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Spectrum Math Grade 5 Chapter 6 Pretest Answers Key
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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.