McGraw Hill Math

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 15.1 Exponents will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 15.1 Exponents

Exercises
FIND THE VALUE
Question 1.
2³ = 8.
Answer:
2³ = 8.

Explanation:
2³ = 2 × 2 × 2
= 4 × 2
= 8.

Question 2.
5²
Answer:
5²  = 25.

Explanation:
5² = 5 × 5
= 25.

Question 3.
12³
Answer:
12³ = 1,728.

Explanation:
12³ = 12 × 12 × 12
= 144 × 12
= 1,728.

Question 4.
4³
Answer:
4³ = 64.

Explanation:
4³ = 4 × 4 × 4
= 16 × 4
= 64.

Question 5.
12²
Answer:
12² = 144.

Explanation:
12² = 12 × 12
= 144.

Question 6.
2.5²
Answer:
2.5² = 6.25.

Explanation:
2.5² = 2.5 × 2.5
= 6.25.

Question 7.
10³
Answer:
10³ = 1000.

Explanation:
10³ = 10 × 10 × 10
= 100 × 10
= 1000.

Question 8.
7⁴
Answer:
7⁴ = 2,401.

Explanation:
7⁴ = 7 × 7 × 7 × 7
= 49 × 7 × 7
= 343 × 7
= 2,401.

Question 9.
1.2²
Answer:
1.2² = 1.44.

Explanation:
1.2² = 1.2 × 1.2
= 1.44.

Question 10.
5⁴
Answer:
5⁴ = 625.

Explanation:
5⁴ = 5× 5 × 5 × 5
= 25 × 5 × 5
= 125 × 5
= 625.

Question 11.
3⁵
Answer:
3⁵  = 243.

Explanation:
3⁵ = 3 × 3 × 3 × 3 × 3
= 9 × 3 × 3 × 3
= 27 × 3 × 3
= 81 × 3
= 243.

Question 12.
(.01)²
Answer:
(.01)² = 0.0001.

Explanation:
(.01)² = .01 × .01
= 0.0001.

Question 13.
2⁷
Answer:
2⁷  = 64.

Explanation:
2⁷ = 2 × 2 × 2 × 2 × 2 × 2 × 2
= 4 × 2 × 2 × 2 × 2 × 2
= 8 × 2 × 2 × 2 × 2
= 16 × 2 × 2
= 32 × 2
= 64.

Question 14.
(.05)³
Answer:
(.05)³ = 0.000125.

Explanation:
(.05)³ = .05 × .05 × .05
= 0.0025 × .05
= 0.000125.

Question 15.
10⁵
Answer:
10⁵ = 100,000.

Explanation:
10⁵ = 10 × 10 × 10 × 10 × 10
= 100 × 10 × 10 × 10
= 1000 × 10 × 10
= 10000 × 10
= 100,000.

Question 16.
(1.1)²
Answer:
(1.1)² = 1.21.

Explanation:
(1.1)² = 1.1 × 1.1
= 1.21.

Question 17.
7³
Answer:
7³ = 343.

Explanation:
7³ = 7 × 7 × 7
= 49 × 7
= 343.

Question 18.
25²
Answer:
25² = 625.

Explanation:
25² = 25 × 25
= 625.

Question 19.
30³
Answer:
30³ = 27,000.

Explanation:
30³ = 30 × 30 × 30
= 900 × 30
= 27,000.

Question 20.
(.002)³
Answer:
(.002)³ = 0.000000008.

Explanation:
(.002)³ = .002 × .002 × .002
= 0.000004 × .002
= 0.000000008.

Question 21.
Jasper was planning to hand out flyers to his friends to spread the word about an upcoming charity event. He wanted to give his six friends enough flyers for them to each give a flyer to six of their own friends. How many flyers will Jasper need?
Answer:
Number of flyers Jasper needs =6.

Explanation:
Number of friends Jasper wants to give the flyers = 6.
Number of flyers he was to give to each = 1.
Number of flyers Jasper needs = Number of friends Jasper wants to give the flyers × Number of flyers he was to give to each
= 6 × 1
= 6.

Question 22.
Oren’s dad offered him a choice of $13.00 total to buy eight newspapers, or 4 cents for the first newspaper, 8 cents for the second newspaper, 16 cents for the third newspaper, and so on up to the eighth newspaper. Which choice of payment should Oren take? Why?
Answer:
$10.20 choice of payment should Oren take because its less cost price than $13.00 offer.

Explanation:
Cost of total to buy eight newspaper Oren’s dad offered him a choice = $13.00.
Cost of first newspaper = 4 cents.
Cost of second newspaper = 8 cents.
Cost of third newspaper = 16 cents.
Cost of fourth newspaper = 32 cents.
Cost of fifth newspaper = 64 cents.
Cost of sixth newspaper = 128 cents.
Cost of seventh newspaper = 256 cents.
Cost of eighth newspaper = 512 cents.
Cost of 8 newspapers = Cost of first newspaper + Cost of second newspaper + Cost of third newspaper + Cost of fourth newspaper + Cost of fifth newspaper + Cost of sixth newspaper + Cost of seventh newspaper + Cost of eighth newspaper
= 4 cents + 8 cents + 16 cents + 32 cents + 64 cents + 128 cents + 256 cents + 512 cents
= 12cents + 16 cents + 32 cents + 64 cents + 128 cents + 256 cents + 512 cents
= 28 cents + 32 cents + 64 cents + 128 cents + 256 cents + 512 cents
= 60 cents + 64 cents + 128 cents + 256 cents + 512 cents
= 124 cents + 128 cents + 256 cents + 512 cents
= 252 cents + 256 cents + 512 cents
= 508 cents + 512 cents
= 1,020 cents.
Conversion:
1 dollar = 100 cents.
=> 1020 cents = 1020 ÷ 100
=> $10.20.

Practice the questions of McGraw Hill Math Grade 4 Answer Key PDF Posttest to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 4 Posttest Answer Key

Fill in each blank. Use the best term from the word bank. You may not use every term.

Question 1.
A(n) ______________ is a group of numbers with an operation symbol.
Answer:
An equation is a group of numbers with an operation symbol.

Question 2.
To find the difference between two numbers, you ____________.
Answer:
To find the difference between two numbers, you subtract.

Question 3.
You ____________ to find out how many in all.
Answer:
You add to find out how many in all.

Question 4.
The ______________ is the number below the fraction bar in a fraction.
Answer:
The denominator is the number below the fraction bar in a fraction.

Question 5.
A(n) _____________ has four equal sides and four equal angles.
Answer:
A square has four equal sides and four equal angles.

Question 6.
A(n) ______________ is the number of equal groups a dividend is divided by in a division problem.
Answer:
A whole is the number of equal groups a dividend is divided by in a division problem.

Question 7.
An array is a good way to show _______________ of objects.
Answer:
An array is a good way to show equal groups of objects.

Question 8.
A(n) _______________ is a shape that has zero sides and zero angles.
Answer:
A circle is a shape that has zero sides and zero angles.

Question 9.
You ______________ to find a number close to an exact amount.
Answer:
You estimate to find a number close to an exact amount.

Question 10.
You ______________ to find how many equal groups a number can be divided into.
Answer:
You divide to find how many equal groups a number can be divided into.

Question 11.
The answer to an addition problem is called the _____________.
Answer:
The answer to an addition problem is called the sum.

Question 12.
You can _______________ two numbers together to find the product.
Answer:
You can multiply two numbers together to find the product.

Question 13.
A(n) _______________ is a symbol used to name part of a whole.
Answer:
A fraction is a symbol used to name part of a whole.

Question 14.
The _______________ is the answer to a division problem.
Answer:
The quotient is the answer to a division problem.

Write each number in standard form.

Question 15.
7 tens
Answer:
70

Explanation:
The standard form of 7 tens is 70.

Question 16.
50 + 1
Answer:
51

Explanation:
The standard form of 50 + 1 = 51.

Question 17.
seventy-seven
Answer:
77

Explanation:
The standard form of seventy-seven is 77.

Question 18.
nineteen
Answer:
19

Explanation:
The standard form of nineteen is 19.

Question 19.
7 hundreds 1 ten 4 ones
Answer:
714

Explanation:
The standard form of 7 hundreds 1 ten 4 ones is 714.

Question 20.
800 + 8
Answer:
808

Explanation:
The standard form of 800 + 8 is 808.

Question 21.

Answer:
104

Explanation:
There is 1 hundreds block and 4 ones cubes
The standard form of the given quick picture is 104.

Question 22.

Answer:
43

Explanation:
There are 4 tens sticks and 3 ones cube
The standard form of the given quick picture is 43.

Question 23.

Answer:
37

Explanation:
There are 3 tens sticks and 7 ones cube
The standard form of the given quick picture is 37.

Skip count. Write the missing numbers.

Question 24.
8, 10, 12, _________, ___________, __________, 20
Answer:
14, 16, 18,

Explanation:
The numbers in the pattern are skip counts of 2
The missing numbers are 14, 16, 18.

Question 25.
70, 80, 90, _________, _________, _________, 130
Answer:
100, 110, 120

Explanation:
The numbers in the pattern are skip counts of 10
The missing numbers are 100, 110, 120.

Question 26.
75, 80, 85, _________, _________, _________, 105
Answer:
90, 95, 100

Explanation:
The numbers in the pattern are skip counts of 5
The missing numbers are 90, 95, 100

Compare each pair of numbers. Write <,> , or = for each.

Question 27.
496 398
Answer:
496  398

Explanation:
The number 496 is greater than 398.

Question 28.
457,824 457,844
Answer:
457,824 457,844

Explanation:
The number 457,824 is less than 457,844.

Question 29.
\(\frac{3}{6}\) \(\frac{1}{2}\)
Answer:
\(\frac{3}{6}\)  \(\frac{1}{2}\)

Explanation:
The number \(\frac{3}{6}\)  is equal to  \(\frac{1}{2}\).

Question 30.
14 41
Answer:
14 41

Explanation:
The number 14 is less than 41.

Question 31.
5.4 5.0
Answer:
5.4 5.0

Explanation:
The number 5.4 is greater than 5.0.

Question 32.
592 595
Answer:
592 595

Explanation:
The number 592 is less than 595.

Add. Write the sum.

Question 33.

Answer:

Explanation:
The sum of 356 and 871 is 1227.

Question 34.

Answer:

Explanation:
The sum of 18437 and 31854 is 50291.

Question 35.

Answer:

Explanation:
The sum of 36792 and 9654 is 46446.

Question 36.

Answer:

Explanation:
The sum of 63121 and 42190 is 105311.

Question 37.

Answer:

Explanation:
The sum of 562 ,711 and 631 is 1904.

Question 38.

Answer:

Explanation:
The sum of 25582 ,72990 and 31854 is 130426.

Question 39.

Answer:

Explanation:
The sum of 5612 , 6453 and 8904 is 20969.

Question 40.

Answer:

Explanation:
The sum of 953 ,110 and 872 is 1935.

Subtract. Write the difference.

Question 41.

Answer:

Explanation:
The difference between 529228 and 337643 is 191585.

Question 42.

Answer:

Explanation:
The difference between 815027 and 56774 is 758253.

Question 43.

Answer:

Explanation:
The difference between 437184 and 72138 is 365046.

Question 44.

Answer:

Explanation:
The difference between 90543 and 90251 is 292.

Round to the nearest thousand to estimate the sum or difference.

Question 45.
82,019 – 78,901 = ____________
Answer:
3000

Explanation:
82019 – 78901
I rounded the numbers to the nearest thousand to estimate the difference
= 82000 – 79000
= 3000
So, the estimated difference between the given numbers is 3000.

Question 46.
351,092 + 238,091 = ____________
Answer:
589000

Explanation:
351,092 + 238,091
I rounded the numbers to the nearest thousand to estimate the sum
= 351000 + 238000
= 589000
So, the estimated sum of the given numbers is 3000.

Round to the nearest hundred to estimate the sum or difference.

Question 47.
74,521 + 676,890 = ____________
Answer:
751400

Explanation:
74,521 + 676,890
I rounded the numbers to the nearest hundred to estimate the sum
= 74500 + 676900
= 751400
So, the estimated sum of the given numbers is 751400.

Question 48.
90,932 – 65,721 = _____________
Answer:
25200

Explanation:
90,932 – 65,721
I rounded the numbers to the nearest hundred to estimate the difference
= 90900 – 65700
= 25200
So, the estimated difference between the given numbers is 25200.

Solve.

Question 49.
A rectangular yard is 8 meters long and 5 meters wide. What is the perimeter of the yard?
Answer:
26 meters

Explanation:
A rectangular yard is 8 meters long and 5 meters wide
l = 8, b = 5
Perimeter of a rectangle = 2l + 2b
= (2×8) + (2×5)
= 16 + 10
= 26
So, perimeter of the rectangular yard is 26 meters.

Question 50.
A sandbox measures 7 feet long and 5 feet wide. What is the area of the sandbox?
Answer:
35 square feet

Explanation:
A sandbox measures 7 feet long and 5 feet wide
l = 7, b = 5
Area of the rectangle = l x b
= 7 x 5
= 35 square feet
So, area of the sandbox is 35 square feet.

Find the product.

Question 51.
4 × 0 = ___________
Answer:
0

Explanation:
Any number multiplied by 0 is 0
So, 4 x 0 = 0.

Question 52.
2 × 8 = ___________
Answer:
16

Explanation:
The product of 2 and 8 is 16
So, 2 x 8 = 16.

Question 53.
9 × 8 = ____________
Answer:
72

Explanation:
The product of 9 and 8 is 72
So, 9 x 8 = 72.

Question 54.
12 × 4 = __________
Answer:
48

Explanation:
The product of 12 and 4 = 48
So, 12 x 4 = 48.

Question 55.
10 × 5 = _____________
Answer:
50

Explanation:
The product of 10 and 5 is 50
so, 10 x 5 = 50.

Question 56.
5 × 1 = ______________
Answer:
5

Explanation:
The product of 5 and 1 is 5
So, 5 x 1 = 5.

Find the quotient.

Question 57.
12 ÷ 3 = ____________
Answer:

Explanation:
12 ÷ 3 = 4
The quotient is 4.

Question 58.
32 ÷ 4 = ____________
Answer:

Explanation:
32 ÷ 4 = 8
The quotient is 8.

Question 59.
35 ÷ 7 = _____________
Answer:

Explanation:
35 ÷ 7 = 5
The quotient is 5.

Question 60.
132 ÷ 12 = _____________
Answer:

Explanation:
132 ÷ 12 = 11
The quotient is 11.

Question 61.
88 ÷ 11 = _____________
Answer:

Explanation:
88 ÷ 11 = 8
The quotient is 8.

Question 62.
60 ÷ 10 = _______________
Answer:

Explanation:
60 ÷ 10 = 6
The quotient is 6.

Question 63.
Which multiplication property is shown in this sentence? 5 × (12 + 15) = (5 × 12)+ (5 × 15)
Answer:
Distributive property

Explanation:
5 × (12 + 15) = (5 × 12)+ (5 × 15) is an example of distributive property of multiplication.

Identify each number as prime or composite.

Question 64.
6 ___________
Answer:
Composite number

Explanation:
6 is a composite number.

Question 65.
11 ______________
Answer:
Prime number

Explanation:
11 is a prime number.

Question 66.
11 ____________
Answer:
Prime number

Explanation:
11 is a prime number.

Question 67.
66 ______________
Answer:
Composite number

Explanation:
66 is a composite number.

Find all the factor pairs of each number.

Question 68.
12 ______________
Answer:
1 x 12, 2 x 6, 3 x 4

Explanation:
The factors pairs of the number 12 are 1 x 12, 2 x 6, 3 x 4.

Question 69.
19 ______________
Answer:
1 x 19

Explanation:
There is only 1 pair of factors for the number 19
The factor pair of 19 is 1 x 19.

Solve. Write the expressions you used and the answers.

Question 70.
Ms. Neal is making a large pot of stew for a family reunion. The recipe calls for 4 times as many peas as carrots. If she uses 2 cups of carrots, how many cups of peas will she need?
Answer:
8 cups of peas

Explanation:
Ms. Neal is making a large pot of stew for a family reunion
The recipe calls for 4 times as many peas as carrots
She uses 2 cups of carrots
So, multiply 4 and 2
4 x 2 = 8
So, Ms. Neal need 8 cups of peas.

Question 71.
A deli has 6 times as many bottles of juice as pickles. If the deli has 54 bottles of juice, how many pickles are in the deli? Use the variable y for the number of pickles.
Answer:
9 pickles

Explanation:
A deli has 6 times as many bottles of juice as pickles
If the deli has 54 bottles of juice
The equation that helps to solve the problem is
6y = 54
y = 54 ÷ 6
y = 9
So, there are 9 pickles.

Write an equivalent fraction for each.

Question 72.
\(\frac{3}{4}\)
Answer:
\(\frac{6}{8}\)

Explanation:
The fraction \(\frac{3}{4}\) is equivalent to \(\frac{6}{8}\).

Question 73.
\(\frac{24}{40}\)
Answer:
\(\frac{24}{40}\)

Explanation:
The equivalent fraction for \(\frac{24}{40}\) is \(\frac{12}{20}\).

Question 74.
\(\frac{4}{36}\)
Answer:
\(\frac{2}{18}\)

Explanation:
The equivalent fraction for \(\frac{4}{36}\) is \(\frac{2}{18}\).

Add or subtract. Write your answers in simplest form.

Question 75.
\(\frac{2}{5}\) + \(\frac{1}{5}\) = ______________
Answer:
\(\frac{3}{5}\)

Explanation:
\(\frac{2}{5}\) + \(\frac{1}{5}\) = \(\frac{3}{5}\).

Question 76.
\(\frac{3}{10}\) + \(\frac{5}{10}\) = ______________
Answer:
\(\frac{8}{10}\)

Explanation:
\(\frac{3}{10}\) + \(\frac{5}{10}\)  = \(\frac{8}{10}\)

Question 77.
78\(\frac{9}{15}\) – 47\(\frac{5}{15}\) = ______________
Answer:
31\(\frac{4}{15}\)

Explanation:
78\(\frac{9}{15}\) – 47\(\frac{5}{15}\) = 31\(\frac{4}{15}\).

Write each fraction as a decimal.

Question 78.
\(\frac{5}{10}\)
Answer:
0.5

Explanation:
The decimal of the fraction \(\frac{5}{10}\) is 0.5.

Question 79.
\(\frac{30}{100}\)
Answer:
0.3

Explanation:
The decimal of the fraction \(\frac{30}{100}\) is 0.3.

Question 80.
\(\frac{78}{100}\)
Answer:
0.78

Explanation:
The decimal of the fraction \(\frac{78}{100}\) is 0.78.

Question 81.
\(\frac{40}{50}\)
Answer:
0.8

Explanation:
The decimal for he fraction \(\frac{40}{50}\) is 0.8.

Question 82.
Plot 1.20 on the number line. Label it A.
Answer:

Explanation:
I plotted the number 1.20 on the number line and labeled it A.

Question 83.
Plot 1\(\frac{70}{100}\) on the number line. Label it B.
Answer:

Explanation:
The decimal of the fraction 1\(\frac{70}{100}\) is 1.7
I plotted the number 1.7 on the number line and labeled it B.

Question 84.
Plot 1\(\frac{2}{5}\) on the number line. Label it C.
Answer:

Explanation:
The decimal of the fraction 1\(\frac{2}{5}\) is 1.4
I plotted the number 1.4 on the number line and labeled it C.

Multiply to find each missing number.

Question 85.
3 m = _____________ cm
Answer:
300 cm

Explanation:
1 meter = 100 cm
3 m = 3 x 100
= 300 cm
So, 3 m = 300 cm.

Question 86.
62 ft = ______________ in
Answer:
744 in

Explanation:
1 ft = 12 in
62 ft = 62 x 12
= 744
So, 62 ft = 744 in.

Question 87.
11 kg = ______________ g
Answer:
11000 g

Explanation:
1 kg = 1000 g
11 kg = 11 x 1000
= 1000 g
So, 11 kg = 11000 g.

Question 88.
Which figure is an obtuse angle? Place a check mark under the correct answer.

Answer:

Explanation:
The first figure is an obtuse angle
So, i placed a check mark under the first figure.

Question 89.
Which figure is a line segment? Place a check mark under the correct answer.

Answer:

Explanation:
The third figure is a line segment
So, i placed a check mark under the third figure.

Question 90.
Which figure is an acute isosceles triangle? Place a check mark under the correct answer.

Answer:

Explanation:
The second figure is an acute isosceles triangle
So, i placed a check mark under second figure.

Question 91.
Which pair of lines is perpendicular? Place a check mark under the correct answer.

Answer:

Explanation:
The second figure is a pair of perpendicular lines
So, i placed a check mark under the second figure.

Use a protractor to measure each angle. You may need to extend its sides.

Question 92.

Answer:

Explanation:
The measure of the given angle is 40°.

Question 93.

Answer:

Explanation:
The measure of the given angle is 150°.

Solve.

Question 94.
A mechanic uses a wrench to turn a bolt. He turns it 62°. After a few minutes, he turns it another 18°. How many degrees did he turn the bolt altogether?
Answer:
80°

Explanation:
A mechanic uses a wrench to turn a bolt. He turns it 62°
After a few minutes, he turns it another 18°
Add 62 and 18
62 + 18 = 80°
So, the mechanic turned the blot for 80°.

Question 95.
A wheel spins forward 122°. Then it spins backward 34°. At what degree measure does the wheel stop spinning?
Answer:
98°

Explanation:
A wheel spins forward 122°
Then it spins backward 34°
Subtract 34 from 122
112° – 34° = 98°
The wheel stop spinning at 98°.

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 7 Test are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Chapter 7 Test Answer Key

Write the following as division problems. Find the quotient.

Question 1.
\(\frac{4}{2}\) ________________
Answer:
2
Dividing 4 by 2 we get 2 as quotient.

Question 2.
\(\frac{5}{3}\) _________________
Answer:
1.6666
Dividing 5 by 3 we get 1.666

Question 3.
\(\frac{8}{5}\) _________________
Answer:
1.6
Dividing 8 by 5 we get 1.6

Question 4.
\(\frac{12}{3}\) _________________
Answer:
4
Dividing 12 by 3 we get 4

Multiply whole numbers by fractions.

Question 5.
6 × \(\frac{1}{8}\) = _______________
Answer:
(3/4)

Explanation:
6 × (1/8)
= (6/8)
= (3/4)

Question 6.
4 × \(\frac{1}{2}\) = _______________
Answer:
2

Explanation:
4 × (1/2)
=2

Question 7.
12 × \(\frac{1}{3}\) = _______________
Answer:
4

Explanation:
12 × (1/3)
= 12/3
= 4

Question 8.
9 × \(\frac{2}{3}\) = _______________
Answer:
6

Explanation:
9 × (2/3)
= 3 × 2
= 6

Question 9.
5 × \(\frac{3}{10}\) = _______________
Answer:
(3/2)

Explanation:
5 × (3/10)
= (3/2)

Question 10.
4 × \(\frac{3}{4}\) = _______________
Answer:
3

Explanation:
4 × (3/4)
= 3

Find the products.

Question 11.
\(\frac{1}{4}\) × \(\frac{1}{8}\) = _______________
Answer:
(1/32)

Explanation:
(1/4) × (1/8)
= (1/32)

Question 12.
\(\frac{1}{6}\) × \(\frac{1}{12}\) = _______________
Answer:
(1/12)

Explanation:
(1/6) × (1/2)
= (1/12)

Question 13.
\(\frac{1}{2}\) × \(\frac{1}{2}\) = _______________
Answer:
1/4

Explanation:
(1/2) × (1/2)
= 1/4

Question 14.
\(\frac{2}{3}\) × \(\frac{2}{3}\) = _______________
Answer:
2/3

Explanation:
(2/3) × (2/3)
= (4/9)

Question 15.
\(\frac{2}{3}\) × \(\frac{3}{4}\) = _______________
Answer:
(1/2)

Explanation:
(2/3) × (3/4)
= (1/2)

Question 16.
\(\frac{3}{4}\) × \(\frac{4}{5}\) = _______________
Answer:
(3/5)

Explanation:
(3/4) × (4/5)
= (3/5)

Tell whether the product will be less than or greater than the whole number being multiplied. Then multiply to prove your answer.

Question 17.
7 × \(\frac{7}{6}\)
Estimate: _______________
Product: _______________
Answer:
Estimate: More than 8

Explanation:
7 × (7/6)
=  (49/6)
Product: 8.1666
Estimate: More than 8

Question 18.
7 × \(\frac{6}{7}\)
Estimate: _______________
Product: _______________
Answer:
Estimate: equal to 6

Explanation:
7 × (6/7)
= 6
Product: 6
Estimate: equal to 6

Question 19.
9 × \(\frac{4}{3}\)
Estimate: _______________
Product: _______________
Answer:
Estimate: equal to 12

Explanation:
9 × (4/3)
= 3 × 4
= 12
Product: 12
Estimate: equal to 12

Question 20.
9 × \(\frac{13}{14}\)
Estimate: _______________
Product: _______________
Answer:
Estimate: More than 8

Explanation:
9 × (13/14)
= (117/14)
= 8.3571
Product: 8.3571
Estimate: More than 8

Question 21.
11 × \(\frac{1}{99}\)
Estimate: _______________
Product: _______________
Answer:
Estimate: More than 0

Explanation:
11 × (1/99)
= (11/99)
= (1/9)
Product: 0.1111
Estimate: More than 0

Question 22.
11 × \(\frac{98}{99}\)
Estimate: _______________
Product: _______________
Answer:
Estimate: More than 10
Explanation:
11 × (98/99)
= (98/9)
= 10.8888
Product: 10.8888
Estimate: More than 10

Solve.

Question 23.
Ricky takes a survey of fifth graders for his Health and Nutrition class. He finds that in his class of 5 24 students, \(\frac{5}{8}\) drink more than one glass of milk a day. How many students drink more than one glass of milk a day?
Answer:
327.5

Explanation:
Number of students in Ricky’s class = 524
Students drink one glass of milk a day = (5/8) of the students
= (5/8) × 524
= (2620/8)
= 1310/4
= 655/2
= 327.5

Question 24.
Penny takes the same survey of sixth graders. She finds that in her class of 29 students, \(\frac{3}{4}\) drink more than one glass of milk a day. How can Penny describe her results?
Answer:
21.75

Explanation:
Number of students = 29
Students that drink one glass of milk a day = (3/4) of students
= (3/4) × 29
= 21.75

Question 25.
Tyler records how many glasses of milk a group of 20 students drink in a day. He writes the following results on a sheet of paper: 2, 4, 3, 3, 4, 2, 2, 3,1,4, 4, 2, 3, 2, 4, 3, 4, 3, 4, and 1. Do most of these students drink 1-2 glasses of milk or 3-4 glasses of milk? Make a table to find the solution.
Answer:
Most of the students drink 3-4 glasses of milk

Explanation:
Number of students = 20
Results of the students = 2, 4, 3, 3, 4, 2, 2, 3,1,4, 4, 2, 3, 2, 4, 3, 4, 3, 4, and 1

Question 26.
What multiplication problem is represented by these arrays?

Answer:
(1/216)

Explanation:
(1/6) × (1/6) × (1/6)
= (1/36) × (1/6)
= (1/216)

Question 27.
April plants a garden on 2\(\frac{1}{4}\) acres. She devotes \(\frac{2}{5}\) of the entire garden to pumpkins. How many acres does April use for pumpkins?
Answer:
(9/10)

Explanation:
Total acres April plants a garden = 2 (1/4) = (9/4)
she devotes garden to pumpkin = (2/5) of total acres
= (2/5) × (9/4)
= (9/10)

Question 28.
Clint plants an apple tree and a peach tree. The apple tree is 3\(\frac{1}{5}\) feet tail. The peach tree is 3 times as tall as the apple tree. How tall is Clint’s peach tree?
Answer:
9(3/5)

Explanation:
Apple tree feet tail = 3(1/5) = (16/5)
Peach tree is 3 times tall than apple tree = 3 × (16/5)
= (48/5)
= 9(3/5)

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 7 Lesson 9 Word Problems with Multiplying Fractions and Mixed Numbers are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 7 Lesson 9 Word Problems with Multiplying Fractions and Mixed Numbers

Solve

Solve the problem using the method you prefer. Show your work.

Question 1.
One booth at the farmer’s market started the day with 4\(\frac{3}{5}\) bushels of apples. By the end of the day, \(\frac{5}{6}\) of the apples were sold. How many bushels of apples were sold?
Answer:
(23/6) or 3(5/6) bushels of apples were sold.

Explanation:
Number of bushels of apples = 4(3/5) = (23/5)
Number of apples sold = (5/6)
Number of Bushels of apples sold = (5/6) × (23/5)
= (23/6)
= 3(5/6)

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 7 Lesson 8 Multiplying by Fractions Greater Than or Less Than 1 are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 7 Lesson 8 Multiplying by Fractions Greater Than or Less Than 1

Solve

Tell whether the product will be less than or greater than the whole number being multiplied. Then multiply to prove your answer.

Question 1.
4 × \(\frac{6}{5}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: more than 4

Question 2.
5 × \(\frac{7}{6}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: More than 5

Explanation:
5 × (7/6)
Product:  5.8333
Estimate: More than 5

Question 3.
7 × \(\frac{3}{3}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: 7

Explanation:
7 × (3/3)
= 7 × 1
=7
Product: 7
Estimate: 7

Question 4.
7 × \(\frac{5}{3}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: More than 11

Explanation:
7 × (5/3)
= 35/3
Product: 11.6666
Estimate: More than 11

Tell whether the product will be less than or greater than the whole number being multiplied. Then multiply to prove your answer.

Question 5.
4 × \(\frac{5}{6}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: More than 3

Explanation:
4 × (5/6)
= 20/6
Product: 3.3333
Estimate: More than 3

Question 6.
9 × \(\frac{7}{8}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: More than 7

Explanation:
9 × (7/8)
= (63/8)
Product: 7.875
Estimate: More than 7

Question 7.
11 × \(\frac{15}{16}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: More than 27

Explanation:
11 × (15/16)
= (165/16)
Product:  27.5
Estimate: More than 27

Question 8.
9 × \(\frac{3}{16}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: More than 1

Explanation:
9 × (3/16)
= (27/16)
Product: 1.6875
Estimate: More than 1

Question 9.
9 × \(\frac{7}{16}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: More than 3

Explanation:
9 × (7/16)
= (63/16)
Product: 3.9375
Estimate: More than 3

Question 10.
9 × \(\frac{15}{16}\)
Estimate: ________________
Product: ________________
Answer:
Estimate: More than 8

Explanation:
9 × (15/16)
= (135/16)
Product: 8.4375
Estimate: More than 8

Draw arrays to model the following and then multiply.

Question 11.
Urban Steel Company is loading several old steel beams. The beams are 12 feet long and \(\frac{4}{3}\) feet wide. Their competitor, Second Story Steel Company, is also loading several steel beams. Second Story Steel’s beams are 12 feet long and \(\frac{3}{4}\) foot wide. How do the areas of these steel beams compare? Label your arrays and show your work.
DRAWING
Answer:
The area of the beams of Urban Steel Company = 16
The area of the beams of Story Steel Company = 9

Explanation:
The length of the beams of Urban Steel Company= 12 and (4/3)
The length of the beams of Story Steel Company = 12 and (3/4)
The area of the beams of Urban Steel Company = 12 × (4/3)
= (48/3)
= 16
The area of the beams of Story Steel Company = 12 × (3/4)
= (36/4)
= 9

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 7 Lesson 7 Comparing Product Sizes are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 7 Lesson 7 Comparing Product Sizes

Solve

Describe how the products compare. Do not multiply. Explain your answer.

Question 1.
How will 4 × 12 compare to 4 × 6?
Description: It will be ___________ as great.
Explanation: 12 is twice as great as ____________.
Answer:
Description: It will be twice as great.

Explanation:
12 is twice as great as 6.
6 × 2 = 12, twice the number.

Question 2.
How will 8 × 10 compare to 8 × 5?
Description: It will be ____________ as ____________.
Explanation: 10 is _____________ as great as _____________.
Answer:
Description: It will be twice as great.

Explanation:
10 is twice as great as 5.
5 × 2 = 10, twice the number.

Question 3.
How will 30 × 24 compare to 30 × 6?
Description: It will be ____________ as ____________.
Explanation: 24 is ____________ than ____________.
Answer:
Description: It will be 4 times as great.

Explanation:
24 is 4 times as great as 6.
6 × 4 = 24, 4 times the number.

Describe how the product sizes compare. Do not multiply.

Question 4.
How will 35 × 35 compare to 35 × 70?
Answer:
Twice greater than 35.

Explanation:
35 is twice less than 70.
35 × 2 = 70

Question 5.
How will 25 × 55 compare to 5 × 55?
Answer:
5 times of the number 5.

Explanation:
25 is 5 times of the number 5.
5 × 5 = 25

Question 6.
How will 20 × 90 compare to 100 × 90?
Answer:
5 times of the number 20.

Explanation:
100 is 5 times of the number 20.
20 × 5 = 100

Question 7.
How will 12 × 60 compare to 6 × 60?
Answer:
Twice the number 6.

Explanation:
12 is twice as great as 6.
6 × 2 = 12, twice the number.

Question 8.
How will 500 × 473 compare to 1,500 × 473?
Answer:
Thrice the number 500.

Explanation:
1500 is thrice the number 500.
500 × 3 = 1500, Thrice the number.

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 7 Lesson 6 Finding Area with Fractions are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 7 Lesson 6 Finding Area with Fractions

Solve

Draw a grid. Then find the area of each rectangle.

Question 1.
4 units wide and \(\frac{3}{4}\) unit tall
area = ____________
Answer:
\(\frac{12}{4}\) = 3 square units

Question 2.
6 units tall and unit \(\frac{1}{3}\) wide
area = ________________
Answer:
2 Square units

Explanation:
Area = 6 × (1/3) = 2 Square units

Question 3.
4 units long and \(\frac{1}{8}\) unit wide
area = _________________
Answer:
Area = (1/2)  Square units

Explanation:
Area = 4 × (1/8)
= (1/2) Square units

Question 4.
1 unit long and \(\frac{1}{3}\) unit wide
area = _________________
Answer:
(1/3) Square units

Explanation:
Area = 1 × (1/3)
= (1/3) Square units

Multiply to find the area of each rectangle.

Question 5.
5 yd long × \(\frac{2}{3}\) yd wide
area = ________________
Answer:
(10/3) Square units

Explanation:
Area = 5 × (2/3)
= (10/3) Square units

Question 6.
8 m long × \(\frac{2}{5}\) m wide
area = ________________
Answer:
(16/5) Square units

Explanation:
Area = 8 × (2/5)
= (16/5) Square units

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 7 Lesson 5 Multiplying a Fraction by a Fraction are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 7 Lesson 5 Multiplying a Fraction by a Fraction

Solve

Find the product. Use any model you want to help solve each problem.

Question 1.
\(\frac{1}{4}\) × \(\frac{1}{8}\) _____________
Answer:
\(\frac{1}{32}\)

Question 2.
\(\frac{1}{6}\) × \(\frac{1}{2}\) _____________
Answer:
(1/12

Explanation:
(1/6) × (1/2) = (1/12)

Question 3.
\(\frac{1}{2}\) × \(\frac{1}{2}\) _____________
Answer:
(1/4)

Explanation:
(1/2) × (1/2) = (1/4)

Question 4.
\(\frac{1}{2}\) × \(\frac{2}{3}\) _____________
Answer:
(1/3)

Explanation:
(1/2) × (2/3) =(1/3)

Question 5.
\(\frac{1}{3}\) × \(\frac{3}{4}\) _____________
Answer:
(1/4)

Explanation:
(1/3) × (3/4) = (1/4)

Question 6.
\(\frac{1}{4}\) × \(\frac{4}{5}\) _____________
Answer:
(1/5)

Explanation:
(1/4) × (4/5) = (1/5)

Question 7.
\(\frac{2}{3}\) × \(\frac{1}{3}\) _____________
Answer:
(2/9)

Explanation:
(2/3) × (1/3) = (2/9)

Question 8.
\(\frac{3}{5}\) × \(\frac{1}{5}\) _____________
Answer:
(3/25)

Explanation:
(3/5) × (1/5) = (3/25)

Question 9.
\(\frac{3}{4}\) × \(\frac{4}{5}\) _____________
Answer:
(3/5)

Explanation:
(3/4) × (4/5) = (3/5)

Multiply.

Question 10.
\(\frac{5}{12}\) × \(\frac{2}{3}\) = _____________
Answer:
(5/18)

Explanation:
(5/12) × (2/3) = (5/18)

Question 11.
\(\frac{2}{15}\) × \(\frac{3}{5}\) = _____________
Answer:
(2/25)

Explanation:
(2/15) × (3/5) = (2/25)

Question 12.
\(\frac{3}{8}\) × \(\frac{3}{8}\) = _____________
Answer:
(9/64)

Explanation:
(3/8) × (3/8) = (9/64)

Question 13.
\(\frac{4}{5}\) × \(\frac{4}{5}\) = _____________
Answer: (16/25)

Explanation:
(4/5) × (4/5) = (16/25)

Question 14.
\(\frac{5}{6}\) × \(\frac{2}{3}\) = _____________
Answer:
(5/9)

Explanation:
(5/6) × (2/3) = (5/9)

Question 15.
\(\frac{5}{12}\) × \(\frac{3}{4}\) = _____________
Answer:
(5/16)

Explanation:
(5/12) × (3/4) = (5/16)

Question 16.
\(\frac{2}{7}\) × \(\frac{7}{12}\) = _____________
Answer:
(1/6)

Explanation:
(2/7) × (7/12) = (1/6)

Question 17.
\(\frac{3}{10}\) × \(\frac{1}{5}\) = _____________
Answer:
(3/50)

Explanation:
(3/10) × (1/5) = (3/50)

Question 18.
\(\frac{3}{11}\) × \(\frac{1}{4}\) = _____________
Answer:
(3/44)
Explanation:
(3/11) × (1/4) = (3/44)

Question 19.
\(\frac{3}{10}\) × \(\frac{1}{4}\) = _____________
Answer: \(\frac{3}{40}\)

Explanation:
(3/10) × (1/4) = (3/40)

Question 20.
\(\frac{3}{8}\) × \(\frac{1}{4}\) = _____________
Answer:
(3/32)

Explanation:
(3/8) × (1/4) = (3/32)

Question 21.
\(\frac{3}{5}\) × \(\frac{1}{4}\) = _____________
Answer:
(3/20)

Explanation:
(3/5) × (1/4) = (3/20)

Solve. Use any model you want to help you solve.

Question 22.
Ed used \(\frac{4}{5}\) of a box of floor tiles. Two-thirds of the tiles he used are green. What fraction of the tiles is green?
Answer:
(8/15)

Explanation:
Number of tiles = (4/5) of the total titles
Number of green tiles = (2/3)rd of the tiles
= (2/3) × (4/5)
= (8/15)

Question 23.
Marge replaces \(\frac{2}{3}\) of the water pipes in her home. Three-eighths of the pipe she uses is copper. What fraction of the pipe is copper?
Answer:
(1/4)

Explanation:
Number of water pipes Marge used in her home = (2/3)
Copper pipes she used = (3/8)th of the total pipes
= (3/8) × (2/3)
= (1/4)

Question 24.
One-half the wood trim in a dining room is oak. Five-sixths of the oak trim is recycled wood. What fraction of the wood trim is recycled?
Answer:
(5/12)

Explanation:
Wood trim in a dining room = 1/2
Recycled wood = (5/6) of the wood trim
= (5/6) × (1/2)
= (5/12)

Question 25.
Max used \(\frac{3}{8}\) of a roll of painter’s tape on the first floor of the house. About \(\frac{1}{4}\) of that tape was used in the kitchen. How much of the tape was used in the kitchen?
Answer:
(3/32)

Explanation:
Number of roll of painter’s tape = (3/8)
Tape used in the kitchen = (1/4) of the tape of painter’s tape
= (1/4) × (3/8)
= (3/32)

Question 26.
Kyle sketched this drawing on a piece of paper. What multiplication problem was he trying to model?

Answer:
(1/15)

Explanation:
(1/5) × (1/3) =(1/15)

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 7 Lesson 4 Multiplying a Whole Number by a Fraction are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 7 Lesson 4 Multiplying a Whole Number by a Fraction

Solve

Find the product. Use any model you like.

Question 1.
4 × \(\frac{1}{8}\) _______________
Answer:
\(\frac{4}{8}\) = \(\frac{1}{2}\)

Question 2.
6 × \(\frac{1}{2}\) _______________
Answer:
3

Explanation:
6 × (1/2) = (6/2) =3

Question 3.
12 × \(\frac{1}{2}\) _______________
Answer:
6

Explanation:
12 × (1/2) = (12/2) =6

Question 4.
9 × \(\frac{1}{3}\) _______________
Answer:
3

Explanation:
9 × (1/3) = (9/3) =3

Question 5.
5 × \(\frac{1}{10}\) _______________
Answer:
(1/2)

Explanation:
5 × (1/10) = (5/10) = (1/2)

Question 6.
3 × \(\frac{1}{3}\) _______________
Answer:
1

Explanation:
3 × (1/3) = (3/3) = 1

Question 7.
24 × \(\frac{1}{3}\) _______________
Answer:
8

Explanation:
24 × (1/3) = (24/3) = 8

Question 8.
32 × \(\frac{1}{4}\) _______________
Answer:
8

Explanation:
32 × (1/4) = (32/4) =8

Question 9.
45 × \(\frac{1}{9}\) _______________
Answer:
5

Explanation:
45 × (1/9) = (45/9) =5

Multiply

Question 10.
12 × \(\frac{2}{3}\) _______________
Answer:
8

Explanation:
12 × (2/3) = 4 × 2 = 8

Question 11.
15 × \(\frac{3}{5}\) _______________
Answer:
9

Explanation:
15 × (3/5)= 3 × 3 = 9

Question 12.
8 × \(\frac{3}{4}\) _______________
Answer:
6

Explanation:
8 × (3/4) = 2 × 3 =6

Question 13.
21 × \(\frac{2}{7}\) _______________
Answer:
6

Explanation:
21 × (2/7) = 3 × 2 = 6

Question 14.
6 × \(\frac{2}{3}\) _______________
Answer:
4

Explanation:
6 × (2/3) = 2 × 2 = 4

Question 15.
39 × \(\frac{2}{3}\) _______________
Answer:
26

Explanation:
39 × (2/3) = 13 × 2 = 26

Question 16.
24 × \(\frac{3}{8}\) _______________
Answer:
9

Explanation:
24 × (3/8) = 3× 3 = 9

Question 17.
30 × \(\frac{3}{5}\) _______________
Answer:
18

Explanation:
30 × (3/5) = 6 × 3 = 18

Question 18.
\(\frac{3}{11}\) × 44 _______________
Answer:
12

Explanation:
(3/11) × 44 = 3 × 4 = 12

Solve.

Question 19.
Maynard’s Mustard prepares 14 bottles of mustard for the farmer’s market. They also prepare \(\frac{3}{7}\) as much ketchup as mustard. How many bottles of ketchup do they prepare?
Answer:
6

Explanation:
Number of mustard bottles= 14
Number of ketchup bottles = (3/7)th of the mustard bottles
= (3/7) × 14
= 3 × 2
=6

Question 20.
Lydia made calzones for the market. She started with 5 cans of tomato sauce. She used \(\frac{2}{5}\) of the cans for the first batch of calzones. How many cans of tomato sauce did she use?
Answer:
2

Explanation:
Number of cans of  tomato sauce = 5
Number of cans she used = (2/5) of the cans
= (2/5) × 5
=2

Question 21.
From start to finish, the bakers at Bountiful Bread spend 10 hours making bread. They spend \(\frac{5}{6}\) of the time waiting for the bread to rise. How much time do they wait for the bread to rise?
Answer:
8.3 hours

Explanation:
Hours to make bread = 10
Waiting time for the bread to rise =  (5/6)th of the hours to make bread
= (5/6) × 10
= (5/3)× 5
= (25/3)
= 8.3 hours

All the solutions provided in McGraw Hill Math Grade 5 Answer Key PDF Chapter 7 Lesson 3 Multiplying Fractions are as per the latest syllabus guidelines.

McGraw-Hill Math Grade 5 Answer Key Chapter 7 Lesson 3 Multiplying Fractions

Solve

Complete the sketch. Find the product. Write your answer in their lowest terms.

Question 1.
Three-fourths of the drama class are boys. Two-thirds of the boys wear glasses. What fraction of the drama class represents boys wearing glasses?

Answer:
One half of the drama class are boys wearing glasses: \(\frac{3}{4}\) × \(\frac{2}{3}\) = \(\frac{6}{12}\) = \(\frac{1}{2}\)

Question 2.
Two-thirds of the actors in the play wear costumes. One fourth of the actors’ costumes need to be repaired. What fraction of the actors’ costumes need to be repaired?

Answer:
(1/6)

Explanation:
Actors in the paly need costume =(2/3)
Actors costume need to be repaired = (1/4)
Actors need to be repaired = (2/3) ×(1/4)
= (1/6)

Question 3.
Five-sixths of the students in the drama class take a bus to school. Three-fourths of those students take the same bus to school. What fraction of the drama class takes the same bus to school?

Answer:
(5/8)

Explanation:
Students that take the drama class = (5/6)
Students that take school bus = (3/4)
Students that takes drama class takes same school bus = (5/6) × (3/4) = (5/8)