# Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns

Go Math Grade 4 Answer Key Contains Factors, Common factors, Divisibilities and Review tests, etc. Which helps students for solving assignments and also for preparing in exams. In this chapter each and every question was explained in a simple way by which students can understand easily. Go Math Grade 4 Answer Key explains each question in a unique and simple way by that students can easily understand the solution.

## Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns

This Go Math Grade 4 Answer Key Chapter 5 Factors, Multiples, and Patterns have Grade 4 solutions that can be understood by anyone. Students, teachers can feel comfortable by this Go Math Grade 4 Answer Key as every question was solved in a simple way. By that students will not face any difficulty in understanding the solution.

### Common Core – Model Factors – Page No. 283

Model Factors

Use tiles to find all the factors of the product.

Record the arrays on grid paper and write the factors shown.

Question 1.

Question 2.
Write the factors of: 30

The Factors Of 30 are: 1,2,3,5,6,10,15,30.

Explanation:
Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 30 when multiplied together.So the factors of 30 are 1,2,3.5,6,10,15,30.

1×30=30
2×15=30
3×10=30
5×6=30
6×5=30
10×3=30
15×2=30
30×1=30

Question 3.
Write the factors of: 45

Answer: The Factors Of 45 are:1,3,5,9,15,45.

Explanation:
Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 45 when multiplied together.So the factors of 45 are:1,3,5,9,15,45.

1×45=45
3×15=45
5×9=45
9×5=45
15×3=45
45×1=45

Question 4.
Write the factors of: 19

Answer: The Factors Of 19 are:1,19.

Explanation:
Since 19 is a Prime number that means it is divisible by 1 and itself. So the factors of  19 are 1,19.

1×19=19
19×1=19.

Question 5.
Write the factors of: 40

Answer: The Factors Of 40 are:1,2,4,5,8,10,20,40.

Explanation:Factors are the numbers which divides the original number completely. The Factors Of 40 are:1,2,4,5,8,10,20,40.

1×40=40
2×20=40
4×10=40
5×8=40
8×5=40
10×4=40
20×2=40
40×1=40

Question 6.
Write the factors of: 36

Answer: The Factors Of 36 are:1,2,3,4,6,9,12,18,36.

Explanation:
Factors are the numbers which divides the original number completely. The factors of 36 are:1,2,3,4,6,9,12,18,36.

1×36=36
2×18=36
3×12=36
4×9=36
6×6=36
9×4=36
12×3=36
18×3=36
36×1=36.

Question 7.
Write the factors of: 22

Answer: The Factors Of 22 are:1,2,11,22.

Explanation:
Factors are the numbers which divides the original number completely. The factors of 22 are:1,2,11,22.

1×22=22
2×11=22
11×2=22
22×1=22.

Question 8.
Write the factors of: 4

Answer: The Factors Of 4 are:1,2,4.

Explanation:
Factors are the numbers which divides the original number completely. The Factors Of 4 are:1,2,4.

1×4=4
2×2=4
4×1=4.

Question 9.
Write the factors of: 26

Answer: The Factors Of 26 are:1,2,13,26.

Explanation:
Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 26 when multiplied together.So the factors of 26 are:1,2,13,26.

1×26=26
2×13=26
13×2=26
26×1=26.

Question 10.
Write the factors of: 49

Answer: The Factors Of 49 are:1,7,49.

Explanation:
Factors are the numbers which divides the original number completely. The Factors Of 49 are:1,7,49.

1×49=49
7×7=49
49×1=49.

Question 11.
Write the factors of: 32

Answer: The Factors Of 32 are:1,2,4,8,16,32.

Explanation:
Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 32 when multiplied together.So the factors of 32 are:1,2,4,8,16,32.

1×32=32
2×16=32
4×8=32
8×4=32
16×2=32
32×1=32.

Question 12.
Write the factors of 23

Answer: The Factors Of 23 are:1,23.

Explanation:
Since 23 is a Prime number that means it is divisible by 1 and itself. So the factors of  23 are 1,23.

1×23=23
23×1=23.

Question 13.
Brooke has to set up 70 chairs in equal rows for the class talent show. But, there is not room for more than 20 rows. What are the possible number of rows that Brooke could set up?

Explanation:
Let the possible no.of rows be X, As there is no room for more than 20 rows so there should not be more than 20 rows.X should be less than or equal to 20(X<=20). As Brooke has 70 chairs to set up in equal rows we will find the factors of 70 and in that we must pick up the numbers which are less than equal to 20.Therefore the factors of 70 are 2,5,7,10,14.

Question 14.
Eduardo thinks of a number between 1 and 20 that has exactly 5 factors. What number is he thinking of?

Explanation: If find factors for 1 to 20 we don’t get exactly 5 factors for any number except 16. So the answer is 16.

### Common Core – Factors – Page No. 284

Lesson Check

Question 1.
Which of the following lists all the factors of 24?
Options:
a. 1, 4, 6, 24
b. 1, 3, 8, 24
c. 3, 4, 6, 8
d. 1, 2, 3, 4, 6, 8, 12, 24

Answer: d(1, 2, 3, 4, 6, 8, 12, 24)

Explanation:Factors are the numbers which divides the original number completely. Here, we can see the numbers which gives the result as 24 when multiplied together.So the factors of 24 are:1, 2, 3, 4, 6, 8, 12, 24.

1×24=24
2×12=24
3×8=24
4×6=24
6×4=4
8×3=24
12×2=24
24×1=24

Question 2.
Natalia has 48 tiles. Which of the following shows a factor pair for the number 48?
Options:
a. 4 and 8
b. 6 and 8
c. 2 and 12
d. 3 and 24

Explanation: 6 and 8 are factor pair for 48 because 6×8=48.

Spiral Review

Question 3.
The Pumpkin Patch is open every day. If it sells 2,750 pounds of pumpkins each day, about how many pounds does it sell in 7 days?
Options:
a. 210 pounds
b. 2,100 pounds
c. 14,000 pounds
d. 21,000 pounds

Explanation: Let’s round off 2750 pounds to 3000 pounds. In one day 3000 pounds pumpkins were sold out, and in
7 days?? —- 3000×7= 21,000 pounds.

Question 4.
What is the remainder in the division problem modeled below?

Options:
a. 2
b. 3
c. 5
d. 17

Explanation: We can see in the above figure 3 circles with 5 sub circles inside it and a pair of  sub circles. Here total sub circles are (3×5)+2=17. If we divide 17 with 3 then we will get reminder as 2. So answer is 2.

Question 5.
Which number sentence is represented by the following array?

Options:
a. 4 × 5 = 20
b. 4 × 4 = 16
c. 5 × 2 = 10
d. 5 × 5 = 25

Explanation: As we can see 4 rows and 5 squares, So 4 × 5 = 20.

Question 6.
Channing jogs 10 miles a week. How many miles will she jog in 52 weeks?
Options:
a. 30 miles
b. 120 miles
c. 200 miles
d. 520 miles

Explanation: No.of weeks = 52. So 1 week = 10 miles, then 52 weeks =?????
52×10=520 miles.

### Page No. 287

Question 1.
Is 4 a factor of 28? Draw a model to help.
Think: Can you make a rectangle with 28 squares in 4 equal rows?

4 ______ a factor of 28.
Type below:
__________

Is 5 a factor of the number? Write yes or no.

Question 2.
27

Explanation: Factors of 27 are 1,3,9,27. So the answer is No.

Question 3.
30

Explanation: As the last digit is 0 which is divisible 5.

Question 4.
36

Explanation: 36 is not divisible by 5, So the answer is no

Question 5.
53

Explanation: Factors of 53 are 1, 53. So the answer is No.

Is 9 a factor of the number? Write yes or no.

Question 6.
54

Explanation: As 54 is divisible by 9.

Question 7.
63

Explanation: 63 is divisible by 9, So the answer is Yes

Question 8.
67

Explanation: 67 is a prime number that means it is divisible by 1 and itself. So the answer is No.

Question 9.
93

Explanation: The factors of 93 are 1,3,31 and 93. So the answer is No.

List all the factor pairs in the table.

Question 10.

1×24=24    1,24
2×12=24     2,12
3×8=24       3,8
4×6=24       4,6

Explanation: Factors of 24.

Question 11.

1×39=39    1,39
3×13=39.   3,13

Explanation: Factors of 39.

Practice: Copy and Solve List all the factor pairs for the number. Make a table to help.

Question 12.
56
1×56=56     1,56
2×23=56     2,23
4×14=56      4,14
7×8=56         7,8
8×7=56         8,7

Explanation: Factors of 56.

Question 13.
64
1×64=64    1,64
2×32=64    2,32
4×16=64    4,16
8×8=64      8,8

Explanation: Factors of 64 and factor pair for 64 is 8,8.

### Page No. 288

Use the table to solve 14–15.

Question 14.
Dirk bought a set of stamps. The number of stamps in the set he bought is divisible by 2, 3, 5, 6, and 9. Which set is it?

Explanation: 90 is divisible by all numbers 2,3,5,6, and 9. So the answer is 90.

Question 15.
Geri wants to put 6 stamps on some pages in her stamp book and 9 stamps on other pages. Explain how she could do this with the stamp set for Sweden.

Answer: 10 pages with 6 stamps and 2 pages with 9 stamps.

Explanation: Geri could break 78 into 60+18, As 60 is divisible by 6, and 18 is divisible by 9. Then she could make 10 pages with 6 stamps as 60÷6=10 and 2 pages with 9 stamps as 18÷9=2.

Question 16.
Use Counterexamples George said if 2 and 4 are factors of a number, then 8 is a factor of the number. Is he correct? Explain.

Explanation: Because if we 12 as an example, 2 and 4 are factors of 12 but not 8.

Question 17.
Classify the numbers. Some numbers may belong in more than one box.

Divisible by 5 and 9 — 45
Divisible by 3 and 9 — 27,45,54,72,81
Divisible by 2 and 6 — 54,72,84.

### Common Core – Factors and Divisibility – Page No. 289

Is 6 a factor of the number? Write yes or no.

Question 1.

Question 2.
56

Explanation: 56 is not divisible by 6. So the answer is No.

Question 3.
42

Explanation: Since 42 is divisible by 6.

Question 4.
66

Explanation: 66 is divisible by 6.

Is 5 a factor of the number? Write yes or no.

Question 5.
38

Explanation: If the end is 0 or 5 then the number is divisible by 5. As the number is 38 the answer is No

Question 6.
45

Explanation: 45 is divisible by 5. So the answer is Yes

Question 7.
60

Explanation: 60 is a factor of 5 because 60 is divisible by 5.

Question 8.
39

Explanation: As 39 is not divisible by 5. So the answer is No.

List all the factor pairs

Question 9.
Factors of 12

1 × 12 = 12; ( 1 , 12 )
2 × 6 = 12; ( 2, 6 )
3 × 4 = 12; ( 3 , 4 )

Question 10.
Factors of 25

1 ×25  = 25; ( 1 , 25 )
5 × 5 = 25; ( 5 , 5 )

Question 11.
List all the factor pairs for 48.

Answer: Factor pairs of 48 are (1,48),(2,24),(3,16),(4,12),(6,8),(12,2),(6,3),(24,2),(48,1).

Explanation: Factor pairs are the pairs when we multiplied both numbers will get the result. Here factor pairs for 48 are
1×48=48     (1,48)
2×24=48      (2,24)
3×16=48      (3,16)
4×12=48      (4,12)
6×8 =48       (6,8)

Problem Solving

Question 12.

Bryson buys a bag of 64 plastic miniature dinosaurs. Could he distribute them equally into six storage containers and not have any left over?

Explanation: 64 is not divisible by 6, So he cannot distribute them equally into six storage containers.

Question 13.
Lori wants to distribute 35 peaches equally into baskets. She will use more than 1 but fewer than 10 baskets. How many baskets does Lori need?

Explanation: First we need to know the factors of 35. The factors of 35 are 1,5,7,35. As Lori uses more than 1 but fewer than 10, the answer is 5 or 7. Lori can distribute 35 peaches equally in 5 or 7 baskets.

### Common Core – Factors – Page No. 290

Lesson Check

Question 1.
Which of the following numbers has 9 as a factor?
Options:
a. 28
b. 30
c. 39
d. 45

Explanation: 45 is divisible 9. So the answer is 45.

Question 2.
Which of the following numbers does NOT have 5 as a factor?
Options:
a. 15
b. 28
c. 30
d. 45

Explanation: 28 is not divisible by 5. So 28 is not a factor of 5.

Spiral Review

Question 3.
Which of the following shows a strategy to use to find 4 × 275?
Options:
a. (4 × 300) + (4 × 25)
b. (4 × 300) – (4 × 25)
c. (4 × 275) – 100
d. (4 × 200) + 75

Explanation: First we must replace 300-25 in the place of 275 then it becomes 4×(300-25), Now we must use the distributive property of multiplication then (4×300)-(4×25). So the answer is b.

Question 4.
Jack broke apart 5 × 216 as (5 × 200) + (5 × 16) to multiply mentally. What strategy did Jack use?
Options:
a. the Commutative Property
b. the Associative Property
c. halving and doubling
d. the Distributive Property

Explanation: Distributive property means if we multiply a sum by a number is same as multiplying each addend by the number and adding the products. This is the strategy Jack used.

Question 5.
Jordan has $55. She earns$67 by doing chores. How much money does Jordan have now?
Options:
a. $122 b.$130
c. $112 d.$12

Explanation: Jordan has $55, she earns by doing chores is$67. So total money is $55+$67=$122. Question 6. Trina has 72 collector’s stamps. She puts 43 of the stamps into a stamp book. How many stamps are left? Options: a. 29 b. 31 c. 39 d. 115 Answer: a Explanation: Stamps left are 72-43=29. ### Page No. 293 Question 1. Lucy has 40 bean plants, 32 tomato plants, and 16 pepper plants. She wants to put the plants in rows with only one type of plant in each row. All rows will have the same number of plants. How many plants can Lucy put in each row? First, read the problem and think about what you need to find. What information will you use? How will you use the information? Answer: We will find common factors for 40,32 and 16. Question 1. Next, make a list. Find the factors for each number in the problem. Answer: Factors of 40 are — 1,2,4,5,8,10,20,40 Factors of 32 are — 1,2,4,8,16,32 Factors of 16 are — 1,2,4,8,16 Question 1. Finally, use the list. Circle the common factors. So, Lucy can put ___ , ___ , ___ , or ___ plants in each row. Answer: 1,2,4,8 Explanation: Because 1,2,4,8, are common factors in 40,32,16. Question 2. What if Lucy has 64 bean plants instead of 40 bean plants? How many plants can Lucy put in each row? Answer: 1,2,4,8,16 Explanation: Here we need to find the factors of 64,32 and 16. We get common factors as 1,2,4,8,16. Question 3. One common factor of two numbers is 40. Another common factor is 10. If both numbers are less than 100, what are the two numbers? ______ and ______ Answer: 40 and 80. Explanation: As the next multiple of 40 is 80. So both 40 and 80 are less than 100 and has a common factor as 10. Question 4. The sum of two numbers is 136. One number is 51. What is the other number? What are the common factors of these two numbers? Answer: 85. Common Factors are 1,17. Explanation: As 136-51= 85 Factors of 51 are 1,3,17,51 Factors of 85 are 1,5,17,85. ### Page No. 294 Question 5. Analyze A number is called a perfect number if it equals the sum of all of its factors except itself. For instance, 6 is a perfect number because its factors are 1, 2, 3, and 6, and 1 + 2 + 3 = 6. What is the next greater perfect number? Answer: 28 Explanation: The factors of 28 are 1,2,4,7,14 and 28. If we add 1+2+4+7+14 we will get 28. So 28 is a perfect number. Question 6. Sona knits 10 squares a day for 7 days. Can she sew together the squares to make 5 equal-sized blankets? Explain. Answer: Yes Explanation: As 10×7= 70 which is a factor of 5. Question 7. Julianne earned$296 working at a grocery store last week. She earns $8 per hour. How many hours did Julianne work? Answer: 37 hours Explanation: Julianne earned$296 in last week. Per hour she earns $8, So total no.of hours did she worked is 296÷8= 37 hours. Question 8. There are 266 students watching a play in the auditorium. There are 10 rows with 20 students in each row and 5 rows with 8 students in each row. How many students are sitting in each of the 2 remaining rows if each of those rows has an equal number of students? Answer: 13 Students Explanation: Total number of students is 266. In which 10 rows were filled with 20 students that means 10×20=200 students, and 5 rows were filled with 8 students which means 5×8= 40 students. The total students filled are 240. And to know how many students filled in the remaining 2 rows we need to subtract 266-240=26, As students are filled in 2 rows 26÷2= 13. Question 9. Ben is planting a garden with 36 zinnias, 18 marigolds, and 24 petunias. Each row will have only one type of plant. Ben says he can put 9 plants in each row. He listed the common factors of 36, 18 and 24 below to support his reasoning. 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 18: 1, 2, 3, 6, 8, 9, 18 24: 1, 2, 3, 4, 6, 8, 9, 12, 24 Is he correct? Explain your answer. If his reasoning is incorrect, explain how he should have found the answer. Answer: No Explanation: The factors of 18 and 24 are incorrect which he listed. And the common factors for 36,24 and 18 are 1,2,3 and 6. So he can put 1,2,3 and 6 plants in a row. ### Common Core – Common Factors – Page No. 295 Problem Solving Common Factors Solve each problem. Question 1. Grace is preparing grab bags for her store’s open house. She has 24 candles, 16 pens, and 40 figurines. Each grab bag will have the same number of items, and all the items in a bag will be the same. How many items can Grace put in each bag? Question 2. Simon is making wreaths to sell. He has 60 bows, 36 silk roses, and 48 silk carnations. He wants to put the same number of items on each wreath. All the items on a wreath will be the same type. How many items can Simon put on each wreath? Answer:1,2,3,4,6 or 12 items Simon puts on each wreath. Explanation: First we will find the common factors of 36,48,60 factors of 36 are: 1,2,3,4,6,9,12,18,36. factors of 48 are: 1,2,3,4,6,8,12,16,24,48 factors of 60 are: 1,2,3,4,5,6,10,12,15,20,30,60. The common factors of 36,48,60 are 1,2,3,4,6,12. So Simon can put 1,2,3,4,6 or 12 items on each wreath. Question 3. Justin has 20 pencils, 25 erasers, and 40 paper clips. He organizes them into groups with the same number of items in each group. All the items in a group will be the same type. How many items can he put in each group? Answer: Justin can put 1 or 5 items in each group. Explanation: We will find common factors of 20,25,40. factors of 20 are: 1,2,4,5,10,20. factors of 25 are: 1,5,25. factors of 40 are: 1,2,4,5,8,10,20,40 So common factors are 1 and 5. Question 4. A food bank has 50 cans of vegetables, 30 loaves of bread, and 100 bottles of water. The volunteers will put the items into boxes. Each box will have the same number of food items and all the items in the box will be the same type. How many items can they put in each box? Answer: 1,2,5, or 10. Explanation: 1,2,5 or 10 are the common factors of 30,50 and 100. factors for 30 are: 1,2,3,5,6,10,15,30 factors for 50 are: 1,2,5,10,25,50 factors of 100 are: 1,2,4,5,10,20,25,50,100 So answer is 1,2,5,10. Question 5. A debate competition has participants from three different schools: 15 from James Elementary, 18 from George Washington School, and 12 from the MLK Jr. Academy. All teams must have the same number of students. Each team can have only students from the same school. How many students can be on each team? Answer: 3 Explanation: Lets find the common factors of 12,15,18 factors of 12 are: 1,2,3,4,6,12 factors of 15 are: 1,3,5,15 factors of 18 are: 1,2,3,6,9,18 3 is the common factor for 12,15,18 ### Common Core – Common Factors – Page No. 296 Lesson Check Question 1. What are all the common factors of 24, 64, and 88? Options: a. 1 and 4 b. 1, 4, and 8 c. 1, 4, 8, and 12 d. 1, 4, 8, and 44 Answer: b Explanation: factors of 24 are: 1,2,3,4,8,12,24 factors of 64 are: 1,2,4,8,16,32,64 factors of 88 are: 1,2,4,8,11,22,44,88 Question 2. Which number is NOT a common factor of 15, 45, and 90? Options: a. 3 b. 5 c. 10 d. 15 Answer: c Explanation: As 15 and 45 are not divisible by 10. Spiral Review Question 3. Dan puts$11 of his allowance in his savings account every week. How much money will he have after 15 weeks?
Options:
a. $165 b.$132
c. $110 d.$26

Explanation: Dan puts $11 in his savings account every week, So after 15 weeks it will be 15×11=165. The total money he will have after 15 weeks is$165.

Question 4.
James is reading a book that is 1,400 pages. He will read the same number of pages each day. If he reads the book in 7 days, how many pages will he read each day?
Options:
a. 20
b. 50
c. 140
d. 200

Explanation: Total no.of.pages is 1400, no.of pages James read each day is 1400÷7= 200

Question 5.
Emma volunteered at an animal shelter for a total of 119 hours over 6 weeks. Which is the best estimate of the number of hours she volunteered each week?
Options:
a. 10 hours
b. 20 hours
c. 120 hours
d. 714 hours

Explanation: Total hours Emma volunteered is 119 hours over 6 weeks, how much she volunteered each week is
119÷6= 19.833 i.e 20 hours. We must round off to the nearest one i.e 20 hours.

Question 6.
Which strategy can be used to multiply 6 × 198 mentally?
Options:
a. 6 × 198 = (6 × 19) + (6 × 8)
b. 6 × 198 = (6 × 200) + (6 × 2)
c. 6 × 198 = (6 × 200) – (6 × 2)
d. 6 × 198 = (6 + 200) × (6 + 2)

Explanation: By Distributive property of multiplication 6×198 can be written as (6 × 200) – (6 × 2).

### Page No. 297

Choose the best term from the box.

Question 1.
A number that is multiplied by another number to find a product is called a

Question 2.
A number is _________ by another number if the quotient is a counting number and the remainder is zero.

List all the factors from least to greatest.

Question 3.
8

Question 4.
14

Is 6 a factor of the number? Write yes or no.

Question 5.
81

Explanation: 81 is not divisible by 6

Question 6.
45

Explanation: 45 is not divisible by 6

Question 7.
42

Explanation: 42 is divisible by 6

Question 8.
56

Explanation: 56 is not divisible by 6

List all the factor pairs in the table.

Question 9.

1×64=64    1,64
2×32=64    2,32
4×16=64    4,16
8×8=64      8,8

Explanation: Factors of 64

Question 10.

1×44=44    1,44
2×22=44    2,22
11×4=44    11,4

List the common factors of the numbers.

Question 11.
9 and 18

Explanation:
Factors of 9 are: 1,3,9
Factors of 18 are: 1,2,3,9,18

Question 12.
20 and 50

Explanation:
Factors of 20 are: 1,2,4,5,10,20
Factors of 50 are: 1,2,5,10,25,50

### Page No. 298

Question 13.
Sean places 28 tomato plants in rows. All rows contain the same number of plants. There are between 5 and 12 plants in each row. How many plants are in each row?

Explanation: There are 28 tomato plants in a row. To find out how many plants in a row we will find the factors of 28 i.e 1,2,4,7,14,28. As there are between 5 and 12 plants 7 is the only number between 5 and 12. So 7 plants are planted in each row.

Question 14.
Ella bought some key chains and spent a total of $24. Each key chain costs the same whole-dollar amount. She bought between 7 and 11 key chains. How many key chains did Ella buy? Answer: 8 Explanation: Ella spent a total of$24. To find how many key chains first we will find the factors of 24. Factors of 24 are
1,2,3,4,6,8,12,24. As Ella bought between 7 and 11 key chains 8 is the only number between 7 and 11. So 8 key chains Ella bought.

Question 15.
Sandy has 16 roses, 8 daisies, and 32 tulips. She wants to arrange all the flowers in the bouquets. Each bouquet has the same number of flowers and the same type of flower. What is the greatest number of flowers that could be in a bouquet?

Answer: 2 roses, 1 daisy, and 4 tulips in 8 bouquets.

Explanation: First we must add all the flowers i.e 16+8+32= 56, Now we can divide 56 flowers equally in each bouquet. Like 2 roses, 1 daisy and 4 tulips in 8 bouquets or 8 roses in 2 bouquets, 8 daisies in 1 bouquet and 8 tulips in 4 bouquets.

Question 16.
Amir arranged 9 photos on a bulletin board. He put the photos in rows. Each row contains the same number of photos. How many photos could be in each row?

Answer: 9 photos in a row and 3 photos in 3 rows or 9 photos in 1 row.

Explanation: Factors of 9 are 1,3,9. So Amir can arrange 9 photos in a row and 3 photos in 3 rows or 9 photos in 1 row.

### Page No. 301

Question 1.
Multiply to list the next five multiples of 4.
4 , _____ , _____ , _____ , _____ , _____
1 × 4
4 , _____ , _____ , _____ , _____ , _____

4     1×4
8     2×4
12   3×4
16   4×4
20   4×5

Explanation: Multiplies of 4

Is the number a factor of 6? Write yes or no.

Question 2.
2

Explanation: 6 is divisible by 2. So 2 is the factor of 6.

Question 3.
6

Explanation: 6 is divisible by 6.

Question 4.
16

Explanation: 16 is not divisible by 6

Question 5.
18

Explanation: 18 is divisible by 6

Is the number a multiple of 6? Write yes or no.

Question 6.
3

Explanation: Multiples of 6 are 6,12,18,24,30, etc.

Question 7.
6

Explanation: 1×6= 6. So 6 is multiple of 6.

Question 8.
16

Explanation: Multiples of 6 are 6,12,18,24,30, etc.

Question 9.
18

Explanation: Multiples of 6 are 6,12,18,24,30, etc.

Is the number a multiple of 3? Write yes or no.

Question 10.
4

Explanation: Multiples of 3 are 3,6,9,12,15,etc.

Question 11.
8

Explanation: Multiples of 3 are 3,6,9,12,15,etc.

Question 12.
24

Explanation: Multiples of 3 are 3,6,9,12,15,etc.

Question 13.
38

Explanation: Multiples of 3 are 3,6,9,12,15,18,21,24,27,30,33,36,39,42,etc.

Question 14.
List the next nine multiples of each number. Find the common multiples.
Multiples of 2: 2, _________________
Multiples of 8: 8, _________________
Common multiples: _________________

Explanation:
Multiples of 2: 2,4,6,8,10,12,14,16,18,20.
Multiples of 8: 8,16,24,32,40,48,56,64,72,80.
So common multiples are: 8,16

Generalize Algebra Find the unknown number.

Question 15.
12, 24, 36, _____

Explanation:
12×1= 12
12×2= 24
12×3= 36
12×4= 28

Question 16.
25, 50, 75, 100, ______

Explanation:
25×1= 25
25×2= 50
25×3= 75
25×4= 100
25×5= 125

Tell whether 20 is a factor or multiple of the number.

Write factor, multiple, or neither.

Question 17.
10

Explanation: 2×10= 20.

Question 18.
20

Explanation:
1×20= 20
20÷1= 20.

Question 19.
30

Explanation:
Factors of 30 are:    1,2,3,5,6,10,15,and 30.
Multiples of 30 are: 30,60,90,etc.

Write true or false. Explain.

Question 20.
Every whole number is a multiple of 1.

Explanation: For every whole number which is multiplied with 1, the result will be that number.

Question 21.
Every whole number is a factor of 1.

Explanation: Not every whole number is a factor of 1.

Question 22.
Julio wears a blue shirt every 3 days. Larry wears a blue shirt every 4 days. On April 12, both Julio and Larry wore a blue shirt. What is the next date that they will both wear a blue shirt?

Explanation:
As Julio wears a blue shirt every 3 days and another shirt in the remaining 4 days, So 4×3 days= 12
Larry wears a blue shirt every 4 days and another shirt in the remaining 3 days, So 3×4 days= 12
12+12= 24. So the next date will be April 24.

### Page No. 302

Complete the Venn diagram. Then use it to solve 23–25.

Question 23.
What multiples of 4 are not factors of 48?

Explanation:
Multiples of 4 are 4,8,12,16,20,24,28,32,36,40,44,48.
Not a factors of 48 are 20,28,32,36,40,44.

Question 24.
What factors of 48 are multiples of 4?

Explanation:
Multiples of 4 are: 4,8,12,16,20,24,28,32,36,40,44,48.
Factors of 48 are: 1,2,4,8,12,16,24,48.

Question 25.
Pose a Problem Look back at Problem 24. Write a similar problem by changing the numbers. Then solve.

Answer: Let’s take factors of 64 are multiples of 8?
8,16,32,64.

Explanation:
Multiples of 8 are: 8,16,24,32,40,48,56,64,72,80
Factors of 64 are: 1,2,4,8,16,32,64

Question 26.
Kia paid $10 for two charms. The price of each charm was a multiple of$2. What are the possible prices of the charms?

Answer: $2,$8 and $4,$6.

Explanation: Since the price was multiple of 2 and Kia paid $10 for two charms, So possible prices are$2+$8=$10
and $4+$6=$10. Question 27. Look for Structure The answer is 9, 18, 27, 36, 45. What is the question? Answer: Write the multiples of 9 Question 28. How do you know whether a number is a multiple of another number? Answer: When the number is divisible by the number then that number is multiple of another number. Explanation: For example, if we take a number i.e 8 which is divisible by 2 and 8 is a multiple of 2. Question 29. For numbers 29a–29e, select True or False for each statement. a. The number 45 is a multiple of 9. i. True ii. False Answer: True Explanation: As 9×5= 45, So 45 is multiple of 9. Question 29. b. The number 4 is a multiple of 16. i. True ii. False Answer: False. Explanation: As 16 is divisible by 4 and not a multiple of 16. Multiple of 16 are : 16,32,48,64,80. Question 29. c. The number 28 is a multiple of 4. i. True ii. False Answer: True. Explanation: 4×7=28. Question 29. d. The number 4 is a factor of 28. i. True ii. False Answer: True. Explanation: Factors of 28 are: 1,2,4,7,14,28. Question 29. e. The number 32 is a factor of 8. i. True ii. False Answer: Explanation: ### Common Core – Factors and Multiples – Page No. 303 Factors and Multiples Is the number a multiple of 8? Write yes or no. Question 1. Question 2. 8 Answer: Yes Explanation: Since 8×1=8, it is a multiple of 8 Question 3. 20 Answer: No Explanation: 20 is not a multiple of 8 Question 4. 40 Answer: Yes Explanation: 8×5=40, So 40 is multiple of 8 List the next nine multiples of each number. Find the common multiples. Question 5. Multiples of 4: Multiples of 7: Common multiples: Answer: Explanation: Multiples of 4: 4,8,12,16,20,24,28,32,36,40. Multiples of 7: 7,14,21,28,35,42,49,56,63,70. Common Multiples: 28, Question 6. Multiples of 3: Multiples of 9: Common multiples: Answer: 9,18,45,54,63, etc. Explanation: Multiples of 3: 3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63. Multiples of 9: 9,18,27,36,45,54,63,72,81,90. Common multiples: 9,18,45,54,63, etc. Question 7. Multiples of 6: Multiples of 8: Common multiples: Answer: 24,48,72. Explanation: Multiples of 6: 6,12,18,24,30,36,42,48,54,60,66,72,78. Multiples of 8: 8,16,24,32,40,48,56,64,72,80. Common multiples: 24,48,72. Tell whether 24 is a factor or multiple of the number. Write factor, multiple, or neither. Question 8. 6 Answer: Multiple Explanation: 6×4=24 Question 9. 36 Answer: Neither Explanation: 36 is not a factor or multiple of 24. Question 10. 48 Answer: Factor Explanation: 24×2= 48, So 48 is a factor of 24 Problem Solving Question 11. Ken paid$12 for two magazines. The cost of each magazine was a multiple of $3. What are the possible prices of the magazines? Answer:$3+$9=$12.

Explanation: As each magazine cost was multiple of $3, The possible price for 2 magazines are$3+$9=$12, which is a multiple of 3

Question 12.
Jodie bought some shirts for $6 each. Marge bought some shirts for$8 each. The girls spent the same amount of money on shirts. What is the least amount they could have spent?

Answer: $24 Explanation: As they spent the same amount of money which means the number should be multiple of$6 and $8, So multiples of 6 are: 6,12,18,24,30,36,42 and multiples of 8 are: 8,16,24,32,40. The least amount they could spend is 24. As 24 is the least common multiple. ### Common Core – Factors and Multiples – Page No. 304 Lesson Check Question 1. Which list shows numbers that are all multiples of 4? Options: a. 2, 4, 6, 8 b. 3, 7, 11, 15, 19 c. 4, 14, 24, 34 d. 4, 8, 12, 16 Answer: d Explanation: Multiples of 4 are 4,8,12,16. Question 2. Which of the following numbers is a common multiple of 5 and 9? Options: a. 9 b. 14 c. 36 d. 45 Answer: 45 Explanation: 5×9= 45 Spiral Review Question 3. Jenny has 50 square tiles. She arranges the tiles into a rectangular array of 4 rows. How many tiles will be left over? Options: a. 0 b. 1 c. 2 d. 4 Answer: 2 Explanation: As Jenny arranges in 4 rows, each row contains 12 tiles. So 12×4= 48. The tiles left are 50-48=2. Question 4. Jerome added two numbers. The sum was 83. One of the numbers was 45. What was the other number? Options: a. 38 b. 48 c. 42 d. 128 Answer: a Explanation: The sum of two numbers is 83, in that one number is 45. To find another number we will do subtraction, i.e 83-45=38. Question 5. There are 18 rows of seats in the auditorium. There are 24 seats in each row. How many seats are in the auditorium in all? Options: a. 42 b. 108 c. 412 d. 432 Answer: d Explanation: No.of rows= 18, each row has 24 seats. So total no.of seats are 18×24= 432. Question 6. The population of Riverdale is 6,735. What is the value of the 7 in the number 6,735? Options: a. 7 b. 700 c. 735 d. 7,000 Answer: b Explanation: In 6,735 the 7 is in the Hundreds Place. So the answer is 7. ### Page No. 307 Question 1. Use the grid to model the factors of 18. Tell whether 18 is prime or composite. Factors of 18: ____ , ____ , ____ , ____ , ____ , ____ Think: 18 has more than two factors. So, 18 is _________ . Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 18 are: 1,2,3,6,9,18. Tell whether the number is prime or composite. Question 2. 11 Think: Does 11 have other factors besides 1 and itself? Answer: Prime number. Explanation: A Prime number is a number that is divisible 1 and itself. Question 3. 73 Answer: Prime number Explanation: A Prime number is a number that is divisible 1 and itself. Question 4. 69 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 69 are: 1,3,23,69. Question 5. 42 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 42 are: 1,2,3,6,7,21,42. Tell whether the number is prime or composite. Question 6. 18 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 18 are: 1,2,3,6,9,18. Question 7. 49 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 49 are 1,7,49. Question 8. 29 Answer: Prime number. Explanation: A Prime number is a number that is divisible 1 and itself. Question 9. 64 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 64 are: 1,2,4,8,32,64. Question 10. 33 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 33 are: 1,3,11,33. Question 11. 89 Answer: Prime number. Explanation: A Prime number is a number that is divisible 1 and itself. Question 12. 52 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 52 are: 1,2,4,13,26,52. Question 13. 76 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 76 are: 1,2,4,19,38,76. Write true or false for each statement. Explain or give an example to support your answer. Question 14. Only odd numbers are prime numbers. Answer: False. Explanation: Not all odd numbers are prime numbers. For example. 39 is an odd number but not a prime number because it is divisible by 3 and 13. Question 15. A composite number cannot have three factors. Answer: False Explanation: A Composite number is a number that has more than two factors. For example. 21 is a composite number and the factors of 21 are 1,3,7,21. Question 16. I am a number between 60 and 100. My ones digit is two less than my tens digit. I am a prime number. What number am I? Answer: 97 Explanation: Prime numbers between 60 to 100 are 61,67,71,73,79,83,89,97. 97 is the number which ones digit is two less than tens digit. Question 17. Name a 2-digit odd number that is prime. Name a 2-digit odd number that is composite. Answer: 2 digit Prime odd numbers are 11,13,17 etc. 2 digit Composite odd numbers are 15,21,39 Explanation: A Prime number is a number that is divisible 1 and itself. The number which has more than two factors is called composite numbers. Question 18. Choose the words that correctly complete the sentence. The number 9 is img 18 because it has img 19 two factors. Type below: __________ ### Page No. 308 The Sieve of Eratosthenes Eratosthenes was a Greek mathematician who lived more than 2,200 years ago. He invented a method of finding prime numbers, which is now called the Sieve of Eratosthenes. Question 19. Follow the steps below to circle all prime numbers less than 100. Then list the prime numbers. STEP 1 Cross out 1, since 1 is not prime. STEP 2 Circle 2, since it is prime. Cross out all other multiples of 2. STEP 3 Circle the next number that is not crossed out. This number is prime. Cross out all the multiples of this number. STEP 4 Repeat Step 3 until every number is either circled or crossed out. So, the prime numbers less than 100 are Answer: 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97. Explanation: A Prime number is a number that is divisible 1 and itself. Question 20. Explain why the multiples of any number other than 1 are not prime numbers. Answer: ### Common Core – Prime and Composite Numbers – Page No. 309 Prime and Composite Numbers Tell whether the number is prime or composite Question 1. Question 2. 68 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 68 are: 1,2,4,17,34,69. Question 3. 52 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 52 are: 1,2,4,13,26,52. Question 4. 63 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 63 are: 1,2,3,7,9,21,63. Question 5. 75 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 75 are: 1,3,5,15,25,75 Question 6. 31 Answer: Prime number. Explanation: 31 is a prime number that means it is divisible by 1 and itself. Question 7. 77 Answer: Composite number. Explanation: The number which has more than two factors is called composite numbers. Factors of 77 are: 1,7,11,77. Question 8. 59 Answer: Prime number Explanation: 59 is a prime number that means it is divisible by 1 and itself. Question 9. 87 Answer: Composite Number. Explanation: The number which has more than two factors is called composite numbers. Factors of 87 are: 1,3,29,87. Question 10. 72 Answer: Composite Number. Explanation: The number which has more than two factors is called composite numbers. Factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. Question 11. 49 Answer: Composite Number. Explanation: The number which has more than two factors is called composite numbers. Factors of 49 are 1,7,49. Question 12. 73 Answer: Prime number. Explanation: A Prime number is a number that is divisible 1 and itself. Problem Solving Question 13. Kai wrote the number 85 on the board. Is 85 prime or composite? Answer: Composite number Explanation: The number which has more than two factors is called composite numbers. Factors of 85 are 1,5,17,85 Question 14. Lisa says that 43 is a 2-digit odd number that is composite. Is she correct? Answer: No Explanation: 43 is a prime number. A Prime number is a number that is divisible 1 and itself. ### Common Core – Prime and Composite Numbers – Page No. 310 Lesson Check Question 1. The number 5 is: Options: a. prime b. composite c. both prime and composite d. neither prime nor composite Answer: Prime number. Explanation: A Prime number is a number that is divisible 1 and itself. Question 2. The number 1 is: Options: a. prime b. composite c. both prime and composite d. neither prime nor composite Answer: d Explanation: A Prime number is a number that is divisible 1 and itself. So prime number should have two divisors but 1 has only one divisor. The number which has more than two factors is called composite numbers. So 1 doesn’t have more than two factors. So 1 is neither Prime nor Composite. Spiral Review Question 3. A recipe for a vegetable dish contains a total of 924 calories. The dish serves 6 people. How many calories are in each serving? Options: a. 134 calories b. 150 calories c. 154 calories d. 231 calories Answer: c Explanation: Total no.of calories are 924, which serves 6 people. To find each serving we will perform division 924÷6= 154 calories. Question 4. A store clerk has 45 shirts to pack in boxes. Each box holds 6 shirts. What is the fewest boxes the clerk will need to pack all the shirts? Options: a. 9 b. 8 c. 7 d. 6 Answer: b Explanation: As the box holds only 6 shirts, 42 shirts are packed in 7 boxes, and the remaining 3 shirts will be packed in another box. So the total number of boxes is 8. Question 5. Which number rounds to 200,000? Options: a. 289,005 b. 251,659 c. 152,909 d. 149,889 Answer: c Explanation: 152,909 is nearest to 200,000. Question 6. What is the word form of the number 602,107? Options: a. six hundred twenty thousand,seventeen b. six hundred two thousand, one hundred seven c. six hundred twenty-one thousand, seventeen d. six hundred two thousand, one hundred seventy Answer: b ### Page No. 313 Use the rule to write the numbers in the pattern. Question 1. Rule: Subtract 10. First term: 100 Answer: 100,90,80,70,60,.. Explanation: 100 100-10= 90 90-10= 80 80-10= 70 70-10= 60 Use the rule to write the numbers in the pattern. Describe another pattern in the numbers. Question 2. Rule: Multiply by 2. First term: 4 4 , _____ , _____ , _____ , _____ , ……. Answer: 4,8,16,32,64,… Explanation: 4 4×2= 8 8×2= 16 16×2= 32 32×2= 64 Question 3. Rule: Skip-count by 6. First term: 12 12 , _____ , _____ , _____ , _____ , ……. Answer: 12,18,24,30,36,… Explanation: 12 12+6= 18 18+6= 24 24+6= 30 30+6= 36 Use the rule to write the first twelve numbers in the pattern. Describe another pattern in the numbers. Question 4. Rule: Add 7. First term: 3 Answer: 3 3+7= 10 10+7= 17 17+7= 34 34+7= 41 41+7= 48 48+7= 55 55+7= 62 62+7= 69 69+7= 76 76+7= 83 83+7= 90. Explanation: Added 7 to the given term. Question 5. 5. Rule: Add 2, add 1. First term: 12 Answer: 12,14,15,17,19,21,22,24,25,27,28,30,31. Explanation: 12 12+2= 14 14+1= 15 15+2= 17 17+1= 19 19+2= 21 21+1= 22 22+2= 24 24+1= 25 25+2= 27 27+1= 28 28+2= 30 30+1= 31 Question 6. Use Patterns Marcie likes to collect stickers, but she also likes to give them away. Currently, Marcie has 87 stickers in her collection. If Marcie collects 5 new stickers each week and gives away 3 stickers each week, how many stickers will Marcie have in her collection after 5 weeks? _______ stickers Answer: 97 stickers Explanation: Marcie has 87 stickers, in 1st week she collects 5 stickers and gives away 3 stickers, that means 87+5-3= 89 2nd week 89+5-3= 91 3rd week 91+5-3= 93 4th week 93+5-3= 95 5th week 95+5-3= 97. ### Page No. 314 Question 7. John is saving for his trip to see the Alamo. He started with$24 in his savings account. Every week he earns $15 for baby-sitting. Out of that, he spends$8 and saves the rest. John uses the rule add 7 to find out how much money he has at the end of each week. What are the first 8 numbers in the pattern?

Answer: $24,$31, $38,$45, $52,$59, $66,$73.

Explanation:
24
24+7= 31
31+7= 38
38+7= 45
45+7= 52
52+7= 59
59+7= 66
66+7= 73.

Question 8.
Draw a check under the column that describes the number.

Pose a Problem

Question 9.
An activity at the Math Fair shows two charts.

Use at least two of the numbers and an operation from the charts to write a pattern problem. Include the first five terms of your pattern in the solution to your problem.
Pose a problem. Solve your problem.
Describe other patterns in the terms you wrote.

10-6= 4   Subtraction.
5×2= 10  Multiplication.

### Common Core – Number Patterns – Page No. 315

Number Patterns

Use the rule to write the first twelve numbers in the pattern.

Describe another pattern in the numbers.

Question 1.
Rule: Add 8. First term: 5

Question 2.
Rule: Subtract 7. First term: 95

Explanation: 95
95-7= 88
88-7= 81
81-7= 74
74-7= 67
67-7= 60
60-7= 53
53-7= 46
46-7= 39
39-7= 32
32-7= 25
25-7= 18
18-7= 11

Question 3.
Rule: Add 15, subtract 10. First term: 4

Explanation: 4
4+15= 19
19-10= 9
9+15= 24
24-10= 14
14+15= 29
29-10= 19
19+15= 34
34-10= 24
24+15= 39
39-10=29
29+15=44
44-10=34

Question 4.
Rule: Add 1, multiply by 2. First term: 2

Explanation: 2
2+1= 2
2×2= 4
4+1= 5
5×2= 10
10+1= 11
11×2= 22
22+1= 23
23×2= 46
46+1= 47
47×2= 94
94+1= 95
95×2= 190.

Problem Solving

Question 5.
Barb is making a bead necklace. She strings 1 white bead, then 3 blue beads, then 1 white bead, and so on. Write the numbers for the first eight beads that are white. What is the rule for the pattern?

Explanation: 1
1+4= 5
5+4= 9
9+4= 13
13+4= 17
17+4= 21
21+4= 25
25+4=29

Question 6.
An artist is arranging tiles in rows to decorate a wall. Each new row has 2 fewer tiles than the row below it. If the first row has 23 tiles, how many tiles will be in the seventh row?

Explanation: 23
23-2= 21
21-2= 19
19-2= 17
17-2= 15
15-2= 13
13-2= 11

### Common Core – Number Patterns – Page No. 316

Lesson Check

Question 1.
The rule for a pattern is add 6. The first term is 5. Which of the following numbers is a term in the pattern?
Options:
a. 6
b. 12
c. 17
d. 22

Explanation: 5
5+6= 11
11+6= 17

Question 2.
What are the next two terms in the pattern 3, 6, 5, 10, 9, 18, 17, . . .?
Options:
a. 16, 15
b. 30, 31
c. 33, 34
d. 34, 33

Explanation: 3
3×2= 6
6-1= 5
5×2= 10
10-1= 9
9×2= 18
18-1= 17
17×2= 34
34-1= 33

Spiral Review

Question 3.
To win a game, Roger needs to score 2,000 points. So far, he has scored 837 points. How many more points does Roger need to score?
Options:
a. 1,163 points
b. 1,173 points
c. 1,237 points
d. 2,837 points

Explanation: Roger has scored 837 points, He needs to score 2000 points to win, So to know how much more points do Roger needs we need to subtract i.e 2,000-837= 1,163.

Question 4.
Sue wants to use mental math to find 7 × 53. Which expression could she use?
Options:
a. (7 × 5) + 3
b. (7 × 5) + (7 × 3)
c. (7 × 50) + 3
d. (7 × 50) + (7 × 3)

Explanation: Distributive property means if we multiply a sum by a number is the same as multiplying each addend by the number and adding the products.

Question 5.
Pat listed numbers that all have 15 as a multiple. Which of the following could be Pat’s list?
Options:
a. 1, 3, 5, 15
b. 1, 5, 10, 15
c. 1, 15, 30, 45
d. 15, 115, 215

Explanation:
1×15= 15
3×5= 15
5×3= 15
15×1= 15

Question 6.
Which is a true statement about 7 and 14?
Options:
a. 7 is a multiple of 14.
b. 14 is a factor of 7.
c. 14 is a common multiple of 7 and 14.
d. 21 is a common multiple of 7 and 14.

Explanation:
7×2=14
14×1=14

### Review/Test – Page No. 317

Question 1.
List all the factors of the number.
14: ______ , ______ , ______ , ______

Explanation: Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 14 when multiplied together. So the factors of 14 are 1,2,7,14.

Question 2.
Select the numbers that have a factor of 5. Mark all that apply.
Options:
a. 15
b. 3
c. 45
d. 5
e. 50
f. 31

Explanation: Factors are the numbers that divide the original number completely.

Question 3.
Jackson was making a poster for his room. He arranged 50 trading cards in the shape of a rectangle on the poster.
For 3a–3e, choose Yes or No to tell whether a possible arrangement of cards is shown.
a. 5 rows of 10 cards
i. yes
ii. no

Explanation: 5 rows of 10 cards that means 5×10= 50. So the answer is Yes.

Question 3.
b. 7 rows of 8 cards
i. yes
ii. no

Explanation: 7×8= 56, There will be extra cards. So the answer is No.

Question 3.
c. 25 rows of 2 cards
i. yes
ii. no

Explanation: 25×2=50. So the answer is Yes

Question 3.
d. 50 rows of 1 card
i. yes
ii. no

Explanation: 50×1=50. So the answer is Yes.

Question 3.
e. 45 rows of 5 cards
i. yes
ii. no

Explanation: 45×5= 225. Which is not equal to 50. So the answer No.

Question 4.
List all the factor pairs in the table.

1×48= 48   1,48
2×24= 48   2,24
3×16= 48   3,16
4×12= 48   4,12
6×8=  48    6,8

Explanation: Factors are the numbers that divide the original number completely. Here, we can see the numbers which give the result as 30 when multiplied together.

### Review/Test – Page No. 318

Question 5.
Classify the numbers. Some numbers may belong in more than one box.

Divisible by 5 and 9: 90
Divisible by 6 and 9: 54,72,90
Divisible by 2 and 6: 54,72,84,90,96

Question 6.
James works in a flower shop. He will put 36 tulips in vases for a wedding. He must use the same number of tulips in each vase. The number of tulips in each vase must be greater than 1 and less than 10. How many tulips could be in each vase?

Answer: 2, 3, 4, 6, 9.

Explanation:

Question 7.
Brady has a card collection with 64 basketball cards, 32 football cards, and 24 baseball cards. He wants to arrange the cards in equal piles, with only one type of card in each pile. How many cards can he put in each pile? Mark all that apply.
Options:
a. 1
b. 2
c. 3
d. 4
e. 8
f. 32

Explanation:
Factors of 64 are 1,2,4,8,16,32,64.
Factors of 32 are 1,2,4,8,16,32.
Factors of 24 are 1,2,3,4,6,8,12,24.
Common factors are 1,2,4,8.

Question 8.
The Garden Club is designing a garden with 24 cosmos, 32 pansies, and 36 marigolds. Each row will have only one type of plant in each row. Ben says he can put 6 plants in each row. He listed the common factors of 24, 32, and 36 below to support his reasoning.
24: 1, 2, 3, 4, 6, 8, 12, 24
32: 1, 2, 4, 6, 9, 16, 32
36: 1, 2, 3, 4, 6, 8, 12, 18, 36
Is he correct? Explain your answer. If his reasoning is incorrect, explain how he should have found the answer.

Answer: No. He can put 1,2,4 plants in each row

Explanation: The factors of 32 are incorrect. He listed as 6 and 9 are factors of 32 which is wrong and 8 is not a factor of 36.
Factors of 32 are 1,2,4,8,16,32.
Factors of 36 are 1,2,3,4,6,9,18,36.
Common factors of 24,32 and 36 are 1,2,4. So he can put 1,2,4 plants in each row.

### Review/Test – Page No. 319

Question 9.

Part A
The museum is hosting a show for July that features the oil paintings by different artists. All artists show the same number of paintings and each will show more than 1 painting. How many artists could be featured in the show?

Explanation:
Factors of 30 are 1,2,3,5,6,10,15,30.

Question 9.
Part B
The museum wants to display all the art pieces in rows. Each row has the same number of pieces and the same type of pieces. How many pieces could be in each row? Explain how you found your answer.

Explanation:
Factors of 30 are 1,2,3,5,6,10,15,30.
Factors of 24 are 1,2,3,4,6,8,12,24
Factors of 21 are 1,3,7,21
Common Factors are 1,3

Question 10.
Charles was skip counting at the Math Club meeting. He started to count by 8s. He said 8, 16, 24, 32, 40, and 48. What number will he say next?

Explanation: Multiples of 8
8×1= 8
8×2= 16
8×3= 24
8×4= 32
8×5= 40
8×6= 48
8×7= 56.

Question 11.
Jill wrote the number 40. If her rule is add 7, what is the fourth number in Jill’s pattern? How can you check your answer?

Explanation:
40
40+7= 47
47+7= 54
54+7= 61, And the fourth number is 61

### Review/Test – Page No. 320

Question 12.
For numbers 12a–12e, select True or False for each statement.
a. The number 36 is a multiple of 9.
i. True
ii. False

Explanation: 9×4= 36.

Question 12.
b. The number 3 is a multiple of 9.
i. True
ii. False

Explanation: Multiples of 9 are 9,18,27,36,45,54,63, etc.

Question 12.
c. The number 54 is a multiple of 9.
i. True
ii. False

Explanation: 9×6= 54

Question 12.
d. The number 3 is a factor of 9.
i. True
ii. False

Explanation: Factors of 9 are 1,3,9.

Question 12.
e. The number 27 is a factor of 9.
i. True
ii. False

Explanation: Factors of 27 are 1,3,9,27

Question 13.
What multiple of 7 is also a factor of 7?

Explanation: 7 is both multiple and a factor of 7.

Question 14.
Manny makes dinner using 1 box of pasta and 1 jar of sauce. If pasta is sold in packages of 6 boxes and sauce is sold in packages of 3 jars, what is the least number of dinners that Manny can make without any supplies leftover?

Manny has 1 box of pasta and 1 jar of sauce and he sold in a package of 6 boxes of pasta and 3 jars of sauce. Let the packages of pasta be 6P and jars of sauce be 3s.
As Manny sold without any leftover 3S=6P,
If we take 1 package of pasta then P=1,
And 3S=6×1, where S= 6/3 which is equal to 2,
So for every package of pasta, we need 2 packages of sauce,
So the minimum purchase is 2 packages of sauce and 1 package of pasta. Since pasta packages are 6 boxes the minimum number of meals is 6.

Question 15.
Serena has several packages of raisins. Each package contains 3 boxes of raisins. Which could be the number of boxes of raisins Serena has? Mark all that apply.
Options:
a. 9
b. 18
c. 23
d. 27
e. 32

Explanation: Factors of 3.

Question 16.
Choose the words that make the sentence true.
The number 7 is because it has two factors.
The number 7 is _________ because it has
_________ two factors.

Answer: The number 7 is a prime number because it has exactly two factors.

Explanation: A Prime number is a number that is divisible 1 and itself.

### Review/Test – Page No. 321

Question 17.
Winnie wrote the following riddle: I am a number between 60 and 100. My ones digit is two less than my tens digit. I am a prime number.
Part A
What number does Winnie’s riddle describe? Explain.

Explanation: 97 is the number which ones digit is two less than tens digit.

Question 17.
Part B
Winnie’s friend Marco guessed that her riddle was about the number 79. Why can’t 79 be the answer to Winnie’s riddle?
Explain.

Answer: It’s wrong because in Winnie’s riddle ones digit is two less than tens digit. But in 79 ones digit is two greater than tens digit.

Explanation: In 79 ones digit is two greater than tens digit. So Marco guess was incorrect.

Question 18.
Classify the numbers as prime or composite.

Answer: Prime numbers are 37, 71
Composite numbers are 65, 82

Explanation:
A Composite number is a number that has more than two factors.
A Prime number is a number that is divisible 1 and itself.

Question 19.
Erica knits 18 squares on Monday. She knits 7 more squares each day from Tuesday through Thursday. How many squares does Erica knit on Friday?

Explanation: 18
18+7= 25
25+7= 32
32+7= 39
39+7= 46.

Question 20.
Use the rule to write the first five terms of the pattern.
First term: 11 ______ ______ ______ ______

Explanation: 11
11+10= 21
21-5= 16
16+10= 26
26-5= 21

### Review/Test – Page No. 322

Question 21.
Elina had 10 tiles to arrange in a rectangular design. She drew a model of the rectangles she could make with the ten tiles.

Part A
How does Elina’s drawing show that the number 10 is a composite number?

Answer: 10 is a composite number because it has more than two factors.

Explanation: The number which has more than two factors is called composite numbers.

Question 21.
Part B
Suppose Elina used 15 tiles to make the rectangular design. How many different rectangles could she make with the 15 tiles? Write a list or draw a picture to show the number and dimensions of the rectangles she could make.

Explanation: one by 15 tiles and second by 3tiles in a row.

Question 21.
Part Cs
Elina’s friend Luke said that he could make more rectangles with 24 tiles than with Elina’s 10 tiles. Do you agree with Luke? Explain.

Explanation: As 24 has more factors than 10.

### Page No. 329

Use the model to write an equivalent fraction.

Question 1.

$$\frac{1}{5}$$ = $$\frac{□}{□}$$

Explanation: From the above figure we can see that there are 5 equal parts and in that 1 part is shaded. So the fraction of the shaded part is 1/5.

Question 2.

$$\frac{2}{3}$$ = $$\frac{□}{□}$$

Explanation: From the above figure we can see that there are 3 equal parts and in that 2 part is shaded. So the fraction of the shaded part is 2/3.

Tell whether the fractions are equivalent. Write = or ≠.

Question 3.
$$\frac{1}{6}$$ _____ $$\frac{2}{12}$$

Explanation: The denominator and numerators are equal for both the fractions. So 1/6=2/12 are equal.

Question 4.
$$\frac{2}{5}$$ _____ $$\frac{6}{10}$$

Explanation: The denominator and numerators are not equal for both the fractions.

Question 5.
$$\frac{4}{12}$$ _____ $$\frac{1}{3}$$

Explanation: The denominator and numerators are equal for both the fractions.

Question 6.
$$\frac{5}{8}$$ _____ $$\frac{2}{4}$$

Explanation: The denominator and numerators are not equal for both the fractions.

Question 7.
$$\frac{5}{6}$$ _____ $$\frac{10}{12}$$

Explanation: The denominator and numerators are equal for both the fractions.

Question 8.
$$\frac{1}{2}$$ _____ $$\frac{5}{10}$$

Explanation: The denominator and numerators are equal for both the fractions.

Question 9.
Manny used 8 tenth-size parts to model $$\frac{8}{10}$$. Ana used fewer parts to model an equivalent fraction. How does the size of a part in Ana’s model compare to the size of a tenth-size part? What size part did Ana use?

Answer: Larger than a tenth-size part. And she used the fifth-size part.

Explanation: A part of Ana’s model is larger than a tenth-size part. And she used the fifth-size part.

Question 10.
Use a Concrete Model How many eighth-size parts do you need to model $$\frac{3}{4}$$? Explain.

Explanation: Let the parts be X, then 1/8×X=3/4. By calculation, we will get X as 6.
So we need 6 parts.

### Page No. 330

Question 11.
Ben brought two pizzas to a party. He says that since 14_ of each pizza is left, the same amount of each pizza is left. What is his error?

Answer: As the size of pizzas is not the same, So 1/4 of leftover pizza is not equal to another.

Question 12.
For numbers 12a–12d, tell whether the fractions are equivalent by selecting the correct symbol.
a. $$\frac{3}{15}$$ _____ $$\frac{1}{6}$$

Question 12.
b. $$\frac{3}{4}$$ _____ $$\frac{16}{20}$$

c. $$\frac{2}{3}$$ _____ $$\frac{8}{12}$$
d. $$\frac{4}{5}$$ _____ $$\frac{8}{10}$$