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Spectrum Math Grade 5 Chapter 6 Posttest Answers Key
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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.
\(\frac{1 \times 1}{3 \times 14}\) = \(\frac{1}{42}\)