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

Check What You Know

Multiply. Write answers in simplest form.

Question 1.
a. $$\frac{1}{2}$$ × $$\frac{1}{3}$$ = ________________
$$\frac{1}{6}$$

Explanation:
Given,
$$\frac{1}{2}$$ × $$\frac{1}{3}$$
Multiply the numerators and denominators.
$$\frac{1 \times 1}{2 \times 3}$$ = $$\frac{1}{6}$$

b. $$\frac{3}{4}$$ × $$\frac{2}{7}$$ = ________________
$$\frac{3}{14}$$

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. $$\frac{1}{4}$$ × $$\frac{4}{5}$$ = ________________
$$\frac{1}{5}$$

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. $$\frac{2}{5}$$ × $$\frac{5}{8}$$ = ________________
$$\frac{1}{4}$$

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. $$\frac{4}{9}$$ × $$\frac{1}{2}$$ = ________________
$$\frac{2}{9}$$

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 × $$\frac{2}{7}$$ = ________________
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 × $$\frac{4}{8}$$ = ________________
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 = ________________
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 = ________________
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 = ________________
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 = ________________
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 = ________________
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 ÷ $$\frac{1}{10}$$ = _______________
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 = ______________
$$\frac{1}{112}$$

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 ÷ $$\frac{1}{4}$$ = _______________
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 = _______________
$$\frac{1}{18}$$

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 = _______________
$$\frac{1}{30}$$

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 ÷ $$\frac{1}{4}$$ = ________________
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 = _______________
$$\frac{1}{20}$$

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 ÷ $$\frac{1}{8}$$ = _______________
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 = ________________
$$\frac{1}{18}$$

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 ÷ $$\frac{1}{5}$$ = ________________
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 = ________________
$$\frac{1}{24}$$

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 ÷ $$\frac{1}{12}$$ = ________________
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

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.
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.
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.
$$\frac{3}{4}$$ 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.
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.
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.
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.

Scroll to Top
Scroll to Top