Practice with the help of **Spectrum Math Grade 5 Answer Key Chapter 6 Pretest **regularly and improve your accuracy in solving questions.

## Spectrum Math Grade 5 Chapter 6 Pretest Answers Key

**Check What You Know**

**Multiply. Write answers in simplest form**.

Question 1.

a. \(\frac{1}{2}\) × \(\frac{1}{3}\) = ________________

Answer:

\(\frac{1}{6}\)

Explanation:

Given,

\(\frac{1}{2}\) × \(\frac{1}{3}\)

Multiply the numerators and denominators.

\(\frac{1 \times 1}{2 \times 3}\) = \(\frac{1}{6}\)

b. \(\frac{3}{4}\) × \(\frac{2}{7}\) = ________________

Answer:

\(\frac{3}{14}\)

Explanation:

Given,

\(\frac{3}{4}\) × \(\frac{2}{7}\)

Multiply the numerators and denominators.

\(\frac{3 \times 2}{4 \times 7}\) = \(\frac{6}{28}\)

Reduce to the simplest form.

\(\frac{3}{14}\)

c. \(\frac{1}{4}\) × \(\frac{4}{5}\) = ________________

Answer:

\(\frac{1}{5}\)

Explanation:

Given,

\(\frac{1}{4}\) × \(\frac{4}{5}\)

Multiply the numerators and denominators.

\(\frac{1 \times 4}{4 \times 5}\) = \(\frac{4}{20}\)

Reduce to the simplest form.

\(\frac{1}{5}\)

Question 2.

a. \(\frac{2}{5}\) × \(\frac{5}{8}\) = ________________

Answer:

\(\frac{1}{4}\)

Explanation:

Given,

\(\frac{2}{5}\) × \(\frac{5}{8}\)

Multiply the numerators and denominators.

\(\frac{2 \times 5}{5 \times 8}\) = \(\frac{10}{40}\)

Reduce to the simplest form.

\(\frac{1}{4}\)

b. \(\frac{4}{9}\) × \(\frac{1}{2}\) = ________________

Answer:

\(\frac{2}{9}\)

Explanation:

Given,

\(\frac{4}{9}\) × \(\frac{1}{2}\)

Multiply the numerators and denominators.

\(\frac{4 \times 1}{9 \times 2}\) = \(\frac{4}{18}\)

Reduce to the simplest form.

\(\frac{2}{9}\)

c. 5 × \(\frac{2}{7}\) = ________________

Answer:

1 \(\frac{3}{7}\)

Explanation:

Given,

5 × \(\frac{2}{7}\)

Write the whole number into fraction.

\(\frac{5}{1}\) × \(\frac{2}{7}\)

Multiply the numerators and denominators.

\(\frac{5 \times 2}{1 \times 7}\) = \(\frac{10}{7}\)

Reduce to the simplest form.

1 \(\frac{3}{7}\)

Question 3.

a. 3 × \(\frac{4}{8}\) = ________________

Answer:

1 \(\frac{1}{2}\)

Explanation:

Given,

3 × \(\frac{4}{8}\)

Write the whole number into fraction.

\(\frac{3}{1}\) × \(\frac{4}{8}\)

Multiply the numerators and denominators.

\(\frac{3 \times 4}{1 \times 8}\) = \(\frac{12}{8}\)

Reduce to the simplest form.

\(\frac{3}{2}\) = 1 \(\frac{1}{2}\)

b. \(\frac{4}{9}\) × 7 = ________________

Answer:

3 \(\frac{1}{9}\)

Explanation:

Given,

\(\frac{4}{9}\) × 7

Write the whole number into fraction.

\(\frac{4}{9}\) × \(\frac{7}{1}\)

Multiply the numerators and denominators.

\(\frac{4 \times 7}{9 \times 1}\) = \(\frac{28}{9}\)

Reduce to the simplest form.

3 \(\frac{1}{9}\)

c. \(\frac{3}{4}\) × 2 = ________________

Answer:

1 \(\frac{1}{2}\)

Explanation:

Given,

\(\frac{3}{4}\) × 2

Write the whole number into fraction.

\(\frac{3}{4}\) × \(\frac{2}{1}\)

Multiply the numerators and denominators.

\(\frac{3 \times 2}{4 \times 1}\) = \(\frac{6}{4}\)

Reduce to the simplest form.

\(\frac{3}{2}\) = 1 \(\frac{1}{2}\)

Question 4.

a. 2\(\frac{3}{4}\) × 2 = ________________

Answer:

5 \(\frac{1}{2}\)

Explanation:

Given,

2\(\frac{3}{4}\) × 2

convert the mixed fraction to improper fraction.

\(\frac{11}{4}\) × 2

Write the whole number into fraction.

\(\frac{11}{4}\) × \(\frac{2}{1}\)

Multiply the numerators and denominators.

\(\frac{11 \times 2}{4 \times 1}\) = \(\frac{22}{4}\)

Reduce to the simplest form.

\(\frac{11}{2}\) = 10 \(\frac{1}{2}\)

b. 1\(\frac{3}{8}\) × 3 = ________________

Answer:

4 \(\frac{1}{8}\)

Explanation:

Given,

1\(\frac{3}{8}\) × 3

Convert the mixed fraction to improper fraction.

\(\frac{11}{8}\) × 3

Write the whole number into fraction.

\(\frac{11}{8}\) × \(\frac{3}{1}\)

Multiply the numerators and denominators.

\(\frac{11 \times 3}{8 \times 1}\) = \(\frac{33}{8}\)

Reduce to the simplest form.

4 \(\frac{1}{8}\)

c. 1\(\frac{1}{2}\) × 2 = ________________

Answer:

3

Explanation:

Given,

1\(\frac{1}{2}\) × 2

convert the mixed fraction to improper fraction.

\(\frac{3}{2}\) × 2

Write the whole number into fraction.

\(\frac{3}{2}\) × \(\frac{2}{1}\)

Multiply the numerators and denominators.

\(\frac{3 \times 2}{2 \times 1}\) = \(\frac{6}{2}\)

Reduce to the simplest form as 3.

**Divide. Write answers in simplest form.**

Question 5.

a. 6 ÷ \(\frac{1}{10}\) = _______________

Answer:

60

Explanation:

Given,

6 ÷ \(\frac{1}{10}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{6}{1}\) ÷ \(\frac{1}{10}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{6}{1}\) × \(\frac{10}{1}\)

Multiply across numerators and denominators.

\(\frac{6 \times 10}{1 \times 1}\) = 60

b. \(\frac{1}{8}\) ÷ 14 = ______________

Answer:

\(\frac{1}{112}\)

Explanation:

Given,

\(\frac{1}{8}\) ÷ 14

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{8}\) ÷ \(\frac{14}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{8}\) × \(\frac{1}{14}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{8 \times 14}\) = \(\frac{1}{112}\)

c. 1 ÷ \(\frac{1}{4}\) = _______________

Answer:

4

Explanation:

Given,

1 ÷ \(\frac{1}{4}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{1}\) ÷ \(\frac{1}{4}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{1}\) × \(\frac{4}{1}\)

Multiply across numerators and denominators.

\(\frac{1 \times 4}{1 \times 1}\) = 4

Question 6.

a. \(\frac{1}{9}\) ÷ 2 = _______________

Answer:

\(\frac{1}{18}\)

Explanation:

Given,

\(\frac{1}{9}\) ÷ 2

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{9}\) ÷ \(\frac{2}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{9}\) × \(\frac{1}{2}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{9 \times 2}\) = \(\frac{1}{18}\)

b. \(\frac{1}{5}\) ÷ 6 = _______________

Answer:

\(\frac{1}{30}\)

Explanation:

Given,

\(\frac{1}{5}\) ÷ 6

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{5}\) ÷ \(\frac{6}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{5}\) × \(\frac{1}{6}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{5 \times }\) = \(\frac{1}{30}\)

c. 7 ÷ \(\frac{1}{4}\) = ________________

Answer:

28

Explanation:

Given,

7 ÷ \(\frac{1}{4}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{7}{1}\) ÷ \(\frac{1}{4}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{7}{1}\) × \(\frac{4}{1}\)

Multiply across numerators and denominators.

\(\frac{7 \times 4}{1 \times 1}\) = 28

Question 7.

a. \(\frac{1}{5}\) ÷ 4 = _______________

Answer:

\(\frac{1}{20}\)

Explanation:

Given,

\(\frac{1}{5}\) ÷ 4

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{5}\) ÷ \(\frac{4}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{5}\) × \(\frac{1}{4}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{5 \times 4}\) = \(\frac{1}{20}\)

b. 11 ÷ \(\frac{1}{8}\) = _______________

Answer:

88

Explanation:

Given,

11 ÷ \(\frac{1}{8}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{11}{1}\) ÷ \(\frac{1}{8}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{11}{1}\) × \(\frac{8}{1}\)

Multiply across numerators and denominators.

\(\frac{11 \times 8}{1 \times 1}\) = 88

c. \(\frac{1}{9}\) ÷ 2 = ________________

Answer:

\(\frac{1}{18}\)

Explanation:

Given,

\(\frac{1}{9}\) ÷ 2

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{9}\) ÷ \(\frac{2}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{9}\) × \(\frac{1}{2}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{9 \times 2}\) = \(\frac{1}{18}\)

Question 8.

a. 3 ÷ \(\frac{1}{5}\) = ________________

Answer:

15

Explanation:

Given,

3 ÷ \(\frac{1}{5}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{3}{1}\) ÷ \(\frac{1}{5}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{3}{1}\) × \(\frac{5}{1}\)

Multiply across numerators and denominators.

\(\frac{3 \times 5}{1 \times 1}\) = 15

b. \(\frac{1}{3}\) ÷ 8 = ________________

Answer:

\(\frac{1}{24}\)

Explanation:

Given,

\(\frac{1}{3}\) ÷ 8

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{3}\) ÷ \(\frac{8}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{3}\) × \(\frac{1}{8}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{3 \times 8}\) = \(\frac{1}{24}\)

c. 6 ÷ \(\frac{1}{12}\) = ________________

Answer:

72

Explanation:

Given,

6 ÷ \(\frac{1}{12}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{6}{1}\) ÷ \(\frac{1}{12}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{6}{1}\) × \(\frac{12}{1}\)

Multiply across numerators and denominators.

\(\frac{6 \times 12}{1 \times 1}\) = 72

**Solve each problem. Write answers in simplest form. Show your work.**

Question 9.

Aimee lives \(\frac{8}{9}\) miles from the park. She has walked \(\frac{3}{5}\) of the way to the park. How far has Aimee walked?

Aimee has walked ___________ miles.

Answer:

Aimee has walked \(\frac{8}{15}\) miles.

Explanation:

Aimee lives \(\frac{8}{9}\) miles from the park.

She has walked \(\frac{3}{5}\) of the way to the park.

Aimee has walked = \(\frac{8}{9}\) × \(\frac{3}{5}\)

Multiply the numerators and denominators.

\(\frac{8 \times 3}{9 \times 5}\) = \(\frac{24}{45}\)

Reduce to the simplest form.

\(\frac{8}{15}\) miles.

Question 10.

Hotah and his 3 friends are each running \(\frac{1}{4}\) of a 2-mile relay race. How far is each person running?

Each person is running _______________ miles.

Answer:

Each person is running \(\frac{1}{2}\) miles.

Explanation:

Hotah and his 3 friends = 4 runners

are each running \(\frac{1}{4}\) of a 2-mile relay race.

Each person ran = \(\frac{1}{4}\) x 2

= \(\frac{2}{4}\)

= \(\frac{1}{2}\)

Question 11.

A single serving of jello requires \(\frac{1}{8}\) cups sugar. How much sugar is needed for 6 servings?

______________ cups are needed.

Answer:

\(\frac{3}{4}\) cups are needed.

Explanation:

A single serving of jello requires \(\frac{1}{8}\) cups sugar.

Number of cups of sugar is needed for 6 servings,

\(\frac{1}{8}\) × 6

convert the whole number to fraction.

\(\frac{1}{8}\) × \(\frac{6}{1}\)

Multiply the numerators and denominators.

\(\frac{1 \times 6}{8 \times 1}\) = \(\frac{6}{8}\)

Reduce to the simplest form.

\(\frac{3}{4}\) cups.

Question 12.

Isabel watched a movie that was 4 hours long. She stood up every \(\frac{1}{4}\) hour to stretch her legs. How many times did Isabel stand up during the movie?

Isabel stood up ______________ times during the movie.

Answer:

16

Explanation:

Isabel watched a movie that was 4 hours long.

She stood up every \(\frac{1}{4}\) hour to stretch her legs.

Number of times did Isabel stand up during the movie,

4 ÷ \(\frac{1}{4}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{4}{1}\) ÷ \(\frac{1}{4}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{4}{1}\) × \(\frac{4}{1}\)

Multiply across numerators and denominators.

\(\frac{4 \times 4}{1 \times 1}\) = 16

Question 13.

Suppose 8 books are stacked on top of one another. Each book is 1\(\frac{5}{9}\) inches thick. How high is the stack of books?

The stack of books is _____________ inches high.

Answer:

The stack of books is 12 \(\frac{4}{9}\) inches high

Explanation:

Suppose 8 books are stacked on top of one another.

Each book is 1\(\frac{5}{9}\) inches thick.

The height of the books stack is = 1\(\frac{5}{9}\) × 8

convert the mixed fraction to improper fraction.

\(\frac{14}{9}\) × 8

Write the whole number into fraction.

\(\frac{14}{9}\) × \(\frac{8}{1}\)

Multiply the numerators and denominators.

\(\frac{14 \times 8}{9 \times 1}\) = \(\frac{112}{9}\)

Reduce to the simplest form.

12 \(\frac{4}{9}\) inches high.

Question 14.

Beth has to carry 9 grocery bags into the house. Each grocery bag weighs 5\(\frac{3}{5}\) pounds. How many pounds does Beth carry in all?

Beth carries ______________ pounds.

Answer:

Beth carries 50 \(\frac{2}{5}\) pounds.

Explanation:

Beth has to carry 9 grocery bags into the house.

Each grocery bag weighs 5\(\frac{3}{5}\) pounds.

Number of pounds does Beth carry in all = 5\(\frac{3}{5}\) × 9

convert the mixed fraction to improper fraction.

\(\frac{28}{5}\) × 9

Write the whole number into fraction.

\(\frac{28}{5}\) × \(\frac{9}{1}\)

Multiply the numerators and denominators.

\(\frac{28 \times 9}{5 \times 1}\) = \(\frac{252}{5}\)

Reduce to the simplest form.

50 \(\frac{2}{5}\) inches high.