe Sides of Polygons Question 3. ________ line segments Answer: 8 line segments Explanation: Question 4. ________ line segments Answer: 5 line segments Explanation: Write whether the shape is open or closed. Question 5. ________ Answer: Open Explanation: The given shape does not start and ends at the same point. So, the shape is open. Question 6. ________ Answer: Closed Explanation: The given shape started and ends at the same point. So, the shape is closed. Problem Solving Question 7. Carl wants to show a closed shape in his drawing. Show and explain how to make the drawing a closed shape. Type below: ___________ Answer: Add a fourth line segment, so the shape starts and ends at the same point. Explanation: Add a fourth line segment, so the shape starts and ends at the same point. Question 8. The shape of a fish pond at a park is shown below. Is the shape open or closed? ________ Answer: Closed Explanation: The given shape started and ends at the same point. So, the shape is closed. ### Describe Plane Shapes – Page No. 702 Lesson Check Question 1. How many line segments does this shape have? Options: a. 2 b. 3 c. 4 d. 5 Answer: d. 5 Explanation: Question 2. Which of these is part of a line, has one endpoint, and continues in one direction? Options: a. ray b. line c. line segment d. point Answer: a. ray Explanation: The line has one endpoint and continues in one direction is called a ray. Spiral Review Question 3. What multiplication sentence does the array show? Options: a. 3 × 8 = 24 b. 4 × 8 = 32 c. 8 × 5 = 40 d. 4 × 9 = 36 Answer: b. 4 × 8 = 32 Explanation: There are 4 rows and 8 columns available. 4 x 8 = 32 is the answer. Question 4. What is the unknown factor and quotient? 9 × ■ = 27 27 ÷ 9 = ■ Options: a. 3 b. 4 c. 5 d. 6 Answer: a. 3 Explanation: 9 x 3 = 27. 27 ÷ 9 = 3. The answer is 3. Question 5. Which fraction is equivalent to $$\frac{4}{8}$$? Options: a. $$\frac{3}{4}$$ b. $$\frac{1}{2}$$ c. $$\frac{1}{4}$$ d. $$\frac{1}{8}$$ Answer: b. $$\frac{1}{2}$$ Explanation: $$\frac{4}{8}$$ = b. $$\frac{1}{2}$$. Question 6. Mr. MacTavish has 30 students from his class going on a field trip to the zoo. He is placing 6 students in each group. How many groups of students from Mr. MacTavish’s class will be going to the zoo? Options: a. 5 b. 6 c. 7 d. 36 Answer: a. 5 Explanation: 1 group = 6 students. 6 x number of groups = 30 students. 6 x s = 30. s = 30 ÷ 6 s = 5. 5 groups of students from Mr. MacTavish’s class will be going to the zoo. ### Describe Angles in Plane Shapes – Page No. 707 Use the corner of a sheet of paper to tell whether the angle is a right angle, less than a right angle, or greater than a right angle. Question 1. less than a right angle Answer: less than a right angle Question 2. ________ Answer: Right Angle: Question 3. ________ Answer: Greater than a right angle Write how many of each type of angle the shape has. Question 4. ________ right ________ less than a right ________ greater than a right Answer: 4 right 0 less than a right 0 greater than a right Explanation: 4 right Angles. 0 less than right angles. 0 greater than right angles. Describe Angles in Plane Shapes Question 5. ________ right ________ less than a right ________ greater than a right Answer: 0 right 0 less than a right 5 greater than a right Explanation: 0 right Angles 0 less than right angles 5 greater than right angles Question 6. ________ right ________ less than a right ________ greater than a right Answer: 2 right 0 less than a right 4 greater than a right Explanation: 2 right angles. 0 less than right angles 4 greater than right angles. Problem Solving Question 7. Jeff has a square piece of art paper. He cuts across it from one corner to the opposite corner to make two pieces. What is the total number of sides and angles in both of the new shapes? ________ sides ________ angle Answer: The new shape has 6 sides and 6 angles Explanation: The new shape has 6 sides and 6 angles Question 8. Kaylee tells Aimee that the shape of a stop sign has at least one right angle. Aimee says that there are no right angles. Who is correct? Explain. ________ Answer: Aimee’s answer is correct Explanation: All the angles are greater than a right angle. Aimee’s answer is correct. ### Describe Angles in Plane Shapes – Page No. 708 Lesson Check Question 1. What describes this angle? Options: a. right angle b. less than a right angle c. greater than a right angle d. small angle Answer: c. greater than a right angle Explanation: The given shape has a greater angle than the right angle. So, the answer is greater than a right angle. Go Math Florida Grade 3 Chapter 12 Answer Key Question 2. How many right angles does this shape have? Options: a. 1 b. 2 c. 3 d. 4 Answer: c. 3 Explanation: Spiral Review Question 3. What fraction of the group is shaded? Options: a. $$\frac{5}{6}$$ b. $$\frac{1}{3}$$ c. $$\frac{1}{6}$$ d. $$\frac{1}{8}$$ Answer: c. $$\frac{1}{6}$$ Explanation: There are 6 circles. And one circle is shaded out of 6 circles. So, answer is $$\frac{1}{6}$$. Question 4. Compare. $$\frac{4}{8}$$ _____ $$\frac{3}{8}$$ Options: a. > b. < c. = d. ÷ Answer: a. > Explanation: Given fractions have the same denominators. So, compare numerators to get the answer. 4 > 3. The answer is $$\frac{4}{8}$$ > $$\frac{3}{8}$$. Question 5. Which of the following does NOT describe a line segment? Options: a. does not end b. is straight c. is part of a line d. has 2 endpoints Answer: a. does not end Explanation: The line segment is a straight line that has two end points. a. does not end not describes a line segment. Question 6. How many line segments does this shape have? Options: a. 5 b. 6 c. 7 d. 8 Answer: c. 7 Explanation: ### Identify Polygons – Page No. 713 Is the shape a polygon? Write yes or no. Question 1. no Answer: No Explanation: No, The given image doesn’t have line segments. Question 2. _____ Answer: Yes Explanation: Yes, A polygon is a closed plane shape that is made up of line segments that meet only at their endpoints. Each line segment in a polygon is a side. Question 3. _____ Answer: No Explanation: No, the given shape is an open shape. It is not a polygon. Go Math Grade 3 Relate Shapes Fractions and Area Question 4. _____ Answer: No Explanation: No, it has a curved path. So, the given shape is not a polygon. Write the number of sides and the number of angles. Then name the polygon. Question 5. _______ sides _______ angles _______ Answer: 6 sides; 6 angles; hexagon Explanation: Question 6. _______ sides _______ angles _______ Answer: 4 sides; 4 angles; quadrilateral Explanation: Problem Solving Question 7. Mr. Murphy has an old coin that has ten sides. If its shape is a polygon, how many angles does the old coin have? _______ angles Answer: 10 angles Explanation: Given that the shape has ten sides. So, the old coin will have 10 angles. Question 8. Lin says that an octagon has six sides. Chris says that it has eight sides. Whose statement is correct? _______ statement Answer: Chris’s statement is correct. Explanation: Chris’s statement is correct. An octagon has eight sides. ### Identify Polygons – Page No. 714 Lesson Check Question 1. Which is a name for this polygon? Options: a. hexagon b. octagon c. quadrilateral d. pentagon Answer: c. quadrilateral Explanation: It has 4 sides and 4 angles. The name of the polygon is quadrilateral. Question 2. How many sides does this polygon have? Options: a. 4 b. 5 c. 6 d. 7 Answer: c. 6 Explanation: Spiral Review Go Math Chapter 12 Grade 3 Answer Key Question 3. How many right angles does this shape have? Options: a. 4 b. 3 c. 2 d. 0 Answer: a. 4 Explanation: Question 4. Erica has 8 necklaces. One fourth of the necklaces are blue. How many necklaces are blue? Options: a. 2 b. 3 c. 4 d. 8 Answer: a. 2 Explanation: Erica has 8 necklaces. One-fourth of the necklaces are blue. So, 2 necklaces are blue. Question 5. Which of these is straight, is part of a line, and has 2 endpoints? Options: a. line b. line segment c. point d. ray Answer: b. line segment Question 6. What describes this angle? Options: a. greater than a right angle b. large angle c. less than a right angle d. right angle Answer: c. less than a right angle ### Unlock the Problem – Page No. 715 Question 1. Look at the polygon. How many pairs of sides are parallel? ________ pair(s) Answer: 1 pair of sides are parallel Question 2. How do you know the shape is a polygon? Type below: ___________ Answer: A polygon is a closed plane shape that is made up of line segments that meet only at their endpoints. Each line segment in a polygon is a side. Question 3. Lines that cross or meet are intersecting lines. Intersecting lines form angles. Answer: Either less than the right angle or more than the right angle. Question 4. The orange and blue line segments meet and form an angle. So, they are __________________ ___________ Answer: Intersecting lines Question 5. Intersecting lines that cross or meet to form right angles are perpendicular lines. Answer: 90 degrees Go Math Grade 3 Chapter 12 Answer Key Pdf Question 6. The red and blue line segments meet to form a right angle. So, they are ________________ ___________ Answer: Perpendicular lines Question 7. Lines that never cross or meet and are always the same distance apart are parallel lines. They do not form any angles. So, the polygon above has _ pair of parallel sides _________ pair(s) Answer: The polygon has 1 pair of parallel sides Question 8. The green and blue line segments would never cross or meet. They are always the same distance apart. So, they appear to be _________________ _________ Answer: Parallel lines ### Describe Sides of Polygons – Page No. 719 Look at the dashed sides of the polygon. Tell if they appear to be intersecting, perpendicular, or parallel. Write all the words that describe the sides. Question 1. parallel Answer: parallel lines Explanation: The dashed sides are not intersecting with each other. So, the given lines are parallel lines. Question 2. _______ _______ Answer: perpendicular lines Explanation: The dashed sides meet to form a right angle. So, they are perpendicular lines. Question 3. _______ Answer: intersecting lines Explanation: The dashed line segments meet and form an angle. So, they are intersecting lines. Question 4. _______ Answer: intersecting lines Explanation: The dashed line segments meet and form an angle. So, they are intersecting lines. Question 5. _______ _______ Answer: perpendicular lines Explanation: The dashed line segments meet to form a right angle. So, they are perpendicular lines. Question 6. _______ Answer: parallel lines Explanation: The dashed line segments would never cross or meet. They are always the same distance apart. So, they are parallel lines. Question 7. _______ Answer: parallel lines Explanation: The dashed line segments would never cross or meet. They are always the same distance apart. So, they are parallel lines. Question 8. _______ Answer: intersecting lines Explanation: The dashed line segments meet and form an angle. So, they are intersecting lines. Place Two Dimensional Shapes on the Page Question 9. _______ _______ Answer: perpendicular lines Explanation: The dashed line segments meet to form a right angle. So, they are perpendicular lines. Problem Solving Use shapes A–D for 10–11. Question 10. Which shapes appear to have parallel sides? _______ ; _______ ; _______ Answer: A, C, D Explanation: A, C, D have lines that appear to never meet and are always the same distance apart. So, they have parallel lines. Question 11. Which shapes appear to have perpendicular sides? _______ ; _______ Answer: B, C Explanation: B, C have lines that meet to form right angles. So, they have perpendicular sides. ### Describe Sides of Polygons – Page No. 720 Lesson Check Question 1. How many pairs of parallel sides does the quadrilateral appear to have? Options: a. 1 b. 2 c. 3 d. 4 Answer: b. 2 Explanation: Side a and a are one pair of parallel lines. Side b and b are one pair of parallel lines. The quadrilateral has 2 pairs of parallel sides. Question 2. Which sides appear to be parallel? Options: a. a and c only b. b and d only c. a and b, c and d d. a and c, b and d Answer: d. a and c, b and d Explanation: a and c are parallel lines. They appear to never meet and are always the same distance apart. They do not form any angles. Similarly, b and d are parallel lines. Spiral Review Question 3. Mr. Lance designed a class banner shaped like the polygon shown. What is the name of the polygon? Options: a. pentagon b. octagon c. hexagon d. decagon Answer: a. pentagon Explanation: The polygon has 5 sides and 5 angles. So, the given polygon is a pentagon. Question 4. How many angles greater than a right angle does this shape have? Options: a. 0 b. 1 c. 2 d. 3 Answer: b. 1 Explanation: One angle is greater than the right angles. Question 5. How many line segments does this shape have? Options: a. 6 b. 7 c. 8 d. 9 Answer: c. 8 Explanation: The given shape has 8 line segments. 3rd Grade Math Assessment 12.4 Practice A Geometry Answers Question 6. Which fraction names the shaded part? Options: a. $$\frac{1}{3}$$ b. $$\frac{1}{4}$$ c. $$\frac{1}{6}$$ d. $$\frac{5}{6}$$ Answer: c. $$\frac{1}{6}$$ Explanation: The given image has 6 parts. 1 part is shaded out of 1 part. The answer is $$\frac{1}{6}$$ ### Mid -Chapter Checkpoint – Page No. 721 Vocabulary Choose the best term from the box to complete the sentence. Question 1. An __________ is formed by two rays that share an endpoint. __________ Answer: Angle Explanation: Question 2. A _____________ is a closed plane shape made up of line segments. ________ Answer: Polygon Question 3. A ____________ forms a square corner. ________ Answer: Right Angle Concepts and Skills Use the corner of a sheet of paper to tell whether the angle is a right angle, less than a right angle, or greater than a right angle. Question 4. ________ Answer: less than a right angle Question 5. ________ Answer: right angle Question 6. ________ Answer: greater than a right angle Write the number of sides and the number of angles. Then name the polygon. Question 7. ________ sides ________ angles ________ Answer: 6 sides; 6 angles Explanation: 6 sides; 6 angles Question 8. ________ sides ________ angles ________ Answer: 4 sides; 4 angles Explanation: 4 sides; 4 angles Question 9. ________ sides ________ angles ________ Answer: 5 sides; 5 angles Explanation: 5 sides; 5 angles ### Mid -Chapter Checkpoint – Page No. 722 Question 10. Anne drew the shape at the right. Is her shape an open shape or a closed shape? ________ Answer: Closed Shape Explanation: The given shape started and ends at the same point. So, the shape is closed. Question 11. This sign tells drivers there is a steep hill ahead. Write the number of sides and the number of angles in the shape of the sign. Then name the shape. ________ sides ________ angles ________ Answer: 4 sides; 4 angles Explanation: 4 sides; 4 angles Question 12. Why is this closed plane shape NOT a polygon? Type below: ________ Answer: 2 × 5 = 10 Explanation: The given shape started and ends at the same point. So, the shape is closed. A polygon is made up of line segments that meet only at their endpoints. So, the given shape is not a polygon. Question 13. Sean drew a shape with 2 fewer sides than an octagon. Which shape did he draw? ________ Answer: pentagon Explanation: octagon has 8 sides. 2 + 8 = 10 sides Question 14. John drew a polygon with two line segments that meet to form a right angle. Circle the words that describe the line segments. Type below: ________ Answer: perpendicular ### Classify Quadrilaterals – Page No. 727 Click all the words that describe the quadrilateral. Question 1. Answer: Square; Rectangle; Rhombus Question 2. Options: a. square b. rectangle c. rhombus d. trapezoid Answer: b. rectangle Explanation: The given shape has two pairs opposite with the same length. Also, all the angles are right angles. The given shape is a rectangle. Question 3. Options: a. square b. rectangle c. rhombus d. trapezoid Answer: d. trapezoid Explanation: Even though the given shape has four sides, they are not equal. Also, it has only two right angles. The given shape is a trapezoid. Use the quadrilaterals below for 4–6. Question 4. Which quadrilaterals appear to have no right angles? ______ ; ______ ; ______ Answer: B, D, and E Explanation: B, D, E don’t have right angles. Question 5. Which quadrilaterals appear to have 4 right angles? ______ ; ______ Answer: A and C Explanation: A and C both shapes have right angles. Question 6. Which quadrilaterals appear to have 4 sides of equal length? ______ ; ______ ; ______ Answer: B, C, and D Explanation: The B, C, and D have all the equal lengths. Problem Solving Question 7. A picture on the wall in Jeremy’s classroom has 4 right angles, 4 sides of equal length, and 2 pairs of opposite sides that are parallel. What quadrilateral best describes the picture? _______ Answer: Square Explanation: A square has 4 right angles, 4 sides of equal length, and 2 pairs of opposite sides that are parallel. Question 8. Sofia has a plate that has 4 sides of equal length, 2 pairs of opposite sides that are parallel, and no right angles. What quadrilateral best describes the plate? _________ Answer: rhombus Explanation: A rhombus has 4 sides of equal length, 2 pairs of opposite sides that are parallel, and no right angles. ### Classify Quadrilaterals – Page No. 728 Lesson Check Question 1. Which word describes the quadrilateral? Options: a. square b. trapezoid c. rhombus d. rectangle Answer: b. trapezoid Explanation: The given quadrilateral doesn’t have right angles. So, it is not a square and a rectangle. Also, the quadrilateral doesn’t have equal sides. So, it is not a rhombus. Question 2. Which quadrilaterals appear to have 2 pairs of opposite sides that are parallel? Options: a. A and B b. A, B, and C c. A only d. B only Answer: a. A and B Explanation: The A and B shapes have 2 pairs of opposite sides that are parallel. Spiral Review Question 3. Aiden drew the polygon shown. What is the name of the polygon he drew? Options: a. decagon b. hexagon c. octagon d. pentagon Answer: a. decagon Explanation: 10 sides; 10 angles Question 4. How many pairs of parallel sides does this shape appear to have? Options: a. 4 b. 2 c. 1 d. 0 Answer: b. 2 Explanation: Side a and a are one pair of parallel lines. Side b and b are one pair of parallel lines. The quadrilateral has 2 pairs of parallel sides. Question 5. What word describes the dashed sides of the shape shown? Options: a. intersecting b. parallel c. perpendicular d. right Answer: b. parallel Explanation: The dashed sides of the shape would never cross or meet. They are always the same distance apart. So, they appear to be parallel lines. Question 6. How many right angles does this shape have? Options: a. 0 b. 1 c. 2 d. 3 Answer: a. 0 Explanation: There are no right angles available for the given shape. ### Draw Quadrilaterals – Page No. 733 Draw a quadrilateral that is described. Name the quadrilateral you drew. Question 1. 4 sides of equal length Answer: square Explanation: A square has four equal sides and four equal angles Question 2. 1 pair of opposite sides that are parallel _________ Answer: trapezoid Explanation: trapezoid Draw a quadrilateral that does not belong. Then explain why. Go Math Grade 3 Practice Book Answer Key Pdf Question 3. Answer: Explanation: The shape is a trapezoid. It has only 1 pair of opposite sides that are parallel. The 3 quadrilaterals shown have 2 pairs of sides that are parallel. Problem Solving Question 4. Layla drew a quadrilateral with 4 right angles and 2 pairs of opposite sides that are parallel. Name the quadrilateral she could have drawn. _________ Answer: square or rectangle Explanation: The square or rectangle has 4 right angles and 2 pairs of opposite sides that are parallel. Question 5. Victor drew a quadrilateral with no right angles and 4 sides of equal length. What quadrilateral could Victor have drawn? _________ Answer: rhombus. Explanation: A rhombus has no right angles and 4 sides of equal length. ### Draw Quadrilaterals – Page No. 734 Lesson Check Question 1. Chloe drew a quadrilateral with 2 pairs of opposite sides that are parallel. Which shape could NOT be Chloe’s quadrilateral? Options: a. rectangle b. rhombus c. square d. trapezoid Answer: d. trapezoid Explanation: A trapezoid will have only one pair of parallel lines. Question 2. Mike drew a quadrilateral with four right angles. Which shape could he have drawn? Options: a. rectangle b. hexagon c. trapezoid d. triangle Answer: a. rectangle Explanation: A rectangle will have four right angles. Spiral Review Question 3. A quadrilateral has 4 right angles and 4 sides of equal length. What is the name of the quadrilateral? Options: a. pentagon b. square c. trapezoid d. hexagon Answer: b. square Explanation: A square has 4 right angles, 4 sides of equal length, and 2 pairs of opposite sides that are parallel. Question 4. Mark drew two lines that form a right angle. Which word describes the lines Mark drew? Options: a. perpendicular b. parallel c. acute d. obtuse Answer: a. perpendicular Explanation: Intersecting lines that cross or meet to form right angles are perpendicular lines. Question 5. Dennis drew the rectangle on grid paper. What is the perimeter of the rectangle Dennis drew? Options: a. 7 units b. 12 units c. 14 units d. 15 units Answer: b. 12 units Explanation: 3 + 3 + 3 + 3 = 12 units. Question 6. Jill drew the rectangle on grid paper. What is the area of the rectangle Jill drew? Options: a. 12 square units b. 15 square units c. 16 square units d. 18 square units Answer: b. 15 square units Explanation: 5 x 3 = 15 square units. ### Describe Triangles – Page No. 739 Use the triangles for 1–3. Write A, B, or C. Then complete the sentences. Question 1. Triangle B has 3 angles less than a right angle and appears to have 3 sides of equal length. Answer: B Question 2. Triangle _________ has 1 right angle and appears to have _________ sides of equal length. Answer: Triangle C has 1 right angle and appears to have 0 sides of equal length. Question 3. Triangle _________ has 1 angle greater than a right angle and appears to have _________ sides of equal length. Answer: Triangle A has 1 angle greater than a right angle and appears to have 2 sides of equal length. Question 4. Kyle, Kathy, and Kelly each drew a triangle. Who drew the triangle that has 1 angle greater than a right angle and appears to have no sides of equal length? _________ Answer: Kathy Explanation: Kathy triangle has 1 angle greater than a right angle and has no sides of equal length. Problem Solving Question 5. Matthew drew the back of his tent. How many sides appear to be of equal length? _________ sides Answer: 2 sides Explanation: a and b are 2 sides have equal lengths. Question 6. Sierra made the triangular picture frame shown. How many angles are greater than a right angle? _________ Answer: 0 Explanation: 0 angles are greater than a right angle. ### Describe Triangles – Page No. 740 Lesson Check Question 1. How many angles less than a right angle does this triangle have? Options: a. 0 b. 1 c. 2 d. 3 Answer: d. 3 Explanation: 3 angles less than a right angle. Question 2. How many sides of equal length does this triangle appear to have? Options: a. 0 b. 1 c. 2 d. 3 Answer: c. 2 Explanation: The two lines forming the right angle are equal in length. Spiral Review Question 3. A quadrilateral has 4 right angles and 2 pairs of opposite sides that are parallel. Which quadrilateral could it be? Options: a. trapezoid b. hexagon c. triangle d. rectangle Answer: d. rectangle Explanation: A rectangle has 4 right angles and 2 pairs of opposite sides that are parallel. Question 4. Mason drew a quadrilateral with only one pair of opposite sides that are parallel. Which quadrilateral did Mason draw? Options: a. square b. rhombus c. trapezoid d. rectangle Answer: c. trapezoid Explanation: A trapezoid will have only one pair of opposite sides that are parallel. Question 5. Which shape has an area of 8 square units and a perimeter of 12 units? Options: a. b. c. d. Answer: a Explanation: a. Area = 2 x 4 = 8 square units; Perimeter = 2 + 4 + 2 + 4 = 12 units. Question 6. What fraction of the square is shaded? Options: a. $$\frac{3}{5}$$ b. $$\frac{5}{3}$$ c. $$\frac{3}{8}$$ d. $$\frac{8}{5}$$ Answer: c. $$\frac{3}{8}$$ Explanation: The image has 8 parts. 3 parts are shaded out of 8 parts. So, $$\frac{3}{8}$$ is the answer. ### Problem Solving Classify Plane Shapes – Page No. 745 Solve each problem. Question 1. Steve drew the shapes below. Write the letter of each shape where it belongs in the Venn diagram. Answer: Question 2. Janice drew the shapes below. Write the letter of each shape where it belongs in the Venn diagram. Answer: 3rd Grade Math Assessment Lesson 12.7 Answer Key Question 3. Beth drew the shapes below. Write the letter of each shape where it belongs in the Venn diagram. Answer: ### Problem Solving Classify Plane Shapes – Page No. 746 Lesson Check Question 1. Which shape would go in the section where the two circles overlap? Options: a. triangle b. trapezoid c. square d. hexagon Answer: c. square Explanation: A square is a rectangle with equal lengths of all sides. Question 2. Which shape could NOT go in the circle labeled All Sides of Equal Length? Options: a. rhombus b. trapezoid c. square d. triangle Answer: b. trapezoid Explanation: A trapezoid will not have All Sides of Equal Length. Spiral Review Question 3. How many angles greater than a right angle does this triangle have? Options: a. 0 b. 1 c. 2 d. 3 Answer: b. 1 Explanation: 1 angle is greater than a right angle. Question 4. How many sides of equal length does this triangle appear to have? Options: a. 0 b. 1 c. 2 d. 3 Answer: d. 3 Explanation: The triangle appears to have 3 sides of equal length. Question 5. Madison drew this shape. How many angles less than a right angle does it have? Options: a. 0 b. 1 c. 3 d. 5 Answer: a. 0 Explanation: 0 Question 6. How many dots are in $$\frac{1}{2}$$ of this group? Options: a. 6 b. 8 c. 9 d. 18 Answer: c. 9 Explanation: 9 dots are in $$\frac{1}{2}$$ of this group. ### Relate Shapes, Fractions, and Area – Page No. 751 Draw lines to divide the shape into equal parts that show the fraction given. Question 1. $$\frac{1}{3}$$ Answer: $$\frac{1}{3}$$ Question 2. $$\frac{1}{8}$$ Answer: Question 3. $$\frac{1}{2}$$ Answer: Draw lines to divide the shape into parts with equal area. Write the area of each part as a unit fraction. Question 4. 4 equal parts $$\frac{□}{□}$$ Answer: $$\frac{1}{4}$$ Question 5. 6 equal parts $$\frac{□}{□}$$ Answer: $$\frac{1}{6}$$ Question 6. 3 equal parts $$\frac{□}{□}$$ Answer: $$\frac{1}{3}$$ Problem Solving Question 7. Robert divided a hexagon into 3 equal parts. Show how he might have divided the hexagon. Write the fraction that names each part of the whole you divided. $$\frac{□}{□}$$ Answer: $$\frac{1}{3}$$ Question 8. Show how you might divide the shape into 8 equal parts. What fraction names the area of each part of the divided shape? $$\frac{□}{□}$$ Answer: $$\frac{1}{8}$$ ### Relate Shapes, Fractions, and Area – Page No. 752 Lesson Check Question 1. What fraction names each part of the divided whole? Options: a. $$\frac{1}{2}$$ b. $$\frac{1}{3}$$ c. $$\frac{1}{4}$$ d. $$\frac{1}{6}$$ Answer: b. $$\frac{1}{3}$$ Explanation: The shape has 3 parts. One part is shaded out of 3. Question 2. What fraction names the whole area that was divided? Options: a. $$\frac{1}{8}$$ b. $$\frac{1}{2}$$ c. $$\frac{8}{8}$$ d. $$\frac{8}{1}$$ Answer: c. $$\frac{8}{8}$$ Explanation: 8 parts are shaded out of 8 parts. So, $$\frac{8}{8}$$ is the answer. Spiral Review Question 3. Lil drew the figure below. Which word does NOT describe the shape? Options: a. plane shape b. closed shape c. open shape d. curved path Answer: c. open shape Explanation: The given shape is started and ended at the same point. So, it is not an open shape. Question 4. How many line segments does this shape have? Options: a. 6 b. 5 c. 4 d. 3 Answer: b. 5 Explanation: 5 Use the Venn diagram for 5–6. Question 5. Which shape would go in the section where the two circles overlap? Options: a. triangle b. square c. trapezoid d. pentagon Answer: b. square Explanation: A square have right angles and all sides with equal lengths. Question 6. Which shape could NOT go in the circle labeled All Sides of Equal Length? Options: a. square b. rhombus c. triangle d. rectangle Answer: d. rectangle Explanation: A rectangle doesn’t have All Sides of Equal Length. ### Review/Test – Page No. 753 Question 1. Which words describe this shape? Mark all that apply. Options: a. polygon b. open shape c. pentagon d. quadrilateral Answer: a. polygon c. pentagon Explanation: A polygon is a closed plane shape that is made up of line segments that meet only at their endpoints. Each line segment in a polygon is a side. So, the shape is a polygon. Also, the shape has five sides and five angles. So, it is a pentagon. Question 2. Umberto drew one side of a quadrilateral with 4 equal sides and no right angles. Draw the other 3 sides to complete Umberto’s shape. Type below: ____________ Answer: Question 3. Mikael saw a painting that included this shape. For numbers 3a–3d, select True or False for each statement about the shape. a. The shape has no right angles. i. True ii. False Answer: ii. False Question 3. b. The shape has 2 angles greater than a right angle. i. True ii. False Answer: ii. False Question 3. c. The shape has 2 right angles. i. True ii. False Answer: i. True Question 3. d. The shape has 1 angle greater than a right angle. i. True ii. False Answer: i. True ### Review/Test – Page No. 754 Question 4. Fran used a Venn Diagram to sort shapes. Part A Draw another plane shape that belongs inside the left circle of the diagram but NOT in the section where the circles overlap. Type below: ____________ Answer: Question 4. Part B How can you describe the shapes in the section where the circles overlap? Type below: ____________ Answer: The shapes in the circle overlap are polygons with right angles. Also, those shapes have 4 sides and 4 angles named as quadrilaterals. Question 5. Match each object in the left column with its name in the right column. Type below: ____________ Answer: Question 6. Describe the angles and sides of this triangle. Type below: ____________ Answer: The triangle has 3 sides of equal length. Also, the triangle has 3 angles with less than a right angle. ### Review/Test – Page No. 755 Question 7. Which words describe this shape. Mark all that apply. Options: a. rectangle b. rhombus c. quadrilateral d. square Answer: a. rectangle c. quadrilateral d. square Explanation: The given shape is a square or rectangle with 4 sides and 4 angles. Question 8. Divide each shape into the number of equal parts shown. Then write the fraction that describes each part of the whole. Type below: ____________ Answer: $$\frac{1}{3}$$ $$\frac{1}{6}$$ $$\frac{1}{8}$$ Explanation: $$\frac{1}{3}$$ $$\frac{1}{6}$$ $$\frac{1}{8}$$ Question 9. Han drew a triangle with 1 angle greater than a right angle. For numbers 9a–9d, choose Yes or No to tell whether the triangle could be the triangle Han drew. a. i. yes ii. no Answer: ii. no Explanation: It has all the angles less than a right angle. Question 9. b. i. yes ii. no Answer: ii. no Explanation: It has one right angle and two angles with less than a right angle. Question 9. c. i. yes ii. no Answer: i. yes Explanation: It has one angle greater than a right angle Question 9. d. i. yes ii. no Answer: i. yes Explanation: It has one angle greater than a right angle ### Review/Test – Page No. 756 Question 10. Look at this group of pattern blocks. Part A Sort the pattern blocks by sides. How many groups did you make? Explain how you sorted the shapes. Type below: ____________ Answer: A has 6 sides 6 angles = hexagon. B has 4 sides 4 angles = quadrilateral C has 4 sides 4 angles = quadrilateral D has 3 sides 3 angles = triangle E has 4 sides 4 angles = quadrilateral F has 4 sides 4 angles = quadrilateral 1 triangle, 4 quadrilateral, and 1 hexagon blocks available. Question 10. Part B Sort the pattern blocks by angles. How many groups did you make? Explain how you sorted the shapes. Type below: ____________ Answer: A and F have greater than a right angle. B has 4 right angles. C, D, and E have all the angles less than a right angle. Question 11. Teresa drew a quadrilateral that had 4 sides of equal length and no right angles. What quadrilateral did she draw? ____________ Answer: rhombus ### Review/Test – Page No. 757 Question 12. Rhea used a Venn diagram to sort shapes. What label could she use for circle A? Type below: ____________ Answer: Right Angle Question 13. Colette drew lines to divide a rectangle into equal parts that each represent $$\frac{1}{6}$$ of the whole area. Her first line is shown. Draw lines to complete Colette’s model. Type below: ____________ Answer: Question 14. Brad drew a quadrilateral. Select the pairs of sides that appear to be parallel. Mark all that apply. Options: a. a and b b. b and d c. c and a d. d and c Answer: b. b and d c. c and a ### Review/Test – Page No. 758 Question 15. Give two reasons that this shape is not a polygon. Type below: ____________ Answer: 1. The shape is not a closed shape. 2. The shape has no line segments. Question 16. A triangle has 1 angle greater than a right angle. What must be true about the other angles? Mark all that apply. Options: a. At least one must be less than a right angle. b. One could be a right angle. c. Both must be less than a right angle. d. One must be greater than a right angle. Answer: c. Both must be less than a right angle. Question 17. Ava drew a quadrilateral with 2 pairs of opposite sides that are parallel. The shape has at least 2 right angles. Draw a shape that Ava could have drawn. Type below: ____________ Answer: Question 18. For 18a–18d, select True or False for each description of a ray. a. straight i. True ii. False Answer: i. True Question 18. b. has 2 endpoints i. True ii. False Answer: ii. False Question 18. c. part of a line i. True ii. False Answer: i. True Question 18. d. continues in 1 direction i. True ii. False Answer: i. True ### Conclusion Go Math Grade 3 Answer Key Chapter 12 Two-Dimensional Shapes for students who want to top. Learn the flexible learning using HMH Go Math Grade 3 Answer Key. Refer Go Math Grade 3 Answer Key PDF for quick support. Get Go Math Grade 3 Answer Key Chapter 12 Two-Dimensional Shapes Extra Practice for more practice. ## Go Math Grade 3 Chapter 4 Answer Key Pdf Multiplication Facts and Strategies ## Go Math Answer Key for Grade 3 Chapter 4 Multiplication Facts and Strategies Go Math Grade 3 Chapter 4 Answer Key Pdf: Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies helps thousands of students to achieve excellent grades. Students can effectively solve problems and grab knowledge and skills by using Go Math Grade 3 Answer Key. Help your students keep up and catch up to do the math with the reference of HMH Go Math Solution Key Grade 3. It’s important to know the process of solving a problem more than finding the correct answer to improve the skills of your students. Go Math Answer Key Grade 3 Chapter 4 Multiplication Facts and Strategies will give all that flexibility to build their confidence to do math in an easy way. ## Multiplication Facts and Strategies Go Math Grade 3 Chapter 4 Answer Key Pdf In order to move successfully, refer to Grade 3 Multiplication Facts. Help your children to move to the next grade level by encouraging them with a lot of practice. Use Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies and achieve your goals easily. Lesson 1: Multiply with 2 and 4 Lesson 2: Multiply with 5 and 10 Lesson 3: Multiply with 3 and 6 Lesson 4: Algebra • Distributive Property Lesson 5: Multiply with 7 Mid-Chapter Checkpoint Lesson 6: Algebra • Associative Property of Multiplication Lesson 7: Algebra • Patterns on the Multiplication Table Lesson 8: Multiply with 8 Lesson 9: Multiply with 9 Lesson 10: Problem Solving • Multiplication Chapter 4 Review/Test ### Multiply with 2 and 4 Page No 195 Write a multiplication sentence for the model. Question 1. Think: There are 2 groups of 5 counters. Answer: 2 × 5 = 10 Explanation: Draw 2 counters. Place 5 Objectives in 2 counters. Count the total number of objectives and them. Add 5 + 5 to get the answer. Finally, you get 10. Question 2. ______ × ______ = ______ Find the product. Answer: 4×3 = 12 Explanation: Look at the above figure. You can see 4 Counters and 3 objectives on each counter. So, you have to multiply 4×3. When you multiply with 4, you can first multiply with 2 and then double the product. Multiply 3 with 2. You will get 2×3 is 6. Now, double the number 6. The final answer is 12. Question 3. 2 × 6 ——– ________ Answer: 2×6 = 12 Explanation: When there is a multiplication requires with 2, you can double the given number 6 to get the final answer. The answer is 6+6 = 12. Question 4. 4 × 8 ——— ________ Answer: 4×8 = 32 Explanation: You can double 2×8 to get 4×8. Multiply 8 with 2. You will get 16. Then, double the product to get the answer to 4×8. You will get 16+16 = 32. So, you get the final answer as 32. Go Math 3rd Grade Homework Book Answers Question 5. 2 × 3 ——– ________ Answer: 2×3 = 6 Explanation: Draw two counters. Place three objectives in two counters. Now, add the objectives in two counters. The final answer is 3+3 = 6. So, 2×3=6 is the answer. Question 6. 4 × 6 ——— _________ Answer: 4×6 = 24 Explanation: You can double 2×6 to get 4×6. Multiply 6 with 2. You will get 12. Then, double the product to get the answer to 4×6. You will get 12+12 = 24. So, you get the final answer as 24. Question 7. 4 × 4 ——— _________ Answer: 4×4 = 16 Explanation: Multiply 4 with 2. 2×4 = 8. Now, double the number 8. 8+8 = 16. The answer for 4×4 is 16 Question 8. 2 × 7 ——– _________ Answer: 2×7 = 14 Explanation: The given multiplication is 2×7. The answer to any number multiplies with 2 is double of that number. So, the 2×7 can find by doing 7+7. The answer is 7+7 = 14. So, the final answer is 2×7 = 14. Question 9. 4 × 5 ——— _________ Answer: 4×5 = 20 Explanation: Firstly, multiply 2×5 to get the answer for 4×5. Then, double the answer of 2×5 to get the final answer. So, do 2×5 = 10. Double the number 10 to get the 4×5 Answer. The double of 10 is 10+10 = 20. The answer to 4×5 is 20. Question 10. 2 × 4 ——– _________ Answer: 2×4 = 8 Explanation: The multiplication begins with 2. So, you can double 4 to get the answer of 2×4. The double of 4 is 4+4 = 8. The answer for 2×4 is 8. Problem Solving Question 11. On Monday, Steven read 9 pages of his new book. To finish the first chapter on Tuesday, he needs to read double the number of pages he read on Monday. How many pages does he need to read on Tuesday? __________ pages Answer: 18 Explanation: Steven read 9 pages of his new book on Monday. He wants to finish his first chapter on Tuesday. To finish the chapter, he needs to double the number of pages he read on Monday. Double of pages read on Monday = 9 x 2 =18. Steven needs to read 18 pages on Tuesday. Go Math Grade 3 Chapter 4 Answer Key Pdf Question 12. Courtney’s school is having a family game night. Each table has 4 players. There are 7 tables in all. How many players are at the game night? __________ players Answer: 28 Explanation: From the given information Courtney’s school is having a family game night. Each table has 4 players. There are 7 tables in all. So, every table has 4 players. To know the total number of players at the game night, we need to multiply 7 with 4. Total Number of players at the game night = 7 x 4 = 28. ### Multiply with 2 and 4 Lesson Check Page No 196 Lesson Check Question 1. Which multiplication sentence matches the model? Options: a. 3 × 2 = 6 b. 4 × 2 = 8 c. 4 × 4 = 16 d. 4 × 8 = 32 Answer: b Explanation: The above figure consists of 4 counters. Also, each counter has two objectives in it. So, we need to multiply the number of counters with a number of objectives. The answer is 4×2 = 8. Question 2. Find the product. 2 × 8 ——- ________ Options: a. 10 b. 14 c. 16 d. 18 Answer: c Explanation: To solve the 2×8, double the number 8. The answer for 2×8 is 8+8. So, the final answer is 2×8 = 16. Question 3. Sean made a picture graph to show his friends’ favorite colors. This is the key for the graph. Each Ο = 2 friends. How many friends does Ο Ο Ο Ο stand for? Options: a. 4 b. 8 c. 20 d. 40 Answer: b Explanation: Sean made 4 picture graphs to show his friends’ favorite colors. Each Ο represents 2 friends. So, to find the final answer, we need to add all the colors. As there are 4 picture graphs you need to do 2+2+2+2 = 8. There are 8 friends available. Question 4. The table shows the lengths of some walking trails. How many feet longer is Mountain Trail than Harmony Trail? Options: a. 216 feet b. 264 feet c. 316 feet d. 528 feet Answer: c Explanation: In the above table, we can see three different walking trails lengths of three persons. The walking trail length of the Mountain is 844feets. The walking trail length of Lake is 792 feet. Also, the Harmony walking trail length is 528 feet. To get How many feet longer is Mountain Trail than Harmony Trail, we need to subtract Harmony walking trail length from Mountain Trail length. So, now we have to do 844-528 which is equal to 316 feet. So, Mountain Trail walked 316 feet than Harmony trail. Question 5. Find the sum. 5 2 7 + 1 5 4 ———- Options: a. 373 b. 581 c. 671 d. 681 Answer: c Explanation: Break apart the addends from the given values. Start with the hundreds. Then, add each place value. Let’s write 527 as 500+20+7 and 154 as 100+50+4. Sum up the above two values. Then you get 600+70+11. Add the ones and then add the 10’s and 100’s. The final answer is 681. Question 6. A bar graph shows that sports books received 9 votes. If the scale is 0 to 20 by twos, where should the bar end for the sports books? Options: a. between 8 and 10 b. on 10 c. on 8 d. between 6 and 8 Answer: c Explanation: As per the given data, the sports books received 9 votes. If we take a bar graph with a scale of 0 to 20 by twos, the graph is 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20. So, the number 9 will lie between numbers 8 to 10. Therefore, the answer is between 8 and 10. ### Multiply with 5 and 10 Page No 201 Find the product. Question 1. 5 × 7 = 35 Answer: 35 Explanation: Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35. Question 2. 5 × 1 = _______ Answer: 5 Explanation: Any number multiplied by 1 is the same number. So, the answer is 5. Question 3. 2 × 10 = _______ Answer: 20 Explanation: A multiple of 10 is any product that has 10 as one of its factors. So, the multiplication of any number with 10 is 10’s of that particular number. The answer is 20. Question 4. ________ = 8 × 5 Answer: 40 Explanation: From Commutative Law of Multiplication, you can write 8 x 5 = 5 x 8. So, to find the multiplication of 5 x 8, Skip count by 5’s until you say 8 numbers. 5, 10, 15, 20, 25, 30, 35, 40. Now, the count of the number is 8. So, the answer for 5 x 8 is 40. Therefore, the answer for 8 x 5 is 40. Question 5. 1 × 10 = ________ Answer: 10 Explanation: Multiplication of any number with 1 is the same number. So, 1 x 10 = 10. Question 6. _______ = 4 × 5 Answer: 20 Explanation: Using the Commutative Law of Multiplication, you can write 4 x 5 = 5 x 4. Now, Skip count by 5’s until you say 4 numbers. 5, 10, 15, 20. Therefore, the answer for 5 x 4 is 20. Question 7. 5 × 10 = _______ Answer: 50 Explanation: Skip-count by 5’s 10 times. You can write as 5, 10, 15, 20, 25, 30, 35, 40, 45, 50. The answer for 5 x 10 is 50. Question 8. 7 × 5 = ________ Answer: 35 Explanation: Write 7 x 5 as 5 x 7 according to the Commutative Law of Multiplication. Now do multiply for 5 x 7. Skip-count by 5’s seven times. Now, you can write as 5, 10, 15, 20, 25, 30, 35. The answer for 5 x 7 is 35. So, the answer for 7 x 5 is also 35. Question 9. _______ = 5 × 5 Answer: 25 Explanation: Skip-count by 5’s 5 times. You can get 5, 10, 15, 20, 25. The answer for 5 x 5 is 25. Chapter 4 Review Test Go Math 3rd Grade Question 10. 5 × 8 = _________ Answer: 40 Explanation: You can Skip-count by 5’s 8 times. Write like 5, 10, 15, 20, 25, 30, 35, 40. So, the answer for 5 x 8 is 40. Question 11. ______ = 5 × 9 Answer: 45 Explanation: The multiplication of 5 × 9 is calculated as Skip-count by 5’s 9 times. You can write as 5, 10, 15, 20, 25, 30, 35, 40, 45. The final answer for 5 × 9 is 45. Question 12. 10 × 0 = _________ Answer: 0 Explanation: Multiplication of any number with 0 is 0. So, the answer for 10 x 0 is 0. Question 13. 5 × 6 ——– ________ Answer: 30 Explanation: Skip count by 5’s until you say 6 numbers. 5, 10, 15, 20, 25, 30. So, the answer for 5 x 6 is 35. Question 14. 10 × 7 ——— ________ Answer: 70 Explanation: Add 10’s until you say 7 numbers. Now, you can write as 10 + 10 + 10 + 10 + 10 + 10 + 10. Now, add the 10’s to get the final answer. There are seven 10’s available. So, the answer is 70. Question 15. 5 × 3 ——– ________ Answer: 15 Explanation: Skip count by 5’s until you say 3 numbers. Write like 5, 10, 15. The answer for 5 x 3 is 15. Question 16. 10 × 4 ——– _________ Answer: 40 Explanation: Add 10’s until you say 4 numbers. Then, write like 10 + 10 + 10 + 10 to get the answer. The answer for 10 x 4 is 40. Question 17. 5 × 0 ——- _________ Answer: 0 Explanation: Multiplication of any number with 0 is 0. So, the answer for 5 x 0 is 0. Question 18. 10 × 8 ——- __________ Answer: 80 Explanation: You have to add 10’s until you say 8 numbers. Write as 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10. Now, add the 10’s to get the final answer. There are eight 10’s available. So, the answer for 10 x 8 is 80. Question 19. 5 × 2 ——- __________ Answer: 10 Explanation: Skip count by 5’s until you say 2 numbers. Write like 5, 10. The answer for 5 x 2 is 10. Question 20. 10 × 6 ——– _________ Answer: 60 Explanation: Add 10’s until you say 6 numbers. Write as 10 + 10 + 10 + 10 + 10 + 10. Now, add the 10’s to get the final answer. So, the answer for 10 x 6 is 60. Problem Solving Question 21. Ginger takes 10 nickels to buy some pencils at the school store. How many cents does Ginger have to spend? ________ cents Answer: 50 Explanation: From the given data, Ginger takes 10 nickels to buy some pencils at the school store. One nickel can be treated as 5 cents. So, 10 nickels value is 10 nickels x 5 cents = 50 cents. Ginger has to spend 50 cents to buy some pencils at the school store. Question 22. The gym at Evergreen School has three basketball courts. There are 5 players on each of the courts. How many players are there in all? __________ players Answer: 15 Explanation: As per the given data, the gym at Evergreen School has three basketball courts. There are 5 players on each of the courts. The number of players in there in all = 3 basketball courts x 5 players = 15 players. 15 players are available in total. ### Multiply with 5 and 10 Lesson Check Page No 202 Question 1. Mrs. Hinely grows roses. There are 6 roses on each of her 10 rose bushes. How many roses in all are on Mrs. Hinely’s rose bushes? Options: a. 16 b. 54 c. 60 d. 66 Answer: 60 Explanation: There are 10 rose bushes available. In each rose bush, Mrs. Hinely growing 6 roses. So, to find the number of roses, you need to multiply 10 x 6. The multiplication of 10 x 6 is 60. The number of roses in all are on Mrs. Hinely’s rose bushes are 60. Question 2. Find the product. 5 × 8 ——- Options: a. 8 b. 16 c. 35 d. 40 Answer: 40 Explanation: Skip-count by 5’s 8 times. Write like 5, 10, 15, 20, 25, 30, 35, 40. So, the answer for 5 x 8 is 40. Spiral Review Question 3. Mr. Miller’s class voted on where to go for a field trip. Use the picture graph to find which choice had the most votes. Options: a. Science Center b. Aquarium c. Zoo d. Museum Answer: c. Zoo Explanation: From the given figure, Mr. Miller’s class voted for a field trip. From the table, every start represents 2 votes. It is mentioned that for the Science Center, Mr. Miller’s given two starts. As one star represents 2 votes, he gave 4 votes for Science Center. Similarly, Aquarium = 3 and a half stars. The half star represents one vote. So, the number of votes given for the Aquarium is 7. For Zoo, he has given 4 stars. So, every start means 2 votes. The total number of votes is 8. Finally, the number of starts for the Museum is 2. So, the total number of votes is 4. Mr. Miller’s class is given a high number of votes for Zoo. So, Mr. Miller’s class wishes to go for Zoo. Question 4. Zack made this table for his survey. How many students were surveyed in all? Options: a. 38 b. 43 c. 47 d. 49 Answer: c. 47 Explanation: Zack prepared a table of flavors and votes. So, every vote represents one person. By adding the total number of votes, we can get the total number of students participated in ina survey. Add 16 + 10 + 9 + 12 = 47. 47 students were surveyed in all to vote for their favorite juice. Question 5. Which of the following numbers is even? 25, 28, 31, 37 Options: a. 25 b. 28 c. 31 d. 37 Answer: b. 28 Explanation: Even numbers are divided by 2. Also, even numbers end with a digit of 0, 2, 4, 6, or 8. So, the given number out of the given numbers is 28. It is ended with 8 and also it can divide by 2. Question 6. Estimate the sum. 4 7 9 + 8 9 ——— Options: a. 568 b. 400 c. 500 d. 600 Answer: a. 568 Explanation: Add the ones. Regroup the ones as tens and ones. So, 9 + 9 = 18. Remain the 8 same and add the 1 to the tens. Add the tens. Regroup the tens as hundreds and tens. Now, add 7 + 8 + 1 = 16. place the 6 in the tens place and move the 1 to hundreds. Add the hundreds now. 4 + 1 = 5. So, now place the numbers in order. The final answer is 568. Note:The option is modified for the above question. There is no correct answer available in the given options. So, option a is changed to the correct answer. The answer is explained with the place value to add two addends method. ### Multiply with 3 and 6 Page No 207 Find the product. Question 1. 6 × 4 = 24 Think: You can use doubles. 3 × 4 = 12 12 + 12 = 24 Answer: 24 Explanation: By using doubles, we can find a 6 x 4 value. First, multiply the factor with half of 6. So, now we can do 3 x 4 = 12. Now, we can double the value of 3 x 4. That is 12 + 12 = 24. So, the answer for 6 x 4 = 24. Question 2. 3 × 7 = _______ Answer: 21 Explanation: Skip count by 3’s until you say 7 numbers. 3, 6, 9, 12, 15, 18, 21. So, the answer for 3 x 7 is 21. Question 3. ________ = 2 × 6 Answer: 12 Explanation: With the Commutative Law of Multiplication, you can write 2 x 6 as 6 x 2. Multiply the factor 2 with 5 and then add the factor to it to get the final answer. First, multiply the factor with 5. That is 5 x 2 = 10. Now, add the factor with the answer of 5 x 2. 10 +2 = 12. The answer for 6 x 2 is 12. So, the answer for 2 x 6 is 12. Question 4. ________ = 3 × 5 Answer: 15 Explanation: You can skip count by 3’s until you say 5 numbers. 3, 6, 9, 12, 15. So, the final answer for 3 x 5 is 15. Question 5. 1 × 3 = ________ Answer: 3 Explanation: Multiplication of any number with 1 is the same number. So, 1 x 3 = 3. Question 6. ________ = 6 × 8 Answer: 48 Explanation: Use doubles to find the answer of 6 x 8. Firstly, multiply 3 x 8 = 24. Then, double the value of 3 x 8. 24 + 24 = 48. The answer for 6 x 8 is 48. Question 7. 3 × 9 = ________ Answer: 27 Explanation: Skip count by 3’s until you say 9 numbers. Write like 3, 6, 9, 12, 15, 18, 21, 24, 27. The answer for 3 x 9 is 27. Question 8. _______ = 6 × 6 Answer: 36 Explanation: Use doubles to find the answer of 6 x 6. Firstly, multiply 3 x 6 = 18. Then, double the value of 3 x 6. 18 + 18 = 36. The answer for 6 x 6 is 36. Question 9. 4 × 3 —— ________ Answer: 12 Explanation: Write 4 x 3 as 3 x 4 according to the Commutative Law of Multiplication. Now do multiplication for 3 x 4. Skip-count by 3’s four times. Now, you can write as 3, 6, 9, 12. The answer for 3 x 4 is 12. So, the answer for 4 x 3 is also 12. Go Math Grade 3 Chapter 4 Pdf Question 10. 6 × 5 —— _________ Answer: 30 Explanation: Multiply the given factor 5 with 5. Then, add 5 to the answer to get the answer for 6 x 5. Firstly, multiply 5 x 5 = 25. Add 5 to 25. 5 + 25 = 30. So, the answer for 6 x 5 is 30. Question 11. 2 × 3 —— _________ Answer: 6 Explanation: Using the Commutative Law of Multiplication, you can write 2 x 3 = 3 x 2. Now, Skip count by 3’s until you say 2 numbers. 3, 6. Therefore, the answer to 3x 2 is 6. The answer for 2 x 3 is 6. Question 12. 6 × 3 ——– _________ Answer: 18 Explanation: Double the value of 3 x 3 to get the answer for 6 x 3. The answer for 3 x 3 = 9. Now, double the value of 9. The answer for 6 x 3 is 9 + 9 = 18. Question 13. 10 × 6 ——- _________ Answer: 60 Explanation: Using the Commutative Law of Multiplication, you can write as 10 x 6 = 6 x 10. Now, multiply the 10 with 5. The answer is 5 x 10 = 50. Now, add the 10 to 50 to get the answer. The answer for 6 x 10 is 10 + 50 = 60. So, the answer for 10 x 6 is 60. Question 14. 3 × 6 ——- __________ Answer: 18 Explanation: Skip-count by 3’s 6 times. You can write as 3, 6, 9, 12, 15, 18. The answer for 3 x 6 is 18. Question 15. 7 × 6 ——- __________ Answer: 42 Explanation: With the help of the Commutative Law of Multiplication, you can change 7 x 6 to 6 x 7. Double the value of 3 x 7 to get 6 x 7. Now, do 3 x 7 = 21. Double the 21. 21 + 21 = 42. The answer for 6 x 7 = 42. So, the answer for 7 x 6 is 42. Question 16. 3 × 0 ——- _________ Answer: 0 Explanation: Multiplication of any number with 0 is 0. So, the answer for 3 x 0 is 0. Question 17. 9 × 6 ——- __________ Answer: 54 Explanation: Write 9 x 6 as 6 x 9 using the Commutative Law of Multiplication. Multiply the 9 with 5. 5 x 9 = 45. Now add the 45 to the 9. So, the answer for 6 x 9 is 45 + 9 = 54. Therefore, the answer for 9 x 6 is 54. Question 18. 3 × 3 ——- __________ Answer: 9 Explanation: Skip count by 3’s until you say 3 numbers. 3, 6, 9. So, the answer for 3 x 3 is 9. Question 19. 10 × 3 ——– ___________ Answer: 30 Explanation: Use Commutative Law of Multiplication to write 10 x 3 to 3 x 10. Now, skip count by 3’s until you say 10 numbers. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30. So, the answer for 3 x 10 is 30. Therefore, the answer for 10 x 3 is 30. Question 20. 1 × 6 ——– ________ Answer: 6 Explanation: Multiplication of any number with 1 is the same number. So, 1 x 6 = 6. Problem Solving Question 21. James got 3 hits in each of his baseball games. He has played 4 baseball games. How many hits has he had in all? _________ hits Answer: 12 hits Explanation: As per the given data, James got 3 hits in each of his baseball games. He has played 4 baseball games. To find the number of hits has he had in all, we need to multiply, 3 hits x 4 baseball games. So, the answer is 3 x 4 = 12 hits. Question 22. Mrs. Burns is buying muffins. There are 6 muffins in each box. If she buys 5 boxes, how many muffins will she buy? __________ muffins Answer: 30 muffins Explanation: From the provided information, Mrs. Burns is buying muffins. She is going to buy 5 boxes each has 6 muffins in it. So, to find the total number of muffins, we need to multiply, number of boxes and number of muffins in it. The total number of muffins = 6 x 5 = 30. She is going to buy 30 muffins. ### Multiply with 3 and 6 Lesson Check Page No 208 Question 1. Paco buys a carton of eggs. The carton has 2 rows of eggs. There are 6 eggs in each row. How many eggs are in the carton? Options: a. 8 b. 12 c. 14 d. 24 Answer: b. 12 Explanation: From the given data, Paco buys a carton of eggs. The carton has 2 rows in it. Every row has 6 eggs. To find the number of eggs, we need to multiply the number of rows and the number of eggs for each row. Therefore, the number of eggs in the carton are 2 x 6 = 12. 12 eggs are available in the carton. Question 2. Find the product. 9 × 3 —— Options: a. 18 b. 24 c. 27 d. 36 Answer: c. 27 Explanation: Use Commutative Law of Multiplication to write 9 x 3 to 3 x 9. Now, skip count by 3’s until you say 9 numbers. 3, 6, 9, 12, 15, 18, 21, 24, 27. So, the answer for 3 x 9 is 27. Therefore, the answer for 9 x 3 is 27. Spiral Review Question 3. Find the difference. 5 6 8 – 2 8 3 ——— Options: a. 285 b. 325 c. 385 d. 851 Answer: a. 285 Explanation: Subtract the ones. 8 – 3 = 5. Then, Subtract the tens. 6 < 8. So, regroup 5 hundreds 6 tens equal to 4 hundreds 8 tens. 16 – 8 = 8. Subtract the hundreds and add them to check the answer. 4 – 2 = 2. The final answer is 285. Go Math Grade 3 Chapter 4 Test Pdf Question 4. Dwight made double the number of baskets in the second half of the basketball game than in the first half. He made 5 baskets in the first half. How many baskets did he make in the second half? Options: a. 7 b. 9 c. 10 d. 20 Answer: c. 10 Explanation: Given that Dwight made double the number of baskets in the second half of the basketball game than in the first half. He made 5 baskets in the first half. So, to find the second-half baskets, we need to double the baskets in the first half. Baskets in the second half = 5 x 2 = 10. Question 5. In Jane’s picture graph, the 😊 smile symbol represents two students. One row in the picture graph has 8 symbols. How many students does that represent? Options: a. 40 b. 32 c. 24 d. 16 Answer: d. 16 Explanation: From Jane’s picture graph, the 😊 smile symbol represents 2 students. The one row in the picture graph has 8 symbols. To find the total number of students, we need to multiply the number of smiles and the number of students for each smile. The number of students for a row is 8 x 2 = 16. Question 6. What multiplication sentence does this array show? Options: a. 5 × 6 = 30 b. 6 × 6 = 36 c. 5 × 5 = 25 d. 1 × 6 = 6 Answer: a. 5 × 6 = 30 Explanation: The given array shows that it has 6 boxes for a row and 5 boxes for a column. So, by multiplying the number of rows x number of columns the correct answer is 6 x 5 = 30. By using the Commutative Law of Multiplication, we can write 6 x 5 = 5 x 6. So, the answer from the given options is 5 × 6 = 30. ### Distributive Property Page No 213 Write one way to break apart the array. Then find the product. Question 1. (3 × 7) + (3 × 7) 42 Answer: 42 Explanation: The given array is 6 x 7. Use the Distributive Property to get the final answer. Break the array rows to make two smaller arrays with the facts 3 and 3. Now, you can write the given array as (3 + 3) x 7. Then, multiply each addend with 7. The equation becomes (3 x 7) +(3 x 7). Now simplify and add them to get the final answer. 21 + 21 = 42. Question 2. _________ Answer: 32 Explanation: The given array has 8 columns and 4 rows. Simplify the answer using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 2 and 2. To get the answer, we have to write 4 x 8. By doing smaller arrays, you can write it as (2 + 2) x 8. Multiply each addend with 8. The equation becomes (2 x 8) +(2 x 8). Now simplify and add them to get the final answer. 16 + 16 = 32. Question 3. ___________ Answer: 54 Explanation: The given figure has 9 columns and 6 rows. Use Distributive Property to get the answer of a given array. Let’s break the array rows with two smaller arrays with the facts 3 and 3. Now, write the equation as 6 x 9 = (3 + 3) x 9. Multiply each 3 with 9. 27 + 27. The final answer is 54. Question 4. _________ Answer: 56 Explanation: The given array has 8 columns and 7 rows. With the help of Distributive Property, you can solve the given array. Break the array columns with two smaller arrays with the facts 4 and 4. Write the equation as (7 x 4) + (7 x 4) = 28 + 28 = 56. Problem Solving Question 5. There are 2 rows of 8 chairs set up in the library for a puppet show. How many chairs are there in all? Use the Distributive Property to solve. ____________ chairs Answer: 16 Explanation: From the given information, there are 2 rows of 8 chairs set up in the library for a puppet show. So, in the array, there are 2 rows and 8 columns. To find the answer, we have to multiply 2 x 8. Using Distributive Property, we can solve 2 x 8. Sum the number 2 with facts 1 and 1. So, we can write as (1 + 1) x 8. Simplify the answer by multiplying each addend to 8. (1 x 8) + (1 x 8) = 8 + 8 = 16. There are 16 chairs available in 2 rows. Go Math Grade 3 Chapter 4 Pdf Lesson 4.4 Extra Practice Answer Key Question 6. A marching band has 4 rows of trumpeters with 10 trumpeters in each row. How many trumpeters are in the marching band? Use the Distributive Property to solve. ___________ trumpeters Answer: 40 Explanation: From the given information, a marching band has 4 rows of trumpeters with 10 trumpeters in each row. To know the number of trumpeters, we have to calculate 4 x 10. With the help of Distributive Property, you can separate the one number with its sums. Now write the 4 with its sums 2 and 2. (2 + 2) x 10. Now, you can multiply each addend with 10. (2 x 10) + (2 x 10) = 20 + 20 = 40. 40 trumpeters are in the marching band. ### Distributive Property Lesson Check Page No 214 Question 1. Which number sentence is an example of the Distributive Property? Options: a. 7 × 6 = 6 × 7 b. 7 × (2 × 3) = (7 × 2) × 3 c. 7 × 6 = (7 × 3) + (7 × 3) d. 7 + 6 = 7 + 3 + 3 Answer: c. 7 × 6 = (7 × 3) + (7 × 3) Explanation: Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 7 × 6 = (7 × 3) + (7 × 3) is the correct answer. Question 2. What is one way to break apart the array? Options: a. (2 × 6) + (2 × 6) b. (4 × 2) + (4 × 2) c. (4 × 4) + (4 × 4) d. (6 × 3) + (6 × 3) Answer: a. (2 × 6) + (2 × 6) Explanation: The given figure has 6 columns and 4 rows. By using Distributive Property, you can find the answer easily. Let’s break the array rows with two smaller arrays with the facts 2 and 2. Now, write the equation as 4 x 6 = (2 + 2) x 6. Multiply each 2 with 6. the equation can be written as (2 x 6) + (2 x 6). Spiral Review Question 3. The school auditorium has 448 chairs set out for the third-grade performance. What is 448 rounded to the nearest ten? Options: a. 500 b. 440 c. 450 d. 400 Answer: c. 450 Explanation: Given that the school auditorium has 448 chairs set out for the third-grade performance. The 448 number lies between 440 and 450. 448 is closer to 450 than it is to 440. So, 448 rounds to 450. Go Math 3rd Grade Chapter 4 Mid Chapter Checkpoint Question 4. Find the difference. 4 0 0 – 2 9 6 ———- Options: a. 104 b. 114 c. 204 d. 296 Answer: a. 104 Explanation: Subtract the ones. 0<6. so regroup 0 tens 0 ones = 1 tens 4 ones. Now, do 10 – 6 = 4. Then, Subtract the tens. 9 = 9. So, so regroup. 4 hundred 9 tens = 3 hundred 4 tens. 9 – 9 = 0. Subtract the hundreds and add them to check the answer. 3 – 2 = 1. The final answer is 104. Question 5. There are 622 fruit snacks in one crate and 186 in another crate. How many fruit snacks are there in all? 6 2 2 + 1 8 6 ———- Options: a. 436 b. 708 c. 768 d. 808 Answer: d. 808 Explanation: Break apart the addends from the given values. Start with the hundreds. Then, add each place value. Let’s write 622 as 600 + 20 + 2 and 186 as 100 + 80 + 6. Sum up the above two values. Then you get 700 + 100 + 8. Add the ones and then add the 10’s and 100’s. The final answer is 808. Question 6. Which sport do 6 students play? a. Football b. Baseball c. Basketball d. Soccer Answer: a. Football Explanation: From the given picture, it is mentioned that the sports students play and the number of students for that game. As mentioned, Football needs 6 students. Baseball needs 12 students. Basketball needs 10 students. Also, Soccer needs 16 students. So, the answer is Football sport required 6 students to play. ### Multiply with 7 Page No 219 Find the product. Question 1. 6 × 7 = 42 Answer: 42 Explanation: By using doubles, we can find a 6 x 7 value. First, multiply the factor with half of 6. So, now we can do 3 x 7 = 21. Now, we can double the value of 3 x 7. That is 21 + 21 = 42. So, the answer for 6 x 7 = 42. Question 2. ________ = 7 × 9 Answer: 63 Explanation: Use the Distributive Property to find the value of 7 x 9. If we take 7 rows and 9 columns of an array, then we can break the array into two smaller arrays with the facts of 9. Now, write the 7 x 9 as 7 x (6 + 3). Multiply the facts with the 7. Then, you get (7 x 6) + (7 x 3). Therefore, you get the answer as 42 + 21 = 63. Question 3. _______ = 1 × 7 Answer: 7 Explanation: Multiplication of any number with 1 is the same number. So, 1 x 7 = 7. Question 4. 3 × 7 = _______ Answer: 21 Explanation: Skip count by 3’s until you say 7 numbers. 3, 6, 9, 12, 15, 18, 21. So, the answer for 3 x 7 is 21. Question 5. 7 × 7 = ________ Answer: 49 Explanation: Let us take the array has 7 columns and 7 rows. Simplify the answer using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 4 and 3. To get the answer, we have to write 7 x 7. By doing smaller arrays, you can write it as (4 + 3) x 7. Multiply each addend with 7. The equation becomes (4 x 7) +(3 x 7). Now simplify and add them to get the final answer. 28 + 21 = 49. Question 6. _______ = 2 × 7 Answer: 14 Explanation: Draw two counters. Place seven objectives in two counters. Now, add the objectives in two counters. The final answer is 7 + 7 = 14. So, 2×7 = 14 is the answer. Question 7. 7 × 8 = _________ Answer: 56 Explanation: Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 7 × 8 = (7 × 4) + (7 × 4) = 28 + 28 = 56. Question 8. ______ = 4 × 7 Answer: 28 Explanation: Firstly, multiply 2×7 to get the answer for 4×7. Then, double the answer of 2×7 to get the final answer. So, do 2×7 = 14. Double the number 14 to get the 4×7 Answer. The double of 14 is 14 +14 = 28. The answer to 4×7 is 28. Go Math Grade 3 Chapter 4 Answer Key Question 9. 7 × 5 ——- __________ Answer: 35 Explanation: From Commutative Law of Multiplication, you can write 7 x 5 = 5 x 7. So, to find the multiplication of 5 x 7, skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35. Therefore, the answer for 7 x 5 is 35. Question 10. 7 × 1 ——- _________ Answer: 7 Explanation: Using the Commutative Law of Multiplication, you can write 7 x 1 = 1 x 7. Multiplication of any number with 1 is the same number. So, 1 x 7 = 7. Question 11. 6 × 7 ——- __________ Answer: 42 Explanation: Use doubles to find the answer of 6 x 7. Firstly, multiply 3 x 7 = 21. Then, double the value of 3 x 7. 21 + 21 = 42. The answer for 6 x 7 is 42. Question 12. 7 × 4 ——- __________ Answer: 28 Explanation: Write 7 x 4 as 4 x 7 according to the Commutative Law of Multiplication. Now, do multiplication for 4 x 7. You can double 2×7 to get 4×7. Multiply 7 with 2. You will get 14. Then, double the product to get the answer to 4×7. You will get 14 +14 = 28. So, you get the final answer as 28. Question 13. 2 × 7 ——- ___________ Answer: 14 Explanation: The given multiplication is 2×7. The answer to any number multiplies with 2 is double of that number. So, the 2×7 can find by doing 7+7. The answer is 7+7 = 14. So, the final answer is 2×7 = 14. Question 14. 10 × 7 —— ____________ Answer: 70 Explanation: A multiple of 10 is any product that has 10 as one of its factors. So, the multiplication of any number with 10 is 10’s of that particular number. The answer is 70. Question 15. 3 × 7 ——- ____________ Answer: 21 Explanation: Skip count by 3’s until you say 7 numbers. Write like 3, 6, 9, 12, 15, 18, 21. The answer for 3 x 7 is 21. Question 16. 7 × 9 —— ___________ Answer: 63 Explanation: Use the Distributive Property to find the value of 7 x 9. If we take 7 rows and 9 columns of an array, then we can break the array into two smaller arrays with the facts of 9. Now, write the 7 x 9 as 7 x (6 + 3). Multiply the facts with the 7. Then, you get (7 x 6) + (7 x 3). Therefore, you get the answer as 42 + 21 = 63. Question 17. 8 × 7 ——- __________ Answer: 56 Explanation: Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 8 x 7 = (4 + 4) x 7 = (4 x 7) + (4 x 7) = 28 + 28 = 56 is the correct answer. Go Math Grade 3 Chapter 4 Review/Test Pdf Question 18. 7 × 0 —— __________ Answer: 0 Explanation: Multiplication of any number with 0 is 0. So, the answer for 7 x 0 is 0. Problem Solving Question 19. Julie buys a pair of earrings for$7. Now she would like to buy the same earrings for 2 of her friends. How much will she spend for all 3 pairs of earrings?
$__________ Answer:$21

Explanation:
From the given information, Julie buys a pair of earrings for $7. She also wants to buy 2 more pairs of earrings for her 2 friends. So, a total she needs to but 3 pairs of earrings. To know the total amount she is going to spend on earrings, we need to multiply the total number of earrings pair with a cost for each earring. So, we can do 3 x$7 = $21. Julie needs to spend$21 to buy 3 pairs of earrings.

Question 20.
Owen and his family will go camping in 8 weeks. There are 7 days in 1 week. How many days are in 8 weeks?
_________ days

56 days

Explanation:
Given that Owen and his family will go camping in 8 weeks. There are 7 days in 1 week. So, to calculate the total number of days in 8 weeks, multiply 8 x 7 = 56. There are 56 days in 8 weeks.

### Multiply with 7 Lesson Check Page No 220

Question 1.
Find the product.
7
× 8
——
Options:
a. 54
b. 56
c. 64
d. 66

b. 56

Explanation:
Distributive Property: The Distributive Property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. So, from the given options, c. 7 × 8 = (7 × 4) + (7 × 4) = 28 + 28 = 56.

Question 2.
What product does the array show?

Options:
a. 14
b. 17
c. 21
d. 24

c. 21

Explanation:
The given array has 7 columns and 3 rows. Simplify the answer using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 1 and 2. To get the answer, we have to write 3 x 7. By doing smaller arrays, you can write it as (1 + 2) x 7. Multiply each addend with 8. The equation becomes (1 x 7) +(2 x 7). Now simplify and add them to get the final answer. 7 + 14 = 21.

Spiral Review

Question 3.
Which statement is true about the numbers below?
6, 12, 18, 24, 30
Options:
a. All of the numbers are odd.
b. Some of the numbers are odd.
c. All of the numbers are even.
d. Some of the numbers are even.

c. 21

Explanation:
All the given numbers are divided by 2. So, the answer is All of the numbers are even

Question 4.
How many more people chose retriever than poodle?

Options:
a. 31
b. 39
c. 41
d. 49

b. 39

Explanation:
To know more people chose retriever than poodle, we have to do subtraction from retriever to poodle. So, 65 – 26 = 39. 39 more people chose retriever than poodle.

Question 5.
What is 94 rounded to the nearest ten?
Options:
a. 90
b. 94
c. 95
d. 100

a. 90

Explanation:

94 is between 90 and 100. 94 is closer to 90 than is to 100. 94 rounded to the nearest ten is 90.

Question 6.
Jack has 5 craft sticks. He needs 4 times that number for a project. How many craft sticks does Jack need altogether?
Options:
a. 9
b. 16
c. 20
d. 24

c. 20

Explanation:
Jack has 5 craft sticks. He needs 4 times that number for a project. To find the total number of craft sticks does Jack needs altogether are 5 x 4 = 20. 20 craft sticks need to Jack.

### Mid-Chapter Checkpoint Page No 221

Vocabulary

Choose the best term from the box to complete the sentence.

Question 1.
A __________ of 4 is any product that has 4 as one of its factors.
_________

Commutative Property of Multiplication

Question 2.
This is an example of the ______________ .
3 × 8 = (3 × 6) + (3 × 2)
This property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
__________

Distributive Property of Multiplication

Concepts and Skills

Write one way to break apart the array.
Then find the product.

Question 3.

__________

7 x 5 = 35

Explanation:

The provided array has 7 columns and 5 rows. Let’s simplify the answer by using Distributive Property. Now, break the array rows to make two smaller arrays with the facts 2 and 3. Now, do 7 x 5. By doing smaller arrays, you can write it as 7 x (2 + 3). Multiply 7 with 2 and 7 with 3. Write (7 x 2) + (7 x 3). Now add them to get the final answer. 14 + 21 = 35.

Question 4.

__________

9 x 4 = 36

Explanation:
The given array has 9 columns and 4 rows. Now, do 9 x 4. Using Distributive Property break the array rows to make two smaller arrays with the 4 facts 2 and 2. Now, add 9 x (2 + 2). Multiply 9 with 2 and 9 with 2. Write (9 x 2) + (9 x 2). Now add them to get the final answer. 18 + 18 = 36.

Find the product.

Go Math Grade 3 Chapter 4 Multiplication Facts and Answers Question 5.
3 × 1 = __________

3

Explanation:
Using the Commutative Law of Multiplication, Write 3 x 1 = 1 x 3. Multiplication of any number with 1 is the same number. So, 1 x 3 = 3.

Question 6.
5 × 6 = _________

30

Explanation:
Skip-count by 5’s 6 times. You can write as 5, 10, 15, 20, 25, 30. The answer for 5 x 6 is 30.

Question 7.
________ = 7 × 7

49

Explanation:
Use Distributive Property, to get the answer. Given 7 x 7. Write the facts for 7. 7 = 4 + 3. Now, write 7 x 7 = 7 x (4 + 3). Multiply 7 with 4 and 7 with 3. (7 x 4) + (7 x 3) = 28 + 21 = 49.

Question 8.
2 × 10 = _________

20

Explanation:
Double the 10 to get the answer for 2 x 10. So, now write 10 + 10 = 20. The answer for 2 x 10 = 20.

Question 9.
2
× 1
——–
_________

2

Explanation:
Add 1 + 1 to get 2 x 1. 1 + 1 = 2. The answer for 2 x 1 = 2.

Question 10.
6
× 6
——–
_________

36

Explanation:
Use doubles to get 6 x 6. First, multiply 3 x 6 = 18. Then, double the value of 3 x 6. 18 + 18 = 36. The answer for 6 x 6 is 36.

Question 11.
8
× 7
——-
__________

56

Explanation:
Use Distributive Property to find 8 x 7 = (4 + 4) x 7 = (4 x 7) + (4 x 7) = 28 + 28 = 56 is the correct answer.

Question 12.
6
× 0
——
___________

0

Explanation:

The multiplication of any number with 0 is 0. So, the answer for 10 x 0 is 0.

Question 13.
3
× 8
——-
__________

24

Explanation:
Skip-count by 3’s 8 times. You can write as 3, 6, 9, 12, 15, 18, 21, 24. The answer for 3 x 8 is 24.

### Mid-Chapter Checkpoint Page No 222

Question 14.
Lori saw 6 lightning bugs. They each had 6 legs. How many legs did the lightning bugs have in all?
__________ legs

36

Explanation:
Given that, Lori saw 6 lightning bugs. Each lightning bug had 6 legs. To find the total number of legs, do 6 x 6 = 36. The lightning bugs have 36 in all.

Question 15.
Zach walked his dog twice a day, for 7 days. Moira walked her dog three times a day for 5 days. Whose dog was walked more times? How many more?
Type below:
_________

Moira’s dog walked more than Zach’s dog. It walked one time more than Zach’s dog.

Explanation:
Zach walked his dog twice a day, for 7 days. So, Zach’s dog walked 7 x 2 = 14 times in total. Moira walked her dog three times a day for 5 days. Moira’s dog walked 3 x 5 = 15 days. So, Moira’s dog walked more times than Zach’s dog. It walked one time more than Zach’s dog.

Question 16.
Annette buys 4 boxes of pencils. There are 8 pencils in each box. Jordan buys 3 boxes of pencils with 10 pencils in each box. Who buys more pencils? How many more?
Type below:
__________

Annette has more pencils than Jordan. He has 2 pencils more than Jordan.

Explanation:
Annette buys 4 boxes of pencils. Each box has 8 pencils in it. So, Annette has 4 x 8 = 32 pencils. Jordan buys 3 boxes of pencils with 10 pencils in each box. So, he has 3 x 10 = 30 pencils. Annette has 2 pencils more than Jordan.

Question 17.
Shelly can paint 4 pictures in a day. How many pictures can she paint in 7 days?
_________ pictures

28

Explanation:
Shelly can paint 4 pictures in a day. In 7 days, she can paint 7 x 4 = 28 pictures.

### Associative Property of Multiplication Page No 227

Write another way to group the factors.
Then find the product.

Question 1.
(3 × 2) × 5
3 × (2 × 5)
30

30

Explanation:
Using the Associative Property of Multiplication, we can write (3 × 2) × 5 = 3 × (2 × 5).
Find (3 × 2) × 5. Multiply 3 x 2 = 6. Then, multiply 6 x 5 = 30.
Find 3 x (2 x 5). Multiply 2 x 5 = 10. Then, multiply 3 x 10 = 30.
So, (3 × 2) × 5 = 3 × (2 × 5). The product value is 30.

Question 2.
(4 × 3) × 2 =
________

(4 × 3) × 2 = 4 x (3 x 2)
24

Explanation:
Use Associative Property of Multiplication to write other groups the factors. (4 × 3) × 2 = 4 x (3 x 2). Now, multiply 4 x 3 = 12. Then, multiply 12 x 2 = 24. So, (4 × 3) × 2 = 24.

Question 3.
2 × (2 × 8) =
________

2 × (2 × 8) = (2 x 2) x 8
32

Explanation:
With Associative Property of Multiplication, 2 × (2 × 8) = (2 x 2) x 8. Now, multiply 2 x 8 = 16. Then, multiply 16 x 2 = 32. So, 2 × (2 × 8) = 32.

Question 4.
9 × (2 × 1) =
________

9 × (2 × 1) = (9 × 2) × 1
18

Explanation:
Using Associative Property of Multiplication, we can write 9 × (2 × 1) = (9 × 2) × 1. Now, multiply 2 x 1 = 2. Then, multiply 2 x 9 = 18. So, 9 × (2 × 1) = 18.

Question 5.
2 × (3 × 6) =
________

2 × (3 × 6) = (2 x 3) x 6
36

Explanation:
With the help of Associative Property of Multiplication, we can write 2 × (3 × 6) = (2 x 3) x 6. Now, multiply 2 x 3 = 6. Then, multiply 6 x 6 = 36. So, 2 × (3 × 6) = 36.

Question 6.
(4 × 2) × 5 =
________

(4 × 2) × 5 = 4 x (2 x 5)
40

Explanation:
Use Associative Property of Multiplication, to write (4 × 2) × 5 = 4 x (2 x 5). Now, multiply 2 x 5 = 10. Then, multiply 4 x 10 = 40. So, (4 × 2) × 5 = 40.

Use parentheses and multiplication properties.
Then, find the product.

Question 7.
9 × 1 × 5
( 9 × 1 ) × 5 = ________

( 9 × 1 ) × 5 = 9 x (1 x 5)
45

Explanation:
Use Associative Property of Multiplication. ( 9 × 1 ) × 5 = 9 x (1 x 5). Now, multiply 9 x 1 = 9. Then, multiply 9 x 5 = 45. So, ( 9 × 1 ) × 5 = 45.

3 × 3 × 2
( 3 × 3 ) × 2 = _________

( 3 × 3 ) × 2 =
18

Explanation:
Use Associative Property of Multiplication. ( 3 × 3 ) × 2 = 3 x (3 x 2). Now, multiply 3 x 3 = 9. Then, multiply 9 x 2 = 18. So, ( 3 × 3 ) × 2 = 18.

Question 9.
2 × 4 × 3
( 2 × 4 ) × 3 = _________

( 2 × 4 ) × 3 = 2 x (4 x 3)
24

Explanation:
Now use Associative Property of Multiplication. ( 2 × 4 ) × 3 = 2 x (4 x 3). Now, multiply 2 x 4 = 8. Then, multiply 8 x 3 = 24. So, ( 2 × 4 ) × 3 = 24.

Question 10.
5 × 2 × 3
( 5 × 2 ) × 3 = _________

( 5 × 2 ) × 3 = 5 x (2 x 3)
30

Explanation:
Use Associative Property of Multiplication. ( 5 × 2 ) × 3 = 5 x (2 x 3). Now, multiply 5 x 2 = 10. Then, multiply 10 x 3 = 30. So, ( 5 × 2 ) × 3 = 30.

Question 11.
7 × 1 × 5
( 7 × 1 ) × 5 = ________

( 7 × 1 ) × 5 = 7 x (1 x 5)
35

Explanation:
Use Associative Property of Multiplication. ( 7 × 1 ) × 5 = 7 x (1 x 5). Now, multiply 7 x 1 = 7. Then, multiply 7 x 5 = 35. So, ( 7 × 1 ) × 5 = 35.

Question 12.
8 × 2 × 3
( 8 × 2 ) × 3 = _________

( 8 × 2 ) × 3 = 8 x (2 x 3)
48

Explanation:
Use Associative Property of Multiplication. ( 8 × 2 ) × 3 = 8 x (2 x 3). Now, multiply 8 x 2 = 16. Then, multiply 16 x 3 = 48. So, ( 8 × 2 ) × 3 = 48.

Question 13.
7 × 2 × 3
( 7 × 2 ) × 3 = ________

( 7 × 2 ) × 3 = 7 x (2 x 3)
42

Explanation:
Use Associative Property of Multiplication. ( 7 × 2 ) × 3 = 7 x (2 x 3). Now, multiply 2 x 3 = 6. Then, multiply 7 x 6 = 42. So, ( 7 × 2 ) × 3 = 42.

Question 14.
4 × 1 × 3
( 4 × 1 ) × 3 = ________

12

Explanation:
Use Associative Property of Multiplication. ( 4 × 1 ) × 3 = 4 x (1 x 3). Now, multiply 4 x 1 = 4. Then, multiply 4 x 3 = 12. So, ( 4 × 1 ) × 3 = 12.

Question 15.
10 × 2 × 4
( 10 × 2 ) × 4 = ________

80

Explanation:
Use Associative Property of Multiplication. ( 10 × 2 ) × 4 = 10 x (2 x 4). Now, multiply 2 x 4 = 8. Then, multiply 10 x 8 = 80. So, ( 10 × 2 ) × 4 = 80.

Problem Solving

Question 16.
Beth and Maria are going to the county fair. Admission costs $4 per person for each day. They plan to go for 3 days. How much will the girls pay in all?$ _________

$24 Explanation: From the given information, County fair admission costs$4 per person for each day. To go for 3 days, it costs, 3 x $4 =$12. Beth and Maria are going to the county fair. So, 2 members are going to the county fair. The total amount is 2 X $12 =$24.

Question 17.
Randy’s garden has 3 rows of carrots with 3 plants in each row. Next year he plans to plant 4 times the number of rows of 3 plants. How many plants will he have next year?
_________ plants

36

Explanation:
From the given information, Randy’s garden has 3 rows of carrots with 3 plants in each row. So, 3 x 3 = 9. To plant 4 times the number of rows of 3 plants, 9 x 4 = 36. 36 plants will have to plant by Randy’s garden next year.

### Associative Property of Multiplication Lesson Check Page No 228

Question 1.
There are 2 benches in each car of a train ride. Two people ride on each bench. If a train has 5 cars, how many people in all can be on a train?
Options:
a. 4
b. 9
c. 10
d. 20

d. 20

Explanation:
Given that there are 2 benches in each car of a train ride. If a train has 5 cars in total, the number of benches = 5 x 2 = 10. From the given information, two people ride on each bench. So, 10 x 2 = 20 people will travel on a train if the train has 5 cars.

Question 2.
Crystal has 2 CDs in each box. She has 3 boxes on each of her 6 shelves. How many CDs does Crystal have in all?
Options:
a. 6
b. 12
c. 18
d. 36

d. 36

Explanation:
The crystal has 3 boxes on each of her 6 shelves. So, she has 3 x 6 = 18 boxes with her. Each box has 2 CDs in it. So, 2 x 18 = 36 CDs available at crystal.

Spiral Review

Question 3.
Find the sum.
4 7 2
+ 1 8 6
——–
Options:
a. 658
b. 648
c. 558
d. 286

30

Explanation:

Add the ones. Add 2 + 6 =8. Then, Add the tens. Regroup hundreds and tens. Add 7 + 8 = 15. Remember to carry over. Add the hundreds. Add 4 + 1 + 1 = 6. Place the one’s, ten’s and hundreds to get the sum. The sum is 658.

Question 4.
Trevor made a picture graph to show how many minutes each student biked last week. This is his key.
Each = 10 minutes.
What does stand for?
Options:
a. 2 minutes
b. 10 minutes
c. 20 minutes
d. 25 minutes

d. 25 minutes

Explanation:
Given = 10 minutes. So, half time symbol = 5 minutes.  Therefore, = 10 + 10 + 5 = 25 minutes.

Question 5.
Madison has 142 stickers in her collection. What is 142 rounded to the nearest ten?
Options:
a. 40
b. 140
c. 150
d. 200

b. 140

Explanation:
The 142 lies between 140 and 150. But the 142 is closer to 140 than it is to 150. So, 142 is rounded to the 140.

Question 6.
There are 5 pages of photos. Each page has 6 photos. How many photos are there in all?
Options:
a. 12
b. 20
c. 24
d. 30

d. 30

Explanation:
Given that there are 5 pages of photos. And, each page has 6 photos. Total photos = 5 x 6 = 30.

### Patterns on the Multiplication Table Page No 233

Is the product even or odd? Write even or odd.

Question 1.
2 × 7 = even
Think: Products with 2 as a factor are even.

even

Explanation:
Products with 2 as a factor are even.

Question 2.
4 × 6 = ________

even

Explanation:
The numbers end with 0, 2, 4, 6, 8 are even numbers. So, 24 is even number. The 4 × 6 an even number.

Go Math Grade 3 Algebra Lesson 4.7 Question 3.
8 × 3 = ________

even

Explanation:
8 is an even number. 3 is an odd number. The product of an odd number and an even number is even. The answer is even.

Question 4.
2 × 3 = _________

even

Explanation:
Products with 2 as a factor are even.

Question 5.
9 × 9 = ________

odd

Explanation:
9 is an odd number. The product of two odd numbers is an odd number. The answer is odd.

Question 6.
5 × 7 = _________

odd

Explanation:
The numbers end with 1,3, 5, 7, 9 are odd numbers. So, 35 is an odd number. The 5 × 7 an odd number.

Question 7.
6 × 3 = ________

even

Explanation:
6 is an even number. 3 is an odd number. The product of an odd number and an even number is even. The answer is even.

Use the multiplication table. Describe a pattern you see.

Question 8.
in the column for 5
_________

The one’s digits repeat 0 and 5. Each number is 5 more than the number above it.

Explanation:
Each number is added with 5. One’s digit is repeated with 0 and 5.

Question 9.
in the row for 10
________

Add 10. All the products are even. The one’s digit is always 0.

Explanation:
All the products are even. Also, the one’s digit is always 0. Add 10 for every product to get the next number to it.

Question 10.
in the rows for 3 and 6
Type below:
_________

The products of 6 are the products of 3 doubled.

Explanation:
Add 3 for row 3. The products of 6 are the products of 3 doubled.

Question 11.
Carl shades a row in the multiplication table. The products in the row are all even. The ones digits in the products repeat 0, 4, 8, 2, 6. What row does Carl shade?

The row for 4.

Explanation:
From the given data, the answer is row 4.

Question 12.
Jenna says that no row or column contains products with only odd numbers. Do you agree? Explain.
_________

Yes, Either the products are all even, or there is an even and odd number pattern.

Explanation:
Jenna said correctly. Either the products are all even, or there is an even and odd number pattern.

### Patterns on the Multiplication Table Lesson Check Page No 234

Question 1.
Which has an even product?
Options:
a. 1 × 9
b. 3 × 3
c. 5 × 7
d. 4 × 9

d. 4 × 9

Explanation:
The product of an odd number and an even number is even. The answer is 4 × 9.

Question 2.
Which describes this pattern?
10, 15, 20, 25, 30
Options:
a. Even and then odd
c. Subtract 5.
d. Multiply by 5.

a. Even and then odd

Explanation:
The given pattern is the combination of even and add.

Spiral Review

Question 3.
Lexi has 2 cans of tennis balls. There are 3 tennis balls in each can. She buys 2 more cans. How many tennis balls does she now have in all?
Options:
a. 12
b. 9
c. 7
d. 6

a. 12

Explanation:
Lexi has 2 cans of tennis balls. There are 3 tennis balls in each can. So, she has 2 x 3 = 6 balls. She buys 2 more cans. So, again 2 cans with 3 tennis balls = 2 x 3 =6. Total = 6 + 6 = 12. 12 tennis balls she is going to have with her.

Use the picture graph.

How many students have green eyes?
Options:
a. 4
b. 8
c. 12
d. 16

d. 16

Explanation:
From the given picture, Green eyes have 4 circles. Each circle =4. 4 x 4 = 16. 16 students have green eyes.

Question 5.
Sasha bought 3 boxes of pencils. If each box has 6 pencils, how many pencils did Sasha buy in all?
Options:
a. 9
b. 12
c. 18
d. 24

b. 12

Explanation:
Sasha bought 3 boxes of pencils. If each box has 6 pencils, 3 x 6 = 12 pencils Sasha can buy in all.

Question 6.
Find the sum.
2 1 9
+ 7 6 3
———–
Options:
a. 992
b. 982
c. 976
d. 972

b. 982

Explanation:
Let’s write 219 as 200+10+9 and 763 as 700+60+3.
Sum up the above two values. Then you get 900+70+12. Add the ones and then add the 10’s and 100’s. The final answer is 982.

### Multiply with 8 Page No 239

Find the product.

Question 1.
8 × 10 = 80

80

Explanation:
8 × 10 = (2 x 4) x 10
Use the Associative Property.
8 × 10 = 2 x (4 x 10)
Multiply. 4 × 10
8 × 10 = 2 x 40
Double the product.
8 × 10 = 40 + 40
8 × 10 = 80

Question 2.
8 × 8 = ________

64

Explanation:
Factor 8 is an even number. 4+ 4
8 x 4 = 32.
32 doubled is 64.
8 x 8 = 64.

Question 3.
8 × 5 = ________

40

Explanation:
8 × 5 = (2 x 4) x 5
Use the Associative Property.
8 × 5 = 2 x (4 x 5)
Multiply. 4 × 5
8 × 5 = 2 x 20
Double the product.
8 × 5 = 20 + 20
8 × 5 = 40

Question 4.
3 × 8 = ________

24

Explanation:
Factor 8 is an even number. 4+ 4
3 x 4 = 12.
12 doubled is 24.
3 x 8 = 24.

Question 5.
_______ = 4 × 8

32

Explanation:
Factor 8 is an even number. 4+ 4
4 x 4 = 16.
16 doubled is 32.
4 x 8 = 32.

Question 6.
8 × 7 = ________

56

Explanation:
8 × 7 = (2 x 4) x 7
Use the Associative Property.
8 × 7 = 2 x (4 x 7)
Multiply. 4 × 7
8 × 7 = 2 x 28
Double the product.
8 × 7 = 28 + 28
8 × 7 = 56.

Question 7.
6 × 8 = ________

48

Explanation:
Factor 8 is an even number. 4+ 4
6 x 4 = 24.
24 doubled is 48.
6 x 8 = 48.

Question 8.
_______ = 9 × 8

72

Explanation:
Factor 8 is an even number. 4+ 4
9 x 4 = 36.
36 doubled is 72.
9 x 8 = 72.

Question 9.
8
× 2
——
________

16

Explanation:
Using the Commutative Law of Multiplication, 2 x 8 = 8 x 2.
Factor 8 is an even number. 4+ 4
2 x 4 = 8.
8 doubled is 16.
2 x 8 = 16.
So, 8 x 2 =16.

Question 10.
6
× 8
——-
________

48

Explanation:
Factor 8 is an even number. 4+ 4
6 x 4 = 24.
24 doubled is 48.
6 x 8 = 48.

Question 11.
8
× 7
——
_________

56

Explanation:
Using the Commutative Law of Multiplication, 8 x 7 = 7 x 8.
Factor 8 is an even number. 4+ 4
7 x 4 = 28.
28 doubled is 56.
7 x 8 = 56.

Question 12.
0
× 8
——-
____________

0

Explanation:

Multiplication of any number with 0 is 0. So, the answer for 0 x 8 is 0.

Question 13.
8
× 5
——
___________

40

Explanation:
8 × 5 = (2 x 4) x 5
Use the Associative Property.
8 × 5 = 2 x (4 x 5)
Multiply. 4 × 5
8 × 5 = 2 x 20
Double the product.
8 × 5 = 20 + 20
8 × 5 = 40.

Question 14.
8
× 8
——–
___________

64

Explanation:
Factor 8 is an even number. 4+ 4
8 x 4 = 32.
32 doubled is 64.
8 x 8 = 64.

Question 15.
9
× 8
——-
___________

72

Explanation:
Factor 8 is an even number. 4+ 4
9 x 4 = 36.
36 doubled is 72.
9 x 8 = 72.

Question 16.
8
× 3
——
___________

24

Explanation:
8 × 3 = (2 x 4) x 3
Use the Associative Property.
8 × 3 = 2 x (4 x 3)
Multiply. 4 × 3
8 × 3 = 2 x 12
Double the product.
8 × 3 = 12 + 12
8 × 3 = 24.

Question 17.
8
× 1
——
___________

8

Explanation:

Multiplication of any number with 1 is the same number. So, 1 x 8 = 8.

Question 18.
4
× 8
——
___________

32

Explanation:
Factor 8 is an even number. 4+ 4
4 x 4 = 16.
16 doubled is 32.
4 x 8 = 32.

Problem Solving

Question 19.
There are 6 teams in the basketball league. Each team has 8 players. How many players are there in all?
____________ players

48

Explanation:
Multiply 6 x 8 to get the total number of players. 6 x 8 = 48 players are in the basketball league.

Question 20.
Lynn has 4 stacks of quarters. There are 8 quarters in each stack. How many quarters does Lynn have in all?
___________ quarters

32

Explanation:
Multiply 4 x 8 to find quarters in stacks. Lynn has 4 x 8 = 32 quarters in total.

Question 21.
Tomas is packing 7 baskets for a fair. He is placing 8 apples in each basket. How many apples are there in all?
___________ apples

56

Explanation:
Multiply 7 x 8 to get the total number of apples. Tomas have 7 x 8 = 56 apples.

Question 22.
There are 10 pencils in each box. If Jenna buys 8 boxes, how many pencils will she buy?
_____________ pencils

80

Explanation:
To get total pencils, if Jenna buys 8 boxes, multiply 10 x 8. So, Jenna buys 10 x 8 = 80 pencils.

### Multiply with 8 Lesson Check Page No 240

Question 1.
Find the product.
5 × 8 = ■
Options:
a. 30
b. 32
c. 42
d. 40

d. 40

Explanation:
Using Commutative Property of Multiplication, write 5 x 8 = 8 x 5
8 × 5 = (2 x 4) x 5
Use the Associative Property.
8 × 5 = 2 x (4 x 5)
Multiply. 4 × 5
8 × 5 = 2 x 20
Double the product.
8 × 5 = 20 + 20
8 × 5 = 40

Question 2.
There are 7 tarantulas in the spider exhibit at the zoo. Each tarantula has 8 legs. How many legs do the 7 tarantulas have in all?
Options:
a. 15
b. 49
c. 56
d. 63

c. 56

Explanation:
Multiply 7 x 8 to find the 7 tarantulas legs. 7 tarantulas have 7 x 8 = 56 legs.

Spiral Review

Question 3.
Find the difference.
6 5 2
– 9 9
———
Options:
a. 99
b. 552
c. 553
d. 653

c. 553

Explanation:
Subtract the ones. 2<9. so regroup 5 tens 2 ones = 4 tens 3 ones. Now, do 12 – 9 = 3. Then, Subtract the tens. 4 < 9. So, regroup 6 hundred 5 tens = 5 hundred 5 tens. 14 – 9 = 5. Subtract the hundreds and add them to check the answer. 5 – 0 = 5. The final answer is 553.

Division and the Distributive Property Lesson 4.8 Answer Key Question 4.
The school library received an order of 232 new books. What is 232 rounded to the nearest ten?
Options:
a. 200
b. 230
c. 240
d. 300

b. 230

Explanation:
The 232 lies between 230 and 240. But the 232 is closer to 230 than it is to 240. So, 232 is rounded to the 230.

Question 5.
Sam’s picture graph shows that 8 students chose pizza as their favorite lunch. This is the key for the graph.
Each ☺ smile = 2 students.
How many ☺ smile should be next to pizza on Sam’s graph?
Options:
a. 2
b. 4
c. 6
d. 8

b. 4

Explanation:
Given 1 smile = 2 students.
2 smiles = 4 students
3 smiles = 6 students
4 smiles = 8 students
4 smiles required for Sam for her next pizza on the graph.

Question 6.
Tashia buys 5 packages of oranges. Each package has 4 oranges. How many oranges in all does Tashia buy?
Options:
a. 1
b. 9
c. 20
d. 25

d. 25

Explanation:
To know the total number of oranges, multiply 5 x 5. Tashia buys 5 x 5 = 25 oranges.

### Multiply with 9 Page No 245

Find the product.

Question 1.
10 × 9 = 90

90

Explanation:
The tens digit is 1 less than the factor that is multiplied by 9. So, ten’s digit number is 10 – 1 = 9. The sum of the digits in the product is always 9. So, to multiply 10 × 9, think the tens digit is 9 and the one’s digit is 0. The product is 90.

Question 2.
2 × 9 = ________

18

Explanation:
9 = 3 + 6
2 × 9 = 2 x (3 + 6)
2 × 9 = (2 × 3) + (2 × 6)
2 × 9 = 6 + 12
2 × 9 = 18.

Question 3.
9 × 4 = ________

36

Explanation:
9 = 3 + 6
9 × 4 = (3 + 6) x 4
9 × 4 = (3 x 4) + (6 x 4)
9 × 4 = 12 + 24
9 × 4 = 36.

Question 4.
0 × 9 = ________

0

Explanation:

Multiplication of any number with 0 is 0. So, the answer for 0 x 9 is 0.

Question 5.
1 × 9 = ________

9

Explanation:

Multiplication of any number with 1 is the same number. So, 1 x 9 = 9.

Question 6.
8 × 9 = ________

72

Explanation:
9 = 3 + 6
8 × 9 = 8 x (3 + 6)
8 × 9 = (8 × 3) + (8 × 6)
8 × 9 = 24 + 48
8 × 9 = 72.

Question 7.
9 × 5 = ________

45

Explanation:
9 = 3 + 6
9 × 5 = (3 + 6) x 5
9 × 5 = (3 x 5) + (6 x 5)
9 × 5 = 15 + 30
9 × 5 = 45.

Question 8.
6 × 9 = ________

54

Explanation:
9 = 3 + 6
6 × 9 = 6 x (3 + 6)
6 × 9 = (6 × 3) + (6 × 6)
6 × 9 = 18 + 36
6 × 9 = 54.

Question 9.
9
× 4
——–
________

36

Explanation:
9 = 3 + 6
9 × 4 = (3 + 6) x 4
9 × 4 = (3 x 4) + (6 x 4)
9 × 4 = 12 + 24
9 × 4 = 36.

Question 10.
5
× 9
——–
________

45

Explanation:
9 = 3 + 6
5 × 9 = 5 x (3 + 6)
5 × 9 = (5 × 3) + (5 × 6)
5 × 9 = 15 + 30
5 × 9 = 45.

Question 11.
9
× 7
——–
________

63

Explanation:
9 = 3 + 6
9 × 7 = (3 + 6) x 7
9 × 7 = (3 x 7) + (6 x 7)
9 × 7 = 21 + 42
9 × 7 = 63.

Question 12.
2
× 9
——–
________

18

Explanation:
9 = 3 + 6
2 × 9 = 2 x (3 + 6)
2 × 9 = (2 × 3) + (2 × 6)
2 × 9 = 6 + 12
2 × 9 = 18.

Question 13.
9
× 9
——–
________

81

Explanation:
The tens digit is 1 less than the factor that is multiplied by 9. So, ten’s digit number is 9 – 1 = 8. The sum of the digits in the product is always 9. So, add 1 to 8 to get one’s digit 1 + 8 = 9. The product is 81.

Question 14.
10
× 9
——–
________

90

Explanation:
The tens digit is 1 less than the factor that is multiplied by 9. So, ten’s digit number is 10 – 1 = 9. The sum of the digits in the product is always 9. So, to multiply 10 × 9, think the tens digit is 9 and the one’s digit is 0. The product is 90.

Question 15.
3
× 9
——–
________

27

Explanation:
9 = 3 + 6
3 × 9 = 3 x (3 + 6)
3 × 9 = (3 × 3) + (3 × 6)
3 × 9 = 9 + 18
3 × 9 = 27.

Question 16.
9
× 8
——–
________

72

Explanation:
9 = 3 + 6
8 × 9 = 8 x (3 + 6)
8 × 9 = (8 × 3) + (8 × 6)
8 × 9 = 24 + 48
8 × 9 = 72.

Question 17.
6
× 9
——–
________

54

Explanation:
9 = 3 + 6
6 × 9 = 6 x (3 + 6)
6 × 9 = (6 × 3) + (6 × 6)
6 × 9 = 18 + 36
6 × 9 = 54.

Question 18.
9
× 1
——–
________

9

Explanation:
Multiplication of any number with 1 is the same number. So, 1 x 9 = 9.

Problem Solving

Question 19.
There are 9 positions on the softball team. Three people are trying out for each position. How many people in all are trying out?
___________ people

27

Explanation:
To find the total number of people trying for a position on the softball team, multiply 9 x 3. 9 x 3 = 27 people are trying for a softball team position.

Question 20.
Carlos bought a book for $9. Now he would like to buy 4 other books for the same price. How much will he have to pay in all for the other 4 books?$ _____________

$36 Explanation: Carlos bought a book for$9. Now he would like to buy 4 other books for the same price. So, to get them all 4 books, he needs to pay 4 x $9 =$36.

### Multiply with 9 Lesson Check Page No 246

Question 1.
Find the product.
7 × 9 = ■
Options:
a. 63
b. 56
c. 45
d. 36

a. 63

Explanation:
9 = 3 + 6
9 × 7 = (3 + 6) x 7
9 × 7 = (3 x 7) + (6 x 7)
9 × 7 = 21 + 42
9 × 7 = 63.

Question 2.
Clare buys 5 tickets for the high school musical. Each ticket costs $9. How much do the tickets cost in all? Options: a.$36
b. $40 c.$45
d. $52 Answer: c.$45

Explanation:
Multiply 5 with $9 to get the total number of tickets. Clare buys 5 tickets for 5 x$9 = $45. Spiral Review Question 3. The table shows the hair color of girls in Kim’s class. How many girls have brown hair? Options: a. 1 b. 3 c. 4 d. 6 Answer: d. 6 Explanation: From the given figure, there are 6 bars available in the Number of Girls for Brown. So, the answer is 6. Question 4. Miles picked up 9 shirts from the dry cleaners. It costs$4 to clean each shirt. How much did Miles spend to have all the shirts cleaned?
Options:
a. $13 b.$22
c. $36 d.$45

c. $36 Explanation: Miles spend 9 x$4 = $36 to have all the shirts cleaned. Question 5. In a picture graph, each picture of a baseball is equal to 5 games won by a team. The row for the Falcons has 7 baseballs. How many games have the Falcons won? Options: a. 40 b. 35 c. 12 d. 7 Answer: a. 63 Explanation: From given data, 1 baseball = 5 games. The row for the Falcons has 7 baseballs. So, Falcons won 7 x 5 = 35 games. Question 6. An array has 8 rows with 4 circles in each row. How many circles are in the array? Options: a. 12 b. 24 c. 32 d. 36 Answer: a. 63 Explanation: 8 x 4 = 32 circles are in the array. ### Multiplication Page No 251 Solve. Question 1. Henry has a new album for his baseball cards. He uses pages that hold 6 cards and pages that hold 3 cards. If Henry has 36 cards, how many different ways can he put them in his album? Henry can put the cards in his album 5 ways. Answer: 5 ways Explanation: Henry can put the cards in 5 ways. They are 1. (1 x 6 cards pages) x (10 x 3 cards pages) = 6 cards + 30 cards = 36 cards. 2. (2 x 6 cards pages) x (8 x 3 cards pages) = 12 cards + 24 cards = 36 cards. 3. (3 x 6 cards pages) x (6 x 3 cards pages) = 18 cards + 18 cards = 36 cards. 4. (4 x 6 cards pages) x (4 x 3 cards pages) = 24 cards + 12 cards = 36 cards. 5. (5 x 6 cards pages) x (2 x 3 cards pages) = 30 cards + 6 cards = 36 cards. Question 2. Ms. Hernandez has 17 tomato plants that she wants to plant in rows. She will put 2 plants in some rows and 1 plant in the others. How many different ways can she plant the tomato plants? Make a table to solve.  Rows With 2 Plants ___8__ ___7___ ____6__ ___5___ __4____ ____3__ _____2_ _____1_ Rows With 1 Plants ____1__ ___3___ ___5___ ___7___ ___9___ ____11__ ___13___ ____15__ Total Plants ____17__ ___17___ __17____ __17____ ___17___ ___17___ ____17__ ____17__ Ms. Hernandez can plant the tomato plants ___8___ Ways. Answer: 8 ways Explanation: Ms. Hernandez wants to grow 2 tomoto plants in one row and 1 in other row. The total number of plants should be 17. So, 1. (8 rows x 2 plants) x (1 row x 1plant) = 16 plants + 1 plant = 17 plants. 2. (7 rows x 2 plants) x (3 rows x 1plant) = 14 plants + 3 plant = 17 plantst. 3. (6 rows x 2 plants) x (5 rows x 1plant) = 12 plants + 5 plant = 17 plants. 4. (5 rows x 2 plants) x (7 rows x 1plant) = 10 plants + 7 plant = 17 plants. 5. (4 rows x 2 plants) x (9 rows x 1plant) = 8 plants + 9 plant = 17 plants. 6. (3 rows x 2 plants) x (11 rows x 1plant) = 6 plants + 11 plant = 17 plants. 7. (2 rows x 2 plants) x (13 rows x 1plant) = 4 plants + 13 plant = 17 plants. 8. (1 rows x 2 plants) x (15 rows x 1plant) = 2 plants + 15 plant = 17 plants. Question 3. Bianca has a total of 25¢. She has some nickels and pennies. How many different combinations of nickels and pennies could Bianca have? Make a table to solve.  Number of Nickels ___1___ ___2___ ____3__ ____4__ Number of Pennies ___20___ ___15___ ___10___ ____5__ Total Value ___25¢___ ___25¢___ ___25¢___ ___25¢___ Bianca could have ___4___ Combination of 25 ¢. Answer: 4 ways Explanation: 1 Nickel = 5 pennies. Bianca can have combinations of nickels and pennies to get 25¢ are 1. 1 Nickel + 20 Pennies = 5 Pennies + 20 Pennies = 25 Pennies = 25¢ 2. 2 Nickels + 15 Pennies = 10 Pennies + 15 Pennies = 25 Pennies = 25¢ 3. 3 Nickels + 10 Pennies = 15 Pennies + 10 Pennies = 25 Pennies = 25¢ 4. 4 Nickels + 5 Pennies = 20 Pennies + 5 Pennies = 25 Pennies = 25¢ ### Multiplication Lesson Check Page No 252 Question 1. The table shows different ways that Cameron can display his 12 model cars on shelves. How many shelves will display 2 cars if 8 of the shelves each display 1 car? Options: a. 1 b. 2 c. 3 d. 4 Question 1. Answer: b. 2 Explanation: 1. (Shelves with 1 car x 2) + (Shelves with 2 cars x 5) = 2 Cars + 10 Cars = 12 Cars 2. (Shelves with 1 car x 4) + (Shelves with 2 cars x 4) = 4 Cars + 8 Cars = 12 Cars 3. (Shelves with 1 car x 6) + (Shelves with 2 cars x 3) = 6 Cars + 6 Cars = 12 Cars 4. (Shelves with 1 car x 8) + (Shelves with 2 cars x 2) = 8 Cars + 4 Cars = 12 Cars 5. (Shelves with 1 car x 10) + (Shelves with 2 cars x 1) = 10 Cars + 2 Cars = 12 Cars Therefore, 2 shelves will display 2 cars if 8 of the shelves each display 1 car. Spiral Review Question 2. Find the sum. 3 1 7 + 1 5 1 ——– Options: a. 166 b. 268 c. 468 d. 568 Answer: c. 468 Explanation: Add the ones. Add 7 + 1 =8. Then, Add the tens. Add 1 + 5 = 6. Add the hundreds. Add 3 + 1 = 4. Place the one’s, ten’s and hundreds to get the sum. The sum is 468. Question 3. The school cafeteria has an order for 238 hot lunches. What is 238 rounded to the nearest ten? Options: a. 300 b. 240 c. 230 d. 200 Answer: b. 240 Explanation: The 238 lies between 230 and 240. But the 238 is closer to 240 than it is to 230. So, 238 is rounded to the 240. Go Math 3rd Grade Lesson 4.10 Homework Question 4. Tyler made a picture graph to show students’ favorite colors. This is the key to his graph. Each = 3 votes. If 12 students voted for green, how many should there be in the green row of the graph? Options: a. 3 b. 4 c. 9 d. 12 Answer: b. 4 Explanation: Each circle = 3 votes. If 12 students voted for green, total votes = 12. Write 12 = 3 + 3 + 3 +3. So, 4 circles represent 12 votes. Question 5. There are 5 bikes in each bike rack at the school. There are 6 bike racks. How many bikes in all are in the bike racks? Options: a. 11 b. 24 c. 25 d. 30 Answer: d. 30 Explanation: To find the total bikes in the bike rack at the school, multiply 5 bikes x 6 bike racks. 5 x 6 = 30 bikes are available in bike racks. ### Review/Test Page No 253 Question 1. Mrs. Ruiz sorted spools of thread into 4 boxes. Each box holds 5 spools. How many spools of thread does Mrs. Ruiz have? Draw circles to model the problem. Then solve. ________ spools Answer: 20 spools Explanation: 4 boxes of spools x 5 spools = 20 spools. Mrs. Ruiz has 20 spools of thread. Question 2. For numbers 2a–2d, select True or False for each multiplication sentence. a. 2 × 8 = 16 i. True ii. False Answer: i. True Explanation: Double 8. 8 + 8 = 16. So, 2 x 8 = 16. Question 2. b. 5 × 8 = 40 i. True ii. False Answer: i. True Explanation: Skip-count by 5’s 8 times. Write like 5, 10, 15, 20, 25, 30, 35, 40. So, the answer for 5 x 8 is 40. Question 2. c. 6 × 8 = 56 i. True ii. False Answer: ii. False Explanation: Use doubles to find the answer of 6 x 8. Firstly, multiply 3 x 8 = 24. Then, double the value of 3 x 8. 24 + 24 = 48. The answer for 6 x 8 is 48. So, 6 × 8 = 56 is false. Question 2. d. 8 × 8 = 64 i. True ii. False Answer: i. True Explanation: Factor 8 is an even number. 4+ 4 8 x 4 = 32. 32 doubled is 64. 8 x 8 = 64. Question 3. Bella is planning to write in a journal. Some pages will have one journal entry on them, and other pages will have two journal entries on them. If Bella wants to make 10 entries, how many different ways can she write them in her journal? ________ different ways Answer: 4 ways Explanation: 1. (1 journal entry x 2) + (2 journal entries x 4) = 2 journals + 8 journals = 10 journals. 2. (1 journal entry x 4) + (2 journal entries x 3) = 4 journals + 6 journals = 10 journals. 3. (1 journal entry x 6) + (2 journal entries x 2) = 6 journals + 4 journals = 10 journals. 4. (1 journal entry x 8) + (2 journal entries x 1) = 8 journals + 2 journals = 10 journals. Bella can use 4 ways to write journals. Question 4. There are 7 days in 1 week. How many days are there in 4 weeks? _______ days Answer: 28 days Explanation: 1 week = 1 x 7 = 7 days. 4 weeks = 4 x 7 = 28 days. ### Review/Test Page No 254 Question 5. Circle groups to show 3 × (2 × 3). Type below: __________ Answer: 18 Explanation: 3 × (2 × 3) = 3 x 6 = 18. Question 6. Dale keeps all of his pairs of shoes in his closet. Select the number of shoes that Dale could have in his closet. Mark all that apply. Options: a. 3 b. 4 c. 6 d. 7 e. 8 Answer: b. 4 c. 6 e. 8 Explanation: Pair of shoes have 2 in number. So, the possible ways are always even. Dale could have 4, 6, 8 in his closet. Question 7. Lisa completed the table to describe the product of a mystery one-digit factor and each number. Part A Give all of the possible numbers that could be Lisa’s mystery one-digit factor. Type below: __________ Answer: 0, 2, 4, 6, 8 Question 7. Part B Explain how you know that you have selected all of the correct possibilities. Type below: __________ Answer: Given that the product numbers are even. The product of an even number with another number is even. So, we should take the mystery factor as an even number. ### Review/Test Page No 255 Question 8. Kate drew 7 octagons. An octagon has 8 sides. How many sides did Kate draw? _________ sides Answer: 56 Explanation: Kate drew 7 octagons. An octagon has 8 sides. Kate draw 8 x 7 = 56 sides. Question 9. José buys 6 bags of flour. Each bag weighs 5 pounds. How many pounds of flour did José buy? _________ pounds Answer: 30 pounds Explanation: 6 x 5 = 30. José spends 30 pounds to buy flours. Question 10. Break apart the array to show 8 × 6 = (4 × 6) + (4 × 6). Answer: Explanation: Break the array of 4 columns and 6 rows to get the answer. Question 11. Circle the symbol that makes the multiplication sentence true. 9 × 6 3 × (3 × 9) _________ Answer: < Explanation: 9 x 6 = 54 3 x 27 = 81 54 < 81. So, 9 x 6 < 3 x (3 x 9) Question 12. Roberto wants to make$2.00 using dollars, half dollar, and quarters. How many different ways can he make $2.00? __________ different ways Answer: 18 Explanation: 0.25 – 8 |6 |4 |4 |2 |2 |0 |0 |0 0.50 – 0 |1 |2 |0 |3 |1 |2 |4 |0 1 -0 |0 |0 |1 |0 |1 |1 |0 |2 ### Review/Test Page No 256 Question 13. A carpenter builds stools that have 3 legs each. How many legs does the carpenter use to build 5 stools? Use the array to explain how you know your answer is correct. _________ legs Answer: 15 legs Explanation: Each stool has 3 legs. To build 5 stools, 5 x 3 = 15 legs. 15 legs need to build 5 stools. Question 14. Etta buys some ribbon and cuts it into 7 pieces that are the same length. Each piece is 9 inches long. How long was the ribbon that Etta bought? _________ inches Answer: 63 inches Explanation: The length of the ribbon is 7 x 9 inches = 63 inches. Question 15. Antoine and 3 friends divide some pennies evenly among themselves. Each friend separates his pennies into 3 equal stacks with 5 pennies in each stack. Write a multiplication sentence that shows the total number of pennies. Type below: _________ Answer: 4 x (5 x 3) Explanation: 5 pennies into 3 equal stacks = 5 x 3 = 15. 15 stacks shared between 4 friends = 4 x 15 = 4 x (5 x 3). Question 16. Luke is making 4 first-aid kits. He wants to put 3 large and 4 small bandages in each kit. How many bandages does he need for the kits? Show your work. _________ bandages Answer: 28 bandages Explanation: Luke wants to put 3 large and 4 small bandages in each kit. So, total = 3 + 4 = 7 bandages. He is making 4 first-aid kits. So, 4 x 7 bandages = 28 bandages. ### Review/Test Page No 257 Question 17. For numbers 17a–17d, select True or False for each equation. a. 3 × 7 = 21 i. True ii. False Answer: i. True Explanation: Skip count by 3’s until you say 7 numbers. 3, 6, 9, 12, 15, 18, 21. So, the answer for 3 x 7 is 21. The answer is true. Question 17. b. 5 × 7 = 28 i. True ii. False Answer: ii. False Explanation: Skip count by 5’s until you say 7 numbers. 5, 10, 15, 20, 25, 30, 35. Now, the count of the number is 7. So, the answer for 5 x 7 is 35. The answer is False. Question 17. c. 8 × 7 = 49 i. True ii. False Answer: ii. False Explanation: Use Distributive Property to find 8 x 7 = (4 + 4) x 7 = (4 x 7) + (4 x 7) = 28 + 28 = 56 is the correct answer. The answer is False. Question 17. d. 9 × 7 = 63 i. True ii. False Answer: i. True Explanation: 9 = 3 + 6 9 × 7 = (3 + 6) x 7 Multiply each addend by 7. 9 × 7 = (3 x 7) + (6 x 7) Add the products. 9 × 7 = 21 + 42 9 × 7 = 63. The answer is true. Question 18. Circle the number that makes the multiplication sentence true. 10 × = 40 Answer: 4 Explanation: The value of 10 x4 = 40. So, the answer is 4. Question 19. For numbers 19a–19d, select Yes or No to indicate whether the number sentence has the same value as 8 × 6. a. 8 + (4 × 2) = ■ i. yes ii. no Answer: ii. no Explanation: 8 x 6 = 48. 8 + (4 x 2) = 8 + 8 =16. The answer is no. Question 19. b. (8 × 4) + (8 × 2) = ■ i. yes ii. no Answer: i. yes Explanation: 8 x 6 = 48. (8 x 4) + (8 x 2) = 32 + 16 = 48. The answer is yes. Question 19. c. (6 × 4) + (6 × 2) = ■ i. yes ii. no Answer: ii. no Explanation: 8 x 6 = 48. (6 × 4) + (6 × 2) = 24 + 12 = 36. The answer is no. Question 19. d. 6 × (4 + 4) = ■ i. yes ii. no Answer: i. yes Explanation: 8 x 6 = 48. 6 × (4 + 4) = 6 x 8 = 48. The answer is yes. Question 20. Chloe bought 4 movie tickets. Each ticket cost$6. What was the total cost of the movie tickets?
$_________ Answer:$24

Explanation:
The total cost of the movie tickets = 4 x $6 =$24.

Question 21.
Write a multiplication sentence using the following numbers and symbols.

Type below:
__________

6 x (5 x 2) = 60

Explanation:
We can write as 6 x (5 x 2) = 60.

### Review/Test Page No 258

Question 22.
Louis started a table showing a multiplication pattern.
Part A
Complete the table. Describe a pattern you see in the products.

Type below:
__________

12, 15, 18, 21, 24, 27, 30. Add 3 to the product to get the next product.

Explanation:
Add 3 to the product to get the next product.
9+3 = 12.
12 + 3 = 15.
15 + 3 = 18.
18 + 3 = 21.
21 + 3 = 24.
24 + 3 = 27.
27 + 3 = 30.

Question 22.
Part B
If you multiplied 3 × 37, would the product be an even number or an odd number? Use the table to explain your reasoning.
__________

When an even number is multiplied by 3 (an odd number), the product is even. When an odd number is multiplied by 3, the product is odd, so the product of 3 × 37 would be odd.

Question 23.
Use the number line to show the product of 4 × 8.

4 × 8 = _______

32

Explanation:
Skip 2 numbers to get the product of 4 multiples. If you skip 2 numbers until you count 8, you can get 32. The answer is 32.

### Conclusion

Find Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies along with an explanation for each question. Get third-grade multiplication facts for better practice. All the questions and answers explained with images, graphs for easy understanding. Do all the activities and check your answers.

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Quickly get Go Math Grade 3 Answer Key and know the process of solving every multiplication to grab the knowledge. We support you with our Go Math Grade 3 Answer Key Chapter 4 Multiplication Facts and Strategies Extra Practice PDF every time.

## Two-Dimensional Figures Go Math Grade 4 Chapter 10 Answer Key Pdf

Lesson 1: Lines, Rays, and Angles

Lesson 2: Classify Triangles by Angles

Lesson 3: Parallel Lines and Perpendicular Lines

Mid-Chapter Checkpoint

Lesson 5: Line Symmetry

Lesson 6: Find and Draw Lines of Symmetry

Lesson 7: Problem Solving • Shape Patterns

Review/Test

### Common Core – New – Page No. 553

Lines, Rays, and Angles

Draw and label an example of the figure.

Question 1.
obtuse ∠ABC

Think: An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.
_________

Explanation:
An obtuse angle is greater than a right angle. The middle letter, B, names the vertex of the angle.

Question 2.
$$\overrightarrow{G H}$$
_________

Explanation:
GH is a ray that has one endpoint and continues without an end in one direction.

Question 3.
acute ∠JKL
_________

Explanation:
Angle JKL is an acute angle that is less than a right angle.

Lines Rays and Angles Lesson 10.1 Question 4.
$$\overline{B C}$$

Explanation:
BC is a line that continues without an end in both directions.

Use the figure for 5–8.

Question 5.
Name a line segment.

line segment EF

Explanation:

EF line is a straight path of points that continues without an end in both directions.

Question 6.
Name a right angle.
∠ _____

∠EJF

Explanation:
EJF is a right angle that forms a square corner.

Question 7.
Name an obtuse angle.
obtuse ∠ _____

∠CEJ

Explanation:
CEJ is an obtuse angle that is greater than a right angle.

Question 8.
Name a ray.

Ray JD

Explanation:
JD is a ray that has one endpoint and continues without an end in one direction.

Problem Solving

Use the figure at the right for 9–11.

Question 9.
Classify ∠AFD
_________

Obtuse Angle

Explanation:
AFD is an obtuse angle that is greater than a right angle.

Question 10.
Classify ∠CFE.
_________

Right Angle

Explanation:
∠CFE is a right angle that forms a square corner.

Question 11.
Name two acute angles.
acute ∠ _____ acute ∠ _____

∠AFB and ∠DFE

Explanation:
∠AFB and ∠DFE are two acute angles with less than a right angle.

### Common Core – New – Page No. 554

Lesson Check

Question 1.
The hands of a clock show the time 12:25.

Which best describes the angle between the hands of the clock?
Options:
a. acute
b. right
c. obtuse
d. straight

c. obtuse

Explanation:
The hands of the time 12:25 are forming greater than a right angle. So, the answer is the Obtuse angle.

Question 2.
Which of the following names two different figures?
Options:
a. $$\overline{A B} \text { and } \overline{B A}$$
b. $$\stackrel{\longleftrightarrow}{A B}$$ and $$\stackrel{\longleftrightarrow}{B A}$$
c. $$\overrightarrow{A B} \text { and } \overrightarrow{B A}$$
d. ∠ABC and ∠CBA

c. $$\overrightarrow{A B} \text { and } \overrightarrow{B A}$$

Explanation:
In $$\overrightarrow{A B}$$, A is an end point and B continues without end in one direction.
In $$\overrightarrow{B A}$$, B is an end point and A continues without an end in one direction.

Spiral Review

Question 3.
Jan’s pencil is 8.5 cm long. Ted’s pencil is longer. Which could be the length of Ted’s pencil?
Options:
a. 0.09 cm
b. 0.8 cm
c. 8.4 cm
d. 9.0 cm

d. 9.0 cm

Explanation:
9 ones is greater than 8 ones. So, 9.0 cm > 8.5 cm

Question 4.
Kayla buys a shirt for $8.19. She pays with a$10 bill. How much change should she receive?
Options:
a. $1.81 b.$1.89
c. $2.19 d.$2.81

a. $1.81 Explanation: Kayla buys a shirt for$8.19. She pays with a $10 bill. To find the change she received,$10 – \$8.19 = 1.81

Sasha donated $$\frac{9}{100}$$ of her class’s entire can collection for the food drive. Which decimal is equivalent to $$\frac{9}{100}$$ ?
Options:
a. 9
b. 0.99
c. 0.9
d. 0.09

d. 0.09

Explanation:
$$\frac{9}{100}$$ is 9 hundredths. So, the decimal is 0.09.

Question 6.
Jose jumped 8 $$\frac{1}{3}$$ feet. This was 2 $$\frac{2}{3}$$ feet farther than Lila jumped. How far did Lila jump?
Options:
a. 5 $$\frac{1}{3}$$
b. 5 $$\frac{2}{3}$$
c. 6 $$\frac{1}{3}$$
d. 11

b. 5 $$\frac{2}{3}$$

Explanation:
Jose jumped 8 $$\frac{1}{3}$$ feet. This was 2 $$\frac{2}{3}$$ feet farther than Lila jumped.
8 $$\frac{1}{3}$$ – 2 $$\frac{2}{3}$$ = $$\frac{25}{3}$$ – $$\frac{8}{3}$$ = $$\frac{7}{3}$$ = 5 $$\frac{2}{3}$$

### Page No. 557

Question 1.
Name the triangle. Tell whether each angle is acute, right, or obtuse.
A name for the triangle is __________ .

Name:
∠F is _________
∠G is _________
∠H is _________

Right Triangle; Triangle FGH;
∠F and ∠H are acute angles.
∠G is Right angle

Explanation:
∠F and ∠H are acute angles with less than a right angle. ∠G is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

Classify each triangle. Write acute, right, or obtuse.

Question 2.

_____

Obtuse triangle;
Angle B and Angle C are both acute.
Angle A is obtuse.

Explanation:
From triangle ABC, Angle B, and Angle C are both acute with less than a right angle. Angle A is obtuse angle that is greater than a right angle.

Question 3.

_____

Obtuse triangle;
Angle A and Angle C are both acute.
Angle B is obtuse.

Explanation:
From triangle ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle. A triangle with an obtuse angle is called an obtuse triangle.

Question 4.

_____

Acute triangle;
Angle A, Angle B, and Angle C are acute angles.

Explanation:
From triangle ABC, Angle A, Angle B, and Angle C are acute angles with less than a right angle. A triangle with three acute angles is called an acute triangle. So, the given triangle is an acute triangle.

Go Math Grade 4 Chapter 10 Lesson 10.2 Answer Key Question 5.

_____

Right Triangle; Triangle ABC;
∠A and ∠C are acute angles.
∠B is Right angle

Explanation:
∠A and ∠C are acute angles with less than a right angle. ∠B is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

Question 6.

_____

Acute triangle;
Angle A, Angle B, and Angle C are acute angles.

Explanation:
From triangle ABC, Angle A, Angle B, and Angle C are acute angles with less than a right angle. A triangle with three acute angles called an acute triangle. So, the given triangle is an acute triangle.

Question 7.

_____

Right Triangle;
∠A and ∠C are acute angles.
∠B is Right angle

Explanation:
∠A and ∠C are acute angles with less than a right angle. ∠B is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

Question 8.
Cross out the figure that does not belong. Explain.

Type below:
_________

Explanation:
From the given image, 1, 3, and 4 have two acute angles, and one obtuse angle. 2 have three acute angles.

### Page No. 558

Use the Venn diagram for 9–10.

Question 9.
Which triangles do NOT have an obtuse angle? Explain.
_______ triangles

4 triangles;
Triangle DEF, Triangle SPN, Triangle ABC, and Triangle GHP don’t have an obtuse angle. Triangle DEF, and Triangle SPN are acute angles. An acute triangle is a triangle with three acute angles. Triangle ABC and Triangle GHP are right angles. A right triangle is a triangle with one right angle. The sum of the triangle is 180 degrees. A right triangle has 90 degrees. So, the remaining angles must be acute angles.

Question 10.
How many triangles have at least two acute angles? Explain.
_______ triangles

4 triangles;
Triangle DEF, Triangle SPN, Triangle ABC, and Triangle GHP at least two acute angles. Triangle DEF, Triangle SPN are acute angles. An acute triangle is a triangle with three acute angles. Triangle ABC, and Triangle GHP are right angles. A right triangle is a triangle with one right angle and two acute angles.

Question 11.
Use the square shown at the right. Draw a line segment from point M to point P. Name and classify the triangles formed by the line segment.

Type below:
_________

Angle MNP and Angle MQP

Explanation:
The line segment from M to P forms Angle MNP and Angle MQP.

Classify Triangles by Angles Lesson 10.2 Question 12.
Write the letter of the triangle under its correct classification.

Type below:
_________

Explanation:
Triangle A and triangle B have three acute angles. So, they are acute triangles. Triangle D and triangle F have one obtuse angle. So, they are obtuse triangles.
Triangle C and triangle E have one right angle. So, they are right triangles.

### Common Core – New – Page No. 559

Classify Triangles

Classify each triangle. Write acute, right, or obtuse.

Question 1.

Think: Angles A and C are both acute.
Angle B is obtuse.

Obtuse triangle;
Angle A and Angle C are both acute.
Angle B is obtuse.

Explanation:
From triangle ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle.

Question 2.

_________

Right Triangle; Triangle DEF;
∠D and ∠F are acute angles.
∠E is Right angle

Explanation:
∠D and ∠F are acute angles with less than a right angle. ∠E is the Right angle that forms a square corner. A triangle that has one right angle is called a right triangle.

Question 3.

_________

Acute triangle;
Angle G, Angle J, and Angle H are acute angles.

Explanation:
From triangle GJH, Angle G, Angle J, and Angle H are acute angles with less than a right angle. A triangle with three acute angles called an acute triangle. So, the given triangle is an acute triangle.

Question 4.

_________

Obtuse triangle;
Angle L and Angle N are both acute.
Angle M is obtuse.

Explanation:
From triangle LMN, Angle L and Angle N are both acute with less than a right angle. Angle M is an obtuse angle that is greater than a right angle. A triangle with an obtuse angle is called an obtuse triangle.

Problem Solving

Question 5.
Use figure ABCD below. Draw a line segment from point B to point D. Name and classify the triangles formed.

Two _________ triangles
△ _________
△ _________

Two Acute triangles.
△ ABD
△ BCD

Explanation:
If we draw a line segment from point B to point D, then there are two triangles formed with less than right angles. They are △ ABD and △ BCD.

Go Math Book Grade 4 Chapter 10 Lesson 2 Answer Key Question 6.
Use figure ABCD below. Draw a line segment from point A to point C. Name and classify the triangles formed.

Two _________ triangles
△ _________
△ _________

Two Acute triangles.
△ ABC

Explanation:
If we draw a line segment from point A to point C, then there are two triangles formed with less than right angles. They are △ ABC and △ ADC.

### Common Core – New – Page No. 560

Lesson Check

Question 1.
Stephen drew this triangle. How many obtuse angles does the triangle have?

Options:
a. 0
b. 1
c. 2
d. 3

a. 0

Explanation:
The given image has three acute angles. So, there are 0 obtuse angles.

Question 2.
Joan was asked to draw a right triangle. How many right angles are in a right triangle?
Options:
a. 0
b. 1
c. 2
d. 3

b. 1

Explanation:
A right triangle has only one right angle.

Spiral Review

Question 3.
Oliver drew the figure below to show light traveling from the sun to Earth. Name the figure he drew.

Options:
a. segment SE
b. ray SE
c. line SE
d. ray ES

b. ray SE

Explanation:
SE is a ray that has one endpoint and continues without an end in one direction.

Question 4.
Armon added $$\frac{1}{10}$$ and $$\frac{8}{100}$$. Which is the correct sum?
Options:
a. $$\frac{18}{10}$$
b. $$\frac{9}{10}$$
c. $$\frac{9}{100}$$
d. $$\frac{18}{100}$$

d. $$\frac{18}{100}$$

Explanation:
$$\frac{1 X 10}{10 X 10}$$ + $$\frac{8}{100}$$ = $$\frac{10}{100}$$ + $$\frac{8}{100}$$ = $$\frac{18}{100}$$

Question 5.
Sam counted out loud by 6s. Jorge counted out loud by 8s. What are the first three numbers both students said?
Options:
a. 8, 16, 24
b. 14, 28, 42
c. 24, 48, 72
d. 48, 96, 144

c. 24, 48, 72

Explanation:
Sam counted out loud by 6s = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72.
Jorge counted out loud by 8s = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
Both students said the first three numbers are 24, 48, 72.

Question 6.
A basketball team averaged 105 points per game. How many points did the team score in 6 games?
Options:
a. 605 points
b. 630 points
c. 900 points
d. 6,030 points

b. 630 points

Explanation:
A basketball team averaged 105 points per game.
They score in 6 games = 6 x 105 = 630 points.

### Page No. 563

Question 1.
Draw and label $$\overline{Q R} \| \overline{S T}$$.
Think: Parallel lines never intersect. Parallel line segments are parts of parallel lines.
Type below:
_________

$$\overline{Q R} \| \overline{S T}$$

Explanation:
Parallel lines never intersect. Parallel line segments are parts of parallel lines.

Use the figure for 2 and 3.

Question 2.
Name two line segments that appear to be parallel.
Type below:
_________

Line Segment CB and Line Segment DF.

Explanation:
Line Segment CB and Line Segment DF are parallel lines. The both lines never intersect and are always the same distance apart.

Question 3.
Name two line segments that appear to be perpendicular.
Type below:
_________

Line Segment CB and Line Segment BF are perpendicular lines.

Explanation:
Line Segment CB and Line Segment DF are perpendicular lines. Both lines intersect to form four right angles.

Use the figure for 4–5.

Question 4.
Name a pair of lines that are perpendicular.
Type below:
_________

FJ and HG are perpendicular lines.

Explanation:
FJ and HG lines intersect each other and form four right angles.

Go Math Workbook Grade 4 Lesson 2.3 Two Dimensional Figures Question 5.
Name a pair of lines that appear to be parallel.
Type below:
_________

DC and FJ are parallel lines.

Explanation:
DC and FJ are never intersected and are always the same distance apart.

Question 6.
$$\overline{R S} \| \overline{T U}$$
Type below:
_________

$$\overline{R S} \| \overline{T U}$$

Explanation:
Parallel lines never intersect. Parallel line segments are parts of parallel lines.

Question 7.
$$\overrightarrow{K L} \text { and } \overrightarrow{K M}$$
Type below:
_________

Explanation:
KL and KM are two rays and start at the same point K.

Question 8.
$$\overline{C D} \perp \overline{D E}$$
Type below:
_________

$$\overline{C D} \perp \overline{D E}$$

Explanation:
$$\overline{C D} \perp \overline{D E}$$ are two lines. They are intersect each other and form four right angles.

Question 9.
$$\overset { \longleftrightarrow }{ JK }$$ ⊥ $$\overset { \longleftrightarrow }{ LM }$$
Type below:
_________

$$\overset { \longleftrightarrow }{ JK }$$ ⊥ $$\overset { \longleftrightarrow }{ LM }$$

Explanation:
JK and LM are two lines and intersected each other to form right angles.

Question 10.
$$\overset { \longleftrightarrow }{ ST }$$ intersecting $$\overset { \longleftrightarrow }{ UV }$$ at point X
Type below:
_________

Explanation:
ST and UV are two lines intersecting at point X.

Question 11.
$$\overset { \longleftrightarrow }{ AB }$$ || $$\overset { \longleftrightarrow }{ FG }$$
Type below:
_________

$$\overset { \longleftrightarrow }{ AB }$$ || $$\overset { \longleftrightarrow }{ FG }$$

Explanation:
Parallel lines never intersect. Parallel line segments are parts of parallel lines.

Use the figure for 12–13.

Question 12.
Dan says that $$\overset { \longleftrightarrow }{ HL }$$ is parallel to $$\overset { \longleftrightarrow }{ IM }$$. Is Dan correct? Explain.
_____

No; HL and IM are not parallel lines. Parallel lines are always the same distance apart. But from the given image, the H and I may intersect if the line is extended.

Question 13.
Name two intersecting line segments that are not perpendicular.
Type below:
_________

JM and KG are two intersecting line segments and also not perpendicular.

### Page No. 564

Use the house plan at the right for 14–16.

Question 14.
What geometric term describes a corner of the living room?
_________

The corner of the living room is a vertex. Corners of any shape are vertexes.

Question 15.
Name three parts of the plan that show line segments.
_________

Kitchen, Living Room, and Master Bedroom.

Question 16.
Name a pair of line segments that appear to be parallel
_________

Two sidelines of Living Room are parallel.
Two sidelines of Master Bedroom are parallel.

Use the map at the right for 17–19.

Question 17.
Name a street that appears to be parallel to S 17th Street.
_________

S 18th Street

Explanation:
S 18th Street is parallel to S 17th Street. They never meet each other and are always the same distance apart.

Question 18.
Use Diagrams Name a street that appears to be parallel to Vernon Street.
_________

Perry Street

Explanation:
Perry Street is parallel to Vernon Street. They never meet each other and are always the same distance apart.

Question 19.
Name a street that appears to be perpendicular to S 19th Street.
_________

Austin Street

Explanation:
Austin Street is perpendicular to S 19th Street. They intersect with each other and form four right angles.

Question 20.
Choose the labels to make a true statement.

Type below:
_________

Line AB is perpendicular to Line EF.

### Common Core – New – Page No. 565

Parallel Lines and Perpendicular Lines

Use the figure for 1–3.

Question 1.
Name a pair of lines that appear to be perpendicular.
Think: Perpendicular lines form right angles.
$$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$ appear to form right angles.
$$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$

$$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$

Explanation:
Perpendicular lines form right angles.
$$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$ appear to form right angles.
$$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ EF }$$

Question 2.
Name a pair of lines that appear to be parallel.
_____ and _____

$$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ CD}$$

Explanation:
Parallel lines never interest each other. $$\overset { \longleftrightarrow }{ AB }$$ and $$\overset { \longleftrightarrow }{ CD}$$ are parallel lines.

Question 3.
Name another pair of lines that appear to be perpendicular.
_____ and _____

$$\overset { \longleftrightarrow }{ CD }$$ and $$\overset { \longleftrightarrow }{ EF }$$

Explanation:
Perpendicular lines form right angles.
$$\overset { \longleftrightarrow }{ CD }$$ and $$\overset { \longleftrightarrow }{ EF }$$ appear to form right angles.
$$\overset { \longleftrightarrow }{ CD }$$ and $$\overset { \longleftrightarrow }{ EF }$$

Draw and label the figure described.

Question 4.
$$\overset { \longleftrightarrow }{ MN }$$ and $$\overset { \longleftrightarrow }{ PQ }$$ intersecting at point R

Explanation:
MN and PQ are two lines and interesting at point R.

Question 5.
$$\overset { \longleftrightarrow }{ WX }$$ || $$\overset { \longleftrightarrow }{ YZ }$$

Explanation:
WX and YZ are parallel lines and they never intersect with each other.

Question 6.
$$\overset { \longleftrightarrow }{ FH }$$ ⊥ $$\overset { \longleftrightarrow }{ JK }$$

Explanation:
FH and JK are two lines that intersect each other to form four right angles.

Problem Solving

Use the street map for 7–8.

Question 7.
Name two streets that intersect but do not appear to be perpendicular.
Type below:
_________

Maple and Oak or Oak and Birch

Explanation:
Maple and Oak or Oak and Birch; They intersect with each other and not perpendicular.

Question 8.
Name two streets that appear to be parallel to each other.
Type below:
_________

Maple and Birch

Explanation:
Maple and Birch are streets and not intersect with each other. They appear to be parallel to each other.

### Common Core – New – Page No. 566

Lesson Check

Question 1.
Which capital letter appears to have perpendicular line segments?
Options:
a. N
b. O
c. T
d. V

c. T

Explanation:
T has two lines and is interesting to form four right angles.

Question 2.
In the figure, which pair of line segments appear to be parallel?

Options:
a. $$\overline{F G} \text { and } \overline{G H}$$
b. $$\overline{F J} \text { and } \overline{G H}$$
c. $$\overline{F G} \text { and } \overline{J H}$$
d. $$\overline{J H} \text { and } \overline{F J}$$

c. $$\overline{F G} \text { and } \overline{J H}$$

Explanation:
$$\overline{F G} \text { and } \overline{J H}$$ are parallel lines that never intersect

Spiral Review

Question 3.
Nolan drew a right triangle. How many acute angles did he draw?
Options:
a. 0
b. 1
c. 2
d. 3

c. 2

Explanation:
A triangle with one right angle will have two acute angles.

Question 4.
Mike drank more than half the juice in his glass. What fraction of the juice could Mike have drunk?
Options:
a. $$\frac{1}{3}$$
b. $$\frac{2}{5}$$
c. $$\frac{3}{6}$$
d. $$\frac{5}{8}$$

d. $$\frac{5}{8}$$

Explanation:
Mike drank more than half the juice in his glass. He drunk $$\frac{5}{8}$$ of the juice.

Question 5.
A school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possible. How many pencils were left?
Options:
a. 2
b. 4
c. 6
d. 142

c. 6

Explanation:
A school principal ordered 1,000 pencils. He gave an equal number to each of 7 teachers until he had given out as many as possible. He shared 142 pencils for each of 7 teachers. So, 142 X 7 = 994. The remaining pencils are 6.

Question 6.
A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. How many ounces of juice did she buy?
Options:
a. 364 ounces
b. 370 ounces
c. 384 ounces
d. 402 ounces

c. 384 ounces

Explanation:
A carton of juice contains 64 ounces. Ms. Wilson bought 6 cartons of juice. 64 X 6 = 384 ounces juice she can buy.

### Page No. 569

Question 1.
Tell whether the quadrilateral is also a trapezoid, parallelogram, rhombus, rectangle, or square.

Think:
____ pairs of parallel sides
____ sides of equal length
____ right angles
Quadrilateral ABCD is also a __________
__________

2 pairs of parallel sides
4 sides of equal length
0 right angles.
Quadrilateral ABCD is also a Rhombus

Explanation:
A Rhombus is a quadrilateral that has 2 pairs of parallel sides and 4 sides of equal lengths.

Classify each figure in as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.

Question 2.

__________

Explanation:
0 pairs of parallel sides
0 sides of equal length
0 right angles.
The quadrilateral doesn’t have a name because it has 0 pairs of parallel sides, 0 sides of equal length, and 0 right angles.

Question 3.

_________
_________
_________

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
4 right angles.
Given quadrilateral is a Rectangle and Parallelogram.
A Rectangle is a quadrilateral that has 2 pairs of parallel sides 2 pairs of sides of equal lengths, and 4 right angles.

Go Math Grade 4 Chapter 10 Pdf Question 4.

_________
_________
_________

Explanation:
2 pairs of parallel sides
4 sides of equal length
0 right angles.
Given quadrilateral is Rhombus and Parallelogram.
A Rhombus is a quadrilateral that has 2 pairs of parallel sides 4 sides of equal lengths, and 0 right angles.

Question 5.

_________
_________

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
0 right angles.
A Parallelogram is a quadrilateral that has 2 pairs of parallel sides 2 pairs of sides of equal lengths, and 0 right angles.

Lesson 10.3 Parallel Lines and Perpendicular Lines Answer Key Question 6.

_________
_________
_________

Explanation:
2 pairs of parallel sides
4 sides of equal length
4 right angles.
A Square is a quadrilateral that has 2 pairs of parallel sides 4 sides of equal lengths, and 4 right angles.

Question 7.

_________
_________

Explanation:
1 pair of parallel sides
0 sides of equal length
0 right angles.
A Square is a quadrilateral that has 1 pair of parallel sides 0 sides of equal lengths, and 0 right angles.

### Page No. 570

Question 8.
Explain how a rhombus and a square are alike, and how they are different.
Type below:
_________

The rhombus and square have 2 pairs of parallel sides and 4 sides of equal length. But the rhombus has 0 right angles and the square has 4 right angles.

Question 9.
Classify the figure. Select all that apply.

Options:
b. trapezoid
c. parallelogram
d. rectangle
e. rhombus
f. square

b. trapezoid
c. parallelogram

Explanation:
A Parallelogram is a quadrilateral that has 2 pairs of parallel sides and 2 pairs of sides of equal lengths, and 0 right angles.

The Louvre Museum is located in Paris, France. Architect I. M. Pei designed the glass and metal structure at the main entrance of the museum. This structure is called the Louvre Pyramid. Below is a diagram of part of the entrance to the Louvre Pyramid.

Question 10.
Describe the quadrilaterals you see in the diagram.
_________
_________

Trapezoid and Rhombus

Explanation:
There are 2 quadrilaterals available in the given image. One is Trapezoid with 1 pair of parallel sides. Another one is Rhombus is with 2 pairs of parallel sides and 4 sides of equal lengths, and 0 right angles.

Question 11.
How many triangles do you see in the diagram? Explain.
______ triangles

11 triangles

Explanation:
The given image has 11 triangles

### Common Core – New – Page No. 571

Classify each figure as many ways as possible. Write quadrilateral, trapezoid, parallelogram, rhombus, rectangle, or square.

Question 1.

Think: 2 pairs of parallel sides
4 sides of equal length
0 right angles

Explanation:
2 pairs of parallel sides
4 sides of equal length
0 right angles

Question 2.

Type below:
_________

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
4 right angles

Question 3.

Type below:
_________

Explanation:
1 pair of parallel sides
2 sides of equal length
0 right angles

Question 4.

Type below:
_________

Explanation:
0 pair of parallel sides
0 sides of equal length
0 right angles

Question 5.

Type below:
_________

Explanation:
2 pairs of parallel sides
4 sides of equal length
0 right angles

Question 6.

Type below:
_________

Explanation:
1 pair of parallel sides
0 sides of equal length
2 right angles

Question 7.

Type below:
_________

Explanation:
2 pairs of parallel sides
2 pairs of sides of equal length
0 right angles

Problem Solving

Question 8.
Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. What figure did Alan draw
_________

Explanation:
Alan drew a polygon with four sides and four angles. All four sides are equal. None of the angles are right angles. Alan drew Quadrilateral or rhombus

Question 9.
Teresa drew a quadrilateral with 2 pairs of parallel sides and 4 right angles. What quadrilateral could she have drawn?
_________

square or rectangle

Explanation:
2 pairs of parallel sides and 4 right angles. she could draw a square or rectangle.

### Common Core – New – Page No. 572

Lesson Check

Question 1.
Joey is asked to name a quadrilateral that is also a rhombus. What should be his answer?
Options:
a. square
b. rectangle
c. parallelogram
d. trapezoid

a. square

Explanation:
The quadrilateral square is also called a rhombus. Both square and rhombus have 2 pairs of parallel sides and 4 sides of equal length.

Question 2.
Which quadrilateral has exactly one pair of parallel sides?
Options:
a. square
b. rhombus
c. parallelogram
d. trapezoid

d. trapezoid

Explanation:
A trapezoid has exactly one pair of parallel sides.

Spiral Review

Question 3.
Terrence has 24 eggs to divide into equal groups. What are all the possible numbers of eggs that Terence could put in each group?
Options:
a. 1, 2, 3, 4
b. 2, 4, 6, 8, 12
c. 1, 2, 3, 4, 6, 8, 12, 24
d. 24, 48, 72, 96

c. 1, 2, 3, 4, 6, 8, 12, 24

Explanation:
Terrence has 24 eggs to divide into equal groups. Terence could put in each group in 1, 2, 3, 4, 6, 8, 12, 24 ways.

Question 4.
In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7. What number
should Jenna say?
Options:
a. 31
b. 35
c. 39
d. 43

b. 35

Explanation:
In a line of students, Jenna is number 8. The teacher says that a rule for a number pattern is add 4. The first student in line says the first term, 7.
7 + 4 = 11
11 + 4 = 15
15 + 4 = 19
19 + 4 = 23
23 + 4 = 27
27 + 4 = 31
31 + 4 = 35.
Jenna says 35.

Question 5.
Lou eats $$\frac{6}{8}$$ of a pizza. What fraction of the pizza is left over?
Options:
a. $$\frac{1}{8}$$
b. $$\frac{1}{4}$$
c. $$\frac{1}{2}$$
d. $$\frac{3}{4}$$

b. $$\frac{1}{4}$$

Explanation:
Lou eats $$\frac{6}{8}$$ of a pizza. So, 6 parts of pizza is finished and remaining 2 parts of pizza is remained. So, the left over pizza is $$\frac{2}{8}$$ = $$\frac{1}{4}$$.

Question 6.
Which capital letter appears to have parallel lines?
Options:
a. D
b. L
c. N
d. T

c. N

Explanation:
N has two parallel lines and never intersect each other.

### Page No. 573

Choose the best term from the box to complete the sentence.

Question 1.
A _______ is part of a line between two endpoints.
_________

line segment

Question 2.
A _______ forms a square corner.
_________

Right angle

Question 3.
An _______ is greater than a right angle and less than a straight angle.
_________

Obtuse angle

Question 4.
The two-dimensional figure that has one endpoint is a ________.
_________

ray

Question 5.
An angle that forms a line is called a _______.
_________

straight line

Question 6.
On the grid below, draw a polygon that has 2 pairs of parallel sides, 2 pairs of sides equal in length, and 2 acute and 2 obtuse angles. Tell all the possible names for the figure.

Type below:
_________

Parallelogram

Explanation:
The possible polygon that has 2 pairs of parallel sides, 2 pairs of sides equal in length, and 2 acute and 2 obtuse angles is Parallelogram.

Draw the figure.

Question 7.
parallel lines
Type below:
_________

Explanation:
QR and ST are two parallel lines. they never intersect each other.

Question 8.
obtuse ∠ABC
Type below:
_________

Explanation:
From triangle, ABC, Angle A, and Angle C are both acute with less than a right angle. Angle B is an obtuse angle that is greater than a right angle.

Question 9.
intersecting lines that are not perpendicular
Type below:
_________

Explanation:
ST and UV are two lines intersecting at point X.

Question 10.
acute ∠RST
Type below:
_________

### Page No. 574

Question 11.
Which triangle has one right angle?
_________

A right triangle has one right angle.

Question 12.
Which figure has 2 pairs of parallel sides, 2 pairs of sides of equal length, and 4 right angles?
_________

A Rectangle has 2 pairs of parallel sides, 2 pairs of sides of equal length, and 4 right angles.

Question 13.
Which quadrilateral can have 2 pairs of parallel sides, all sides with equal length, and no right angles?
_________

Rhombus can have 2 pairs of parallel sides, all sides with equal length, and no right angles.

Question 14.
What is the correct name of the figure shown?

_________

Ray

Explanation:
EF is a ray that has one endpoint and continues without an end in one direction.

Question 15.
Describe the angles of an obtuse triangle.
Type below:
_________

An obtuse triangle (or obtuse-angled triangle) is a triangle with one obtuse angle (greater than 90°) and two acute angles.

### Page No. 577

Tell whether the parts on each side of the line match. Is the line a line of symmetry? Write yes or no.

Question 1.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 2.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 3.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 4.

____

No;

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape.

Tell if the blue line appears to be a line of symmetry. Write yes or no.

Question 5.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 6.

____

No;

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 7.

____

No;

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 8.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Tell if the blue line appears to be a line of symmetry. Write yes or no.

Question 9.

____

No;

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 10.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 11.

____

No;

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 12.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 13.
Which best describes the symmetry in the letter I?

Type below:
________

The two parts of the folded I match exactly. The fold line is a line of symmetry.

Explanation:
Take the Horizontal line in the middle of the Letter I. Cut out the tracing. Fold the tracing over a horizontal line. The two parts of the folded I match exactly. The fold line is a line of symmetry.

### Page No. 578

Question 14.
Which shape has a correctly drawn line of symmetry?

a. What do you need to find?
Type below:
________

Find the shape that has an exact line of symmetry.

Question 14.
b. How can you tell if the line of symmetry is correct?
Type below:
________

If the two parts of the folded match exactly, then the line is a line of symmetry.

Question 14.
c. Tell how you solved the problem.
Type below:
________

From fig 1 to 4, the fig 2 is has a line of symmetry that can exactly separate the two parts equally.

Question 14.
d. Circle the correct shape above.
Type below:
________

Question 15.
Reason Abstractly Draw a line of symmetry in the figure shown.

Question 16.
Evie’s birthday is on the 18th of May. Since May is the 5th month, Evie wrote the date as shown.

Evie says all the numbers she wrote have line symmetry. Is she correct? Explain.

No; The number 5 doesn’t have a line of symmetry. So, Evie explanation is wrong.

### Common Core – New – Page No. 579

Line Symmetry

Tell if the dashed line appears to be a line of symmetry. Write yes or no.

Question 1.

yes

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 2.

____

No;

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 3.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 4.

____

No;

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape.

____

No;

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 6.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Question 7.

____

No;

Explanation:
The line of symmetry divides a shape into two parts that are not with the same size and shape.

Question 8.

____

Yes;

Explanation:
The line of symmetry divides a shape into two parts that are the same size and shape.

Complete the design by reflecting over the line of symmetry.

Question 9.

Question 10.

Problem Solving

Question 11.
Kara uses the pattern below to make paper dolls. The dashed line represents a line of symmetry. A complete doll includes the reflection of the pattern over the line of symmetry. Complete the design to show what one of Kara’s paper dolls looks like.

### Common Core – New – Page No. 580

Lesson Check

Question 1.
Which best describes the line of symmetry in the letter D?

Options:
a. horizontal
b. vertical
c. diagonal
d. half turn

a. horizontal

Explanation:
The horizontal line of symmetry in the letter D can exactly separate two parts equally.

Question 2.
Which shape has a correctly drawn line of symmetry?
Options:
a.
b.
c.
d.

b.

Explanation:
Image b has the line of symmetry that separates two parts equally.

Spiral Review

Question 3.
The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. How many unit cubes will each group get?
Options:
a. 40
b. 44
c. 45
d. 48

c. 45

Explanation:
The class has 360 unit cubes in a bag. Johnnie divides the unit cubes equally among 8 groups. 360/8= 45.

Question 4.
There are 5,280 feet in one mile. How many feet are there in 6 miles?
Options:
a. 30,680
b. 31,260
c. 31,608
d. 31,680

d. 31,680

Explanation:
There are 5,280 feet in one mile. So, for 6 miles = 6 x 5, 280 = 31,680.

Question 5.
Sue has 4 pieces of wood. The lengths of her pieces of wood are $$\frac{1}{3}$$ foot, $$\frac{2}{5}$$ foot, $$\frac{3}{10}$$ foot, and $$\frac{1}{4}$$ foot. Which piece of wood is the shortest?
Options:
a. the $$\frac{1}{3}$$ foot piece
b. the $$\frac{2}{5}$$ foot piece
c. the $$\frac{3}{10}$$ foot piece
d. the $$\frac{1}{4}$$ foot piece

d. the $$\frac{1}{4}$$ foot piece

Explanation:
The lengths of $$\frac{1}{4}$$ foot piece is less compared to other lengths.

Question 6.
Alice has $$\frac{1}{5}$$ as many miniature cars as Sylvester has. Sylvester has 35 miniature cars. How many miniature cars does Alice have?
Options:
a. 7
b. 9
c. 40
d. 175

a. 7

Explanation:
Alice has $$\frac{1}{5}$$ as many miniature cars as Sylvester has. Sylvester has 35 miniature cars. Alice have $$\frac{1}{5}$$ X 35 = 7 miniature cars.

### Page No. 583

Question 1.
The shape at the right has line symmetry. Draw the 2 lines of symmetry.

Type below:
_________

Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1.

Question 2.

_________

more than 1

Explanation:

There is more than 1 line of symmetries that separates two parts equally.

Question 3.

_________

more than 1

Explanation:

There is more than 1 lines of symmetries that separates two parts equally.

Question 4.

_________

1 line

Explanation:

There is 1 line of symmetry that separates two parts equally.

Find and Draw Lines of Symmetry Lesson 10.6 Question 5.

_________

zero lines

Explanation:
There is no line of symmetries that separates two parts equally.

Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1.

Question 6.

_________

more than 1

Explanation:

There is more than 1 line of symmetries that separates two parts equally.

Question 7.

_________

zero lines

Explanation:
There is no line of symmetry that separates two parts equally.

Question 8.

_________

zero lines

Explanation:
There is no line of symmetry that separates two parts equally.

Question 9.

_________

1 line

Explanation:

There is 1 line of symmetry that separates two parts equally.

Practice: Copy and Solve Does the design have line symmetry?
Write yes or no. If your answer is yes, draw all lines of symmetry.

Question 10.

____

Yes;

Question 11.

_____

No;

Question 12.

_____

Yes;

Question 13.

_____

No;

Question 14.
Draw a figure that has 5 sides and exactly 1 line of symmetry.
Type below:
_________

Explanation:
the above 5 sides shape has only 1 line symmetry

### Page No. 584

Use the chart for 15–17.

Question 15.
Which letters appear to have only 1 line of symmetry?
Type below:
_________

A, B, C, D, E, T, U, V, W

Explanation:
The letters A, B, C, D, E, T, U, V, W have only 1 line of symmetry.

Question 16.
Which letters appear to have zero lines of symmetry?
Type below:
_________

J, N, S

Explanation:
The letters J, N, S have only zero lines of symmetry.

Question 17.
The letter C has horizontal symmetry. The letter A has vertical symmetry. Which letters appear to have both horizontal and vertical symmetry?
Type below:
_________

H and I

Explanation:
The letters H and I have both horizontal and vertical symmetry.

Question 18.
Verify the Reasoning of Others Jeff says that the shape has only 2 lines of symmetry.
Does his statement make sense? Explain.

Type below:
_________

No; Jeff’s explanation is wrong. Because the given shape has only 2 lines of symmetry.

Question 19.
Match each figure with the correct number of lines of symmetry it has.

Type below:
_________

### Common Core – New – Page No. 585

Find and Draw Lines of Symmetry

Tell whether the shape appears to have zero lines, 1 line, or more than 1 line of symmetry. Write zero, 1, or more than 1.

Question 1.

1

more than 1

Explanation:
There is more than 1 line of symmetry that separates two parts equally.

Question 2.

________

more than 1

Explanation:
There is more than 1 line of symmetry that separates two parts equally.

Question 3.

________

Zero

Explanation:
There are 0 lines of symmetries.

Question 4.

________

more than 1

Explanation:

There is more than 1 line of symmetry that separates two parts equally.

Does the design have line symmetry? Write yes or no.

Question 5.

_____

Yes;

Question 6.

_____

Yes;

_____

No;

Question 8.

______

Yes;

Draw a shape for the statement. Draw the line or lines of symmetry.

Question 9.
zero lines of symmetry

Question 10.
1 line of symmetry

Question 11.
2 lines of symmetry

Problem Solving

Use the chart for 12–13.

Question 12.
Which number or numbers appear to have only 1 line of symmetry?
_____

3

Explanation:
The number 3 has only 1 line of symmetry.

Question 13.
Which number or numbers appear to have 2 lines of symmetry?
_____

0 and 8

Explanation:
The numbers 0 and 8 appear to have 2 lines of symmetry.

### Common Core – New – Page No. 586

Lesson Check

Question 1.
How many lines of symmetry does this shape appear to have?

Options:
a. 0
b. 2
c. 6
d. 12

c. 6

Explanation:

The given shape has 6 lines of symmetries.

Question 2.
Which of the following shapes appears to have exactly 1 line of symmetry?
Options:
a.
b.
c.
d.

d.

Explanation:

The trapezoid has exactly 1 line of symmetry.

Spiral Review

Question 3.
Richard practiced each of 3 piano solos for $$\frac{5}{12}$$ hour. How long did he practice in all?
Options:
a. $$\frac{2}{3}$$ hours
b. 1 $$\frac{1}{4}$$ hours
c. 1 $$\frac{1}{3}$$ hours
d. 1 $$\frac{5}{12}$$ hours

b. 1 $$\frac{1}{4}$$ hours

Explanation:
Richard practiced each of 3 piano solos for $$\frac{5}{12}$$ hour. $$\frac{5}{12}$$ hour = 1 $$\frac{1}{4}$$ hours hours.

Question 4.
Which of the following decimals is equivalent to three and ten hundredths?
Options:
a. 0.30
b. 0.31
c. 3.01
d. 3.1

d. 3.1

Explanation:
three and ten hundredths = 310 hundredths = 3.1

Go Math 4th Grade Chapter 10 Review Test Answer Key Question 5.
Lynne used $$\frac{3}{8}$$ cup of flour and $$\frac{1}{3}$$ cup of sugar in a recipe. Which number below is a common denominator for $$\frac{3}{8}$$ and $$\frac{1}{3}$$?
Options:
a. 8
b. 12
c. 16
d. 24

d. 24

Explanation:
Lynne used $$\frac{3}{8}$$ cup of flour and $$\frac{1}{3}$$ cup of sugar in a recipe. To find the common denominator for $$\frac{3}{8}$$ and $$\frac{1}{3}$$, multiply 8 X3 and 3 X 8 = 24.

Question 6.
Kevin draws a figure that has four sides. All sides have the same length. His figure has no right angles. What figure does Kevin draw?
Options:
a. square
b. trapezoid
c. rhombus
d. rectangle

c. rhombus

Explanation:

### Page No. 589

Question 1.
Marisol is making a pattern with blocks. What might the missing shape be?
First, look at the blocks.

Next, describe the pattern.
Type below:
_________

The first image 1 has three line segments. The next shape will have four line segments.

Question 1.
Finally, draw the missing shape.

Type below:
_________

Question 2.
Use the shapes to write a number pattern. Then describe the pattern in the numbers.

Shape 1: Triangle
Shape 2: Square
Shape 3: Pentagon
Shape 4: Hexagon
Shape 5: Heptagon

Question 3.
What if the pattern continued? Write an expression to describe the number of sides the sixth shape has in Marisol’s pattern.
Type below:
_________

If the pattern continued, then the next shape will have one more extra line segment to it. The sixth shape will become the octagon.
Shape 6: Octagon

Question 4.
Sahil made a pattern using circles. The first nine circles are shown. Describe the pattern. If Sahil continues the pattern, what might the next three circles be?

Type below:
_________

The pattern is repeated for every three circles. One big circle followed by two small circles.

### Page No. 590

Use the toy quilt designs for 5–6.

Question 5.
Lu is making a quilt that is 20 squares wide and has 24 rows. The border of the quilt is made by using each toy design equally as often. Each square can hold one design. How many of each design does she use for the border?
______ times

The border will have 20 squares two times, and 24 squares two times as well, that is the perimeter or the border, because a quilt has 4 sides:
20 X 2 + 24 X 2 = 40 + 48 = 88
So, the border will have 88 squares in total. So if the border can have only one design, Lu can use any toy design 88 times if she wants the border to have the same toy design in it.

Question 6.
Communicate Starting in the first square of her quilt, Lu lined up her toy designs in this order: plane, car, fire truck, helicopter, crane, and wagon. Using this pattern unit, which design will Lu place in the fifteenth square? Explain how you found your answer.
_________

The answer is fire truck. As the pattern repeats, the fifteenth square will fire truck.

Question 7.
Missy uses 1 hexagonal, 2 rectangular, and 4 triangular pieces of fabric to make 1 bug design for a quilt. If she uses 70 pieces in all to make bug designs, how many of each shape does she use?
Hexagonal: _________ shapes
Rectangular: _________ shapes
Triangular: _________ shapes

Hexagonal: 10 shapes
Rectangular: 10 shapes
Triangular: 10 shapes
(1 x 10) + (2 x 10) + (4 x 10) = 10 + 20 + 40 = 70 pieces in all.

Question 8.
Norris drew the pattern shown.

Label the circles to show the colors in the fourth figure of the pattern.
Type below:
_________

### Common Core – New – Page No. 591

Problem Solving Shape Patterns

Solve each Problem.

Question 1.
Marta is using this pattern to decorate a picture frame. Describe the pattern. Draw what might be the next three figures in the pattern.

Possible answer: the pattern repeats: one trangle followed by two squares.

The pattern repeats one triangle followed by two squares.

Question 2.
Describe the pattern. Draw what might be the next three figures in the pattern. How many circles are in the sixth figure in the pattern?

_____ circles

Add one more column with 1 more circle than in the previous column; 21.

Question 3.
Larry stencils this pattern to make a border at the top of his bedroom walls. Describe the pattern. Draw what might be the missing figure in the pattern.

2 triangles placed side to side followed by 2 sets of 2 triangles placed vertex to vertex

### Common Core – New – Page No. 592

Lesson Check

Question 1.
What might be the next three figures in this pattern?

Options:
a.
b.
c.
d.

a.

Explanation:
the pattern has odd numbers of up arrows then even number of down arrows. So, the next three figures are .

Question 2.
Which might be the missing figure in the following pattern?

Options:
a.
b.
c.
d.

a.

Explanation:
From the pattern, the missing image will have vertical rectangle with the circle and X mark in it.

Spiral Review

Question 3.
Chad has two pieces of wood. One piece is $$\frac{7}{12}$$ foot long. The second piece is $$\frac{5}{12}$$ foot longer than the first piece. How long is the second piece?
Options:
a. $$\frac{2}{12}$$ foot
b. $$\frac{1}{2}$$ foot
c. $$\frac{12}{18}$$ foot
d. 1 foot

d. 1 foot

Explanation:
$$\frac{7}{12}$$ + $$\frac{5}{12}$$ = $$\frac{12}{12}$$ = 1 foot.

Question 4.
Olivia finished a race in 40.64 seconds. Patty finished the race in 40.39 seconds. Miguel finished the race in 41.44 seconds. Chad finished the race in 40.46 seconds. Who finished the race in the least time?
Options:
a. Olivia
b. Patty
c. Miguel

b. Patty

Explanation:
Patty finished the race in 40.39 seconds that is the least time compared to others.

Question 5.
Justin bought 6 ribbons for an art project. Each ribbon is $$\frac{1}{4}$$ yard long. How many yards of ribbon did Justin buy?
Options:
a. $$\frac{2}{3}$$ yard
b. 1 $$\frac{1}{4}$$ yards
c. 1 $$\frac{1}{2}$$ yards
d. 1 $$\frac{3}{4}$$ yards

c. 1 $$\frac{1}{2}$$ yards

Explanation:
Justin bought 6 ribbons for an art project. Each ribbon is $$\frac{1}{4}$$ yard long. So, 6 X $$\frac{1}{4}$$ = $$\frac{3}{2}$$ = 1 $$\frac{1}{2}$$ yards.

Question 6.
Kyle and Andrea were asked to make a list of prime numbers.
Kyle: 1, 3, 7, 19, 23
Andrea: 2, 3, 5, 7, 11
Whose list is correct?
Options:
a. Only Kyle’s list
b. Only Andrea’s list
c. Both lists are correct.
d. Neither list is correct.

b. Only Andrea’s list

Explanation:
1 is not a prime number. So, the answer is Only Andrea’s list is correct.

### Page No. 593

Question 1.
Gavin is designing a kite. He sketched a picture of the kite.
How many right angles does the kite appear to have?

_____ right angles

0 right angles

Explanation:
There is no right angles in the given shape.

Question 2.
Write the letter of the triangle under its correct classification.

Explanation:
C and F are Acute angles with less than right angles.
B and D are Obtuse Angles with more than right angles.
A and E are Right Angles.

Question 3.
Select the angles that identify an obtuse triangle. Mark all that apply.
Options:
a. acute, acute, acute
b. acute, acute, obtuse
c. right, acute, acute
d. obtuse, right, acute

b. acute, acute, obtuse

Explanation:
An obtuse triangle will have one obtuse angle and two acute angles.

### Page No. 594

Question 4.
Write the word that describes the part of Figure A written below.

$$\overline{E B}$$ _________
$$\overset { \longleftrightarrow }{ AB }$$ _________
$$\overrightarrow{G A}$$ _________
∠EBG _________
∠CGB _________

$$\overline{E B}$$ line segment.
$$\overset { \longleftrightarrow }{ AB }$$ Line.
$$\overrightarrow{G A}$$ Ray.
∠EBG right angle.
∠CGB acute angle.

Explanation:
$$\overline{E B}$$ is a line segment that has two endpoints connected to form a line.
$$\overset { \longleftrightarrow }{ AB }$$ is a Line that continues without an end in both directions.
$$\overrightarrow{G A}$$ is a Ray that has one endpoint and continues without an end in one direction.
∠EBG right angle.
∠CGB is an acute angle with less than the right angle.

Question 5.
What term best describes the figure shown below?

perpendicular lines

Explanation:
The lines are forming four right angles they form squares. So, the both lines are perpendicular lines.

Question 6.
Naomi leaves for her trip to Los Angeles on the 12th day of August. Since August is the 8th month, Naomi wrote the date as shown.

Naomi says all the numbers she wrote have line symmetry. Is she correct? Explain your thinking.
_______

Naomi is incorrect. The number 2 does not have a line of symmetry because if it were cut out, there would be no way to fold it in half so that the two parts matched exactly.

### Page No. 595

Question 7.
Max made a pennant that looks like a triangle. How can you classify the triangle based upon its angles?

The triangle is a(n) ____________ triangle.

The triangle is an acute triangle.

Explanation:
The triangle is an acute triangle.  because it has angles with less than right angles.

Question 8.
Choose the labels to make a true statement.

_____ is parallel to ______

Line AB is parallel to line CD.

Explanation:
From the given image, Line AB is parallel to line CD.

Question 9.
Classify the figure. Select all that apply.

Options:
b. trapezoid
c. parallelogram
d. rectangle
e. rhombus
f. square

b. trapezoid
c. parallelogram
d. rectangle

Explanation:
The given image has 2 parallel sides, 2 pairs of sides of length, and four right angles. So, the possible answers are quadrilateral, trapezoid, parallelogram, and rectangle.

Question 10.
Lily designed a deck in her backyard that looks like a quadrilateral that has only 1 pair of parallel sides. How can you classify the figure?

Explanation:
Lily designed a deck in her backyard that looks like a quadrilateral that has only 1 pair of parallel sides. So, the answer is a trapezoid.

### Page No. 596

Question 11.
Match each figure with the correct number of lines of symmetry it has.

Explanation:
Image 1: 1 line of symmetry
Image 2: 2 lines of symmetry
Image 3: 0 lines of symmetry
Image 4: More than 2 lines of symmetry.

Question 12.
Barb drew the pattern shown.

Use the square shown to draw the missing pattern. □

Explanation:
The fourth shape must consist of one extra square box in the top line and bottom line.

Question 13.
Claudia drew the figure below. Draw a line of symmetry on Claudia’s figure.

Explanation:
The image can have one line symmetry.

Question 14.
Write the word or words that best describe this figure.

_________

Ray

Explanation:
The ray that has one endpoint and continues without an end in one direction.

Question 15.
How many acute angles does a right triangle have?
A right triangle has ____ acute angles.

A right triangle has 2 acute angles.

### Page No. 597

Question 16.
Mike drew a figure with opposite sides parallel. Write the pairs of parallel sides. What figure is it?

Line DG is parallel to Line FE and Line DE is parallel to Line GF; the figure is a parallelogram.

Question 17.
Circle the letter that does not have line symmetry.

Explanation:
The S does not have line symmetry.

Question 18.
Joseph made a pattern using ovals and rectangles. The first four figures of his pattern are shown. Draw the next figure in the pattern.

Question 19.
Jeremy drew Figure 1 and Louisa drew Figure 2.

Part A
Jeremy says both figures are rectangles. Do you agree with Jeremy?
_____

Yes; both figures have 2 pairs of parallel sides, opposite sides that are equal in length, and 4 right angles.

Question 19.
Part B
Louisa says both figures are rhombuses. Do you agree with Louisa?
_____

No; figure 2 is a rhombus since it has 2 pairs of parallel sides and 4 sides of equal length. Figure 1 does not have 4 sides of equal length so it cannot be a rhombus.

### Page No. 598

Question 20.
Veronica found the number of lines of symmetry for the figure below. How many lines of symmetry does it have?

______ lines of symmetry

2 lines of symmetry

Explanation:
the given shape can have 2 lines of symmetry.

Question 21.
Jordan drew the pattern below.

Part A
Describe the pattern.

Each figure has 2 more squares than the preceding figure.

Question 21.
Part B
Write a rule using numbers to find the number of squares in any figure in the pattern.

multiply the figure number by 2.

Question 21.
Part C
Draw Figure 5.

### Page No. 603

Tell what fraction of the circle the shaded angle represents.

Question 1.

$$\frac{□}{□}$$

$$\frac{1}{2}$$

Explanation:
Half of the part is shaded out of the circle. So, the answer is 1/2.

Question 2.

$$\frac{□}{□}$$

$$\frac{1}{4}$$

Explanation:
$$\frac{1}{4}$$ part of the circle is shaded out of the circle.

Question 3.

$$\frac{□}{□}$$

$$\frac{3}{4}$$

Explanation:
3 parts of the circle is shaded out of the circle

Question 4.

$$\frac{□}{□}$$

$$\frac{1}{1}$$ = 1

Explanation:

Question 5.

$$\frac{□}{□}$$

$$\frac{1}{2}$$

Explanation:
Half of the part is shaded out of the circle. So, the answer is 1/2.

Question 6.

$$\frac{□}{□}$$

$$\frac{1}{12}$$

Tell whether the angle on the circle shows a $$\frac{1}{4}, \frac{1}{2}, \frac{3}{4}$$, or 1 full turn clockwise or counterclockwise.

Question 7.

Type below:
________

$$\frac{3}{4}$$; counterclockwise

Explanation:
The image shows the counterclockwise and formed the fraction of $$\frac{3}{4}$$.

Question 8.

Type below:
________

$$\frac{1}{2}$$; clockwise

Explanation:
The image shows the clockwise and formed the fraction of $$\frac{1}{2}$$.

Question 9.

Type below:
________

$$\frac{1}{4}$$; clockwise

Explanation:
The image shows the clockwise and formed the fraction of $$\frac{1}{4}$$.

Question 10.
Susan watched the game from 1 p.m. to 1:30 p.m. Describe the turn the minute hand made.

Type below:
________

The minute hand made a $$\frac{1}{2}$$ turn clockwise.

Question 11.
Compare the angles in Exercises 1 and 5. Does the position of the angle affect the size of the angle? Explain.
_____

No; The size of the angle does not depend on the lengths of its sides.

### Page No. 604

Question 12.
Malcolm drew this angle on the circle. Which of the following describes the angle? Mark all that apply.

Options:
a. $$\frac{3}{4}$$ turn
b. $$\frac{1}{4}$$ turn
c. clockwise
d. counterclockwise

a. $$\frac{3}{4}$$ turn
d. counterclockwise

Explanation:
The image show the $$\frac{3}{4}$$ turn and also the counterclockwise.

Sense or Nonsense?

Question 13.
Whose statement makes sense? Whose statement is nonsense? Explain your reasoning.

Type below:
__________

The girl’s statement makes sense. The boy’s statement makes non-sense. Because from the figure it is clearly shown that the shaded part is $$\frac{1}{4}$$ of the circle. There is no particular direction given to measure the shaded part.