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

## Spectrum Math Grade 5 Chapter 6 Posttest Answers Key

**Check What You Learned**

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

Question 1.

a. \(\frac{1}{4}\) × \(\frac{8}{9}\) = ______________

Answer:

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

Explanation:

Given,

\(\frac{1}{4}\) × \(\frac{8}{9}\)

Multiply the numerators and denominators.

\(\frac{1 \times 8}{4 \times 9}\) = \(\frac{8}{36}\)

Reduce to the simplest form.

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

b. \(\frac{3}{5}\) × \(\frac{5}{6}\) = ______________

Answer:

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

Explanation:

Given,

\(\frac{3}{5}\) × \(\frac{5}{6}\)

Multiply the numerators and denominators.

\(\frac{3 \times 5}{5 \times 6}\) = \(\frac{15}{30}\)

Reduce to the simplest form.

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

c. \(\frac{5}{7}\) × \(\frac{1}{2}\) = ______________

Answer:

\(\frac{5}{14}\)

Explanation:

Given,

\(\frac{5}{7}\) × \(\frac{1}{2}\)

Multiply the numerators and denominators.

\(\frac{5 \times 1}{7 \times 2}\) = \(\frac{5}{14}\)

Question 2.

a. \(\frac{11}{12}\) × \(\frac{2}{3}\) = ______________

Answer:

\(\frac{11}{18}\)

Explanation:

Given,

\(\frac{11}{12}\) × \(\frac{2}{3}\)

Multiply the numerators and denominators.

\(\frac{11 \times 2}{12 \times 3}\) = \(\frac{22}{36}\)

Reduce to the simplest form.

\(\frac{11}{18}\)

b. \(\frac{3}{7}\) × \(\frac{4}{5}\) = ______________

Answer:

\(\frac{12}{35}\)

Explanation:

Given,

\(\frac{3}{7}\) × \(\frac{4}{5}\)

Multiply the numerators and denominators.

\(\frac{3 \times 4}{7 \times 5}\) = \(\frac{12}{35}\)

c. \(\frac{3}{4}\) × \(\frac{3}{8}\) = ______________

Answer:

\(\frac{9}{32}\)

Explanation:

Given,

\(\frac{3}{4}\) × \(\frac{3}{8}\)

Multiply the numerators and denominators.

\(\frac{3 \times 3}{4 \times 8}\) = \(\frac{9}{32}\)

Question 3.

a. 3 × \(\frac{5}{8}\) = ______________

Answer:

1 \(\frac{7}{8}\)

Explanation:

Given,

3 × \(\frac{5}{8}\)

Write the whole number into fraction.

\(\frac{3}{1}\) × \(\frac{5}{8}\)

Multiply the numerators and denominators.

\(\frac{3 \times 5}{1 \times 8}\) = \(\frac{15}{8}\)

Reduce to the simplest form.

1 \(\frac{7}{8}\)

b. \(\frac{1}{6}\) × 4 = ______________

Answer:

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

Explanation:

Given,

\(\frac{1}{6}\) × 4

Write the whole number into fraction.

\(\frac{1}{6}\) × \(\frac{4}{1}\)

Multiply the numerators and denominators.

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

Reduce to the simplest form.

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

c. \(\frac{1}{3}\) × 9 = ______________

Answer:

3

Explanation:

Given,

\(\frac{1}{3}\) × 9

Write the whole number into fraction.

\(\frac{1}{3}\) × \(\frac{9}{1}\)

Multiply the numerators and denominators.

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

Question 4.

a. 2\(\frac{7}{8}\) × 2 = ______________

Answer:

5 \(\frac{3}{4}\)

Explanation:

Given,

2\(\frac{7}{8}\) × 2

Convert the mixed fraction to improper fraction.

\(\frac{23}{8}\) × 2

Write the whole number into fraction.

\(\frac{23}{8}\) × \(\frac{2}{1}\)

Multiply the numerators and denominators.

\(\frac{23 \times 2}{8 \times 1}\) = \(\frac{46}{8}\)

Reduce to the simplest form.

\(\frac{23}{4}\) = 5 \(\frac{3}{4}\)

b. 1\(\frac{7}{12}\) × 9 = ______________

Answer:

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

Explanation:

Given,

1\(\frac{7}{12}\) × 9

Convert the mixed fraction to improper fraction.

\(\frac{19}{12}\) × 9

Write the whole number into fraction.

\(\frac{19}{12}\) × \(\frac{9}{1}\)

Multiply the numerators and denominators.

\(\frac{19 \times 9}{12 \times 1}\) = \(\frac{171}{12}\)

Reduce to the simplest form.

\(\frac{57}{4}\) = 4 \(\frac{1}{4}\)

c. 3\(\frac{3}{10}\) × 8 = ______________

Answer:

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

Explanation:

Given,

3\(\frac{3}{10}\) × 8

Convert the mixed fraction to improper fraction.

\(\frac{33}{10}\) × 8

Write the whole number into fraction.

\(\frac{33}{10}\) × \(\frac{8}{1}\)

Multiply the numerators and denominators.

\(\frac{33 \times 8}{10 \times 1}\) = \(\frac{264}{10}\)

Reduce to the simplest form.

\(\frac{132}{5}\) = 26 \(\frac{2}{5}\)

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

Question 5.

a. 6 ÷ \(\frac{1}{8}\) = _____________

Answer:

48

Explanation:

Given,

6 ÷ \(\frac{1}{8}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{6}{1}\) ÷ \(\frac{1}{8}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{6}{1}\) × \(\frac{8}{1}\)

Multiply across numerators and denominators.

\(\frac{6 \times 8}{1 \times 1}\) = 48

b. \(\frac{1}{9}\) ÷ 4 = _______________

Answer:

\(\frac{1}{36}\)

Explanation:

Given,

\(\frac{1}{9}\) ÷ 4

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{9}\) ÷ \(\frac{4}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{9}\) × \(\frac{1}{4}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{9 \times 4}\) = \(\frac{1}{36}\)

c. 2 ÷ \(\frac{1}{10}\) = ________________

Answer:

20

Explanation:

Given,

2 ÷ \(\frac{1}{10}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{2}{1}\) ÷ \(\frac{1}{10}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{2}{1}\) × \(\frac{10}{1}\)

Multiply across numerators and denominators.

\(\frac{2 \times 10}{1 \times 1}\) = 20

Question 6.

a. \(\frac{1}{3}\) ÷ 10 = ________________

Answer:

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

Explanation:

Given,

\(\frac{1}{3}\) ÷ 10

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{3}\) ÷ \(\frac{10}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{3}\) × \(\frac{1}{10}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{3 \times 10}\) = \(\frac{1}{30}\)

b. \(\frac{1}{5}\) ÷ 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.

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

c. 2 ÷ \(\frac{1}{8}\) = _________________

Answer:

16

Explanation:

Given,

2 ÷ \(\frac{1}{8}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{2}{1}\) ÷ \(\frac{1}{8}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{2}{1}\) × \(\frac{8}{1}\)

Multiply across numerators and denominators.

\(\frac{2 \times 8}{1 \times 1}\) = 16

Question 7.

a. \(\frac{1}{5}\) ÷ 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.

\(\frac{1 \times 1}{5 \times 6}\) = \(\frac{1}{30}\)

b. 5 ÷ \(\frac{1}{3}\) = _________________

Answer:

15

Explanation:

Given,

5 ÷ \(\frac{1}{3}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{5}{1}\) ÷ \(\frac{1}{3}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{5}{1}\) × \(\frac{3}{1}\)

Multiply across numerators and denominators.

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

c. \(\frac{1}{8}\) ÷ 3 = _________________

Answer:

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

Explanation:

Given,

\(\frac{1}{8}\) ÷ 3

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{8}\) ÷ \(\frac{3}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{8}\) × \(\frac{1}{3}\)

Multiply across numerators and denominators.

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

Question 8.

a. \(\frac{1}{3}\) ÷ 7 = ________________

Answer:

\(\frac{1}{21}\)

Explanation:

Given,

\(\frac{1}{3}\) ÷ 7

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{3}\) ÷ \(\frac{7}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{3}\) × \(\frac{1}{7}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{3 \times 7}\) = \(\frac{1}{21}\)

b. 5 ÷ \(\frac{1}{10}\) = ________________

Answer:

50

Explanation:

Given,

5 ÷ \(\frac{1}{10}\)

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{5}{1}\) ÷ \(\frac{1}{10}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{5}{1}\) × \(\frac{10}{1}\)

Multiply across numerators and denominators.

\(\frac{5 \times 10}{1 \times 1}\) = \(\frac{1}{50}\)

c. \(\frac{1}{7}\) ÷ 12 = ________________

Answer:

\(\frac{1}{84}\)

Explanation:

Given,

\(\frac{1}{7}\) ÷ 12

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{7}\) ÷ \(\frac{12}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{7}\) × \(\frac{1}{12}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{7 \times 12}\) = \(\frac{1}{84}\)

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

Question 9.

Five new dresses have been sewn. Chelsea did \(\frac{1}{7}\) of the total sewing. What fraction of each dress did Chelsea sew?

Chelsea sewed ____________ of each dress.

Answer:

Chelsea sewed \(\frac{1}{35}\) of each dress.

Explanation:

Given,

Five new dresses have been sewn.

Chelsea did \(\frac{1}{7}\) of the total sewing.

fraction of each dress did Chelsea sew,

\(\frac{1}{7}\) ÷ 5

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{7}\) ÷ \(\frac{5}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{7}\) × \(\frac{1}{5}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{7 \times 5}\) = \(\frac{1}{35}\)

Question 10.

A group of friends ordered 2 pizzas. Each friend ate \(\frac{1}{2}\) of a pizza. What fraction of the 2 total pizzas did each friend eat?

Each friend ate ____________ of the total pizza.

Answer:

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

Explanation:

A group of friends ordered 2 pizzas.

Each friend ate \(\frac{1}{2}\) of a pizza.

The fraction of the 2 total pizzas did each friend eat,

\(\frac{1}{2}\) ÷ 2

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{2}\) ÷ \(\frac{2}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{2}\) × \(\frac{1}{2}\)

Multiply across numerators and denominators.

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

Question 11.

A race track was \(\frac{1}{4}\) mile long. If Martha ran around the race track 5\(\frac{1}{9}\) times, how many miles did Martha run?

Martha ran ______________ miles.

Answer:

Martha ran 1 \(\frac{5}{18}\) miles.

Explanation:

A race track was \(\frac{1}{4}\) mile long.

If Martha ran around the race track 5\(\frac{1}{9}\) times.

Total miles did Martha run,

\(\frac{1}{4}\) × 5\(\frac{1}{9}\)

Convert the mixed fraction to improper fraction.

\(\frac{1}{4}\) × \(\frac{46}{9}\)

Multiply the numerators and denominators.

\(\frac{1 \times 46}{4 \times 9}\) = \(\frac{46}{36}\)

Reduce to the simplest form.

\(\frac{23}{18}\) = 1 \(\frac{5}{18}\)

Question 12.

Andrew cut a rope \(\frac{1}{7}\) of a yard long into 8 equal pieces. How long will each piece of rope be?

Each piece of rope will be _______________ yard long.

Answer:

Each piece of rope will be \(\frac{1}{56}\) yard long.

Explanation:

Andrew cut a rope \(\frac{1}{7}\) of a yard long into 8 equal pieces.

Length of each piece of rope be,

\(\frac{1}{7}\) ÷ 8

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{7}\) ÷ \(\frac{8}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{7}\) × \(\frac{1}{8}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{7 \times 8}\) = \(\frac{1}{56}\)

Question 13.

Roberto studied 1\(\frac{2}{5}\) hour every day for 7 days. How many hours did Roberto study in 7 days?

Roberto studied _____________ hours.

Answer:

9 \(\frac{4}{5}\)

Question 14.

Ms. Perez bought \(\frac{1}{3}\) pound of seed for 14 gardens. If each garden gets an equal amount of seed, how much seed will be in each garden?

Each garden will have ____________ pound of seed.

Answer:

Each garden will have \(\frac{1}{42}\) pound of seed.

Explanation:

Ms. Perez bought \(\frac{1}{3}\) pound of seed for 14 gardens.

If each garden gets an equal amount of seed,

Number of seed will be in each garden,

\(\frac{1}{3}\) ÷ 14

To divide a whole number by a fraction,

first write the whole number as a fraction.

\(\frac{1}{3}\) ÷ \(\frac{14}{1}\)

Then, multiply by the reciprocal of the divisor.

\(\frac{1}{3}\) × \(\frac{1}{14}\)

Multiply across numerators and denominators.

\(\frac{1 \times 1}{3 \times 14}\) = \(\frac{1}{42}\)