Apply understanding of multiplication and division to divide fractions by fractions

Help Questions

Praxis Math › Apply understanding of multiplication and division to divide fractions by fractions

Questions 1 - 3

1

Solve:

$\frac{\frac{2}{21}}{\frac{5}{7}}$

$\frac{2}{15}$

$\frac{3}{13}$

$\frac{2}{11}$

$\frac{4}{15}$

Explanation

In order to divide a fraction by a second fraction, we can change the problem to a division problem by multiplying the first fraction by the reciprocal of the second fraction. It can be written algebraically in the following way:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}$

Let's use this rule to solve our problem.

$\frac{\frac{2}{21}}{\frac{5}{7}}$

Rewrite.

$\frac{\frac{2}{21}}{\frac{5}{7}}=\frac{2}{21}\times\frac{7}{5}$

Cross out like terms.

$\frac{2}{21}\times\frac{7}{5}=\frac{2}{3}\times\frac{1}{5}$

Solve.

$\frac{2}{3}\times\frac{1}{5}=\frac{2}{15}$

2

Solve:

$\frac{\frac{1}{3}}{\frac{1}{8}}$

$2\tfrac{2}{3}$

$3\tfrac{2}{3}$

$2\tfrac{1}{3}$

$3\tfrac{1}{3}$

Cannot be determined

Explanation

In order to divide a fraction by a second fraction, we can change the problem to a division problem by multiplying the first fraction by the reciprocal of the second fraction. It can be written algebraically in the following way:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}$

Let's use this rule to solve our problem.

$\frac{\frac{1}{3}}{\frac{1}{8}}$

Rewrite.

$\frac{\frac{1}{3}}{\frac{1}{8}}=\frac{1}{3}\times\frac{8}{1}$

Solve.

$\frac{1}{3}\times\frac{8}{1}=\frac{8}{3}$

Convert to a mixed number.

$\frac{8}{3}=2\tfrac{2}{3}$

3

Solve:

$\frac{\frac{5}{16}}{\frac{3}{4}}$

$\frac{5}{12}$

$\frac{5}{11}$

$\frac{5}{13}$

$\frac{6}{11}$

$\frac{6}{13}$

Explanation

In order to divide a fraction by a second fraction, we can change the problem to a division problem by multiplying the first fraction by the reciprocal of the second fraction. It can be written algebraically in the following way:

$\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}$

Let's use this rule to solve our problem.

$\frac{\frac{5}{16}}{\frac{3}{4}}$

Rewrite.

$\frac{\frac{5}{16}}{\frac{3}{4}}=\frac{5}{16}\times\frac{4}{3}$

Cross out like terms.

$\frac{5}{16}\times\frac{4}{3}=\frac{5}{4}\times\frac{1}{3}$

Solve.

$\frac{5}{4}\times\frac{1}{3}=\frac{5}{12}$

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