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

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Multiply. Write answers in simplest form.

Question 1.
a. $$\frac{1}{4}$$ × $$\frac{8}{9}$$ = ______________
$$\frac{2}{9}$$

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. $$\frac{3}{5}$$ × $$\frac{5}{6}$$ = ______________
$$\frac{1}{2}$$

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. $$\frac{5}{7}$$ × $$\frac{1}{2}$$ = ______________
$$\frac{5}{14}$$

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. $$\frac{11}{12}$$ × $$\frac{2}{3}$$ = ______________
$$\frac{11}{18}$$

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. $$\frac{3}{7}$$ × $$\frac{4}{5}$$ = ______________
$$\frac{12}{35}$$

Explanation:
Given,
$$\frac{3}{7}$$ × $$\frac{4}{5}$$
Multiply the numerators and denominators.
$$\frac{3 \times 4}{7 \times 5}$$ = $$\frac{12}{35}$$

c. $$\frac{3}{4}$$ × $$\frac{3}{8}$$ = ______________
$$\frac{9}{32}$$

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 × $$\frac{5}{8}$$ = ______________
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 = ______________
$$\frac{2}{3}$$

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 = ______________
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 = ______________
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 = ______________
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 = ______________
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 ÷ $$\frac{1}{8}$$ = _____________
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 = _______________
$$\frac{1}{36}$$

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 ÷ $$\frac{1}{10}$$ = ________________
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 = ________________
$$\frac{1}{30}$$

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 = ________________
$$\frac{1}{20}$$

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 ÷ $$\frac{1}{8}$$ = _________________
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 = _________________
$$\frac{1}{30}$$

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 ÷ $$\frac{1}{3}$$ = _________________
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 = _________________
$$\frac{1}{24}$$

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 = ________________
$$\frac{1}{21}$$

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 ÷ $$\frac{1}{10}$$ = ________________
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 = ________________
$$\frac{1}{84}$$

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.
$$\frac{1 \times 1}{7 \times 12}$$ = $$\frac{1}{84}$$

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.
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.
$$\frac{1}{4}$$

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.
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.
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.
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.
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.
$$\frac{1 \times 1}{3 \times 14}$$ = $$\frac{1}{42}$$

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