How to multiply fractions

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SSAT Upper Level Quantitative › How to multiply fractions

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Multiply these fractions:

$\frac{1}{4}\cdot \frac{2}{5}$

$\frac{1}{10}$

CORRECT

$\frac{1}{5}$

$\frac{1}{20}$

$\frac{2}{9}$

Explanation

To multiply the fractions, simply multiply the numerators together and the denominators together.

$\frac{1}{4}\cdot \frac{2}{5}=\frac{1\cdot 2}{4\cdot 5}=\frac{2}{20}$

Then simplify the fraction accordingly:

$\frac{2\div 2}{20\div 2}=\frac{1}{10}$

Multiply these fractions:

$\frac{2}{3}\cdot \frac{1}{7}$

$\frac{2}{21}$

CORRECT

$\frac{2}{11}$

$\frac{3}{11}$

$\frac{2}{23}$

Explanation

To multiply the fractions, simply multiply the numerators together and the denominators together.

$\frac{2}{3}\cdot \frac{1}{7}=\frac{2\cdot 1}{3\cdot 7}=\frac{2}{21}$

Since this fraction is in its simplest form, that is the final answer.

Simplify the expression.

$\left ( {\frac{1}{2} + \frac{1}{4}}\right ) * \left ({\frac{1}{2} - \frac{1}{4}}\right )$

$\frac{3}{16}$

CORRECT

$\frac{1}{8}$

$\frac{5}{12}$

$\frac{5}{16}$

Explanation

$\left ( {\frac{1}{2} + \frac{1}{4}}\right ) * \left ({\frac{1}{2} - \frac{1}{4}}\right )$

Start with the terms in parentheses, using the order of operations. Find the least common denominator.

$\left ( {\frac{1* 2}{2* 2} + \frac{1}{4}}\right ) *\left ({\frac{1* 2}{2*2} - \frac{1}{4}}\right )$

$\left ( {\frac{2}{4} + \frac{1}{4}}\right ) * \left ({\frac{ 2}{4} - \frac{1}{4}}\right )$

Add the fractions in parentheses.

$\left ( {\frac{2+1}{4} } \right ) * \left ({\frac{2-1}{4} } \right )$

Multiply the fractions and simplify.

${\frac{3}{4} } *{\frac{1}{4} } = \frac{3 * 1}{4 * 4} = \frac{3}{16}$

In the morning, Tina ate $\frac{1}{4}$ of a cake. For her afternoon snack she ate $\frac{5}{6}$ as much as she did in the morning. What fraction of the cake did Tina eat for her afternoon snack?

$\frac{5}{24}$

CORRECT

$\frac{3}{10}$

${}\frac{5}{14}$

$\frac{1}{5}$

Explanation

Multiply $\frac{1}{4}$ by $\frac{5}{6}$ to find how much cake Tina ate in the afternoon.

$\frac{1}{4}\times\frac{5}{6}=\frac{5\times1}{4\times6}=\frac{5}{24}$

Multiply these fractions:

$\frac{5}{12}\cdot \frac{2}{7}$

$\frac{5}{42}$

CORRECT

$\frac{10}{19}$

$\frac{5}{84}$

$\frac{10}{42}$

Explanation

To multiply the fractions, simply multiply the numerators together and the denominators together.

$\frac{5}{12}\cdot \frac{2}{7}=\frac{5\cdot 2}{12\cdot 7}=\frac{10}{84}$

Then simplify the fraction accordingly:

$\frac{10\div 2}{84\div 2}=\frac{5}{42}$

A certain recipe for a batch of chocolate cookies calls for $\frac{9}{10}$ of a cup of sugar to be used. If Mike only wants to make $\frac{3}{4}$ of a batch, how much of a cup of sugar should he use?

$\frac{27}{40}$

CORRECT

$\frac{6}{7}$

$\frac{1}{9}$

$\frac{9}{10}$

Explanation

Multiply $\frac{9}{10}$ by $\frac{3}{4}$ to find out how much sugar he needs to use.

$\frac{9}{10}\times \frac{3}{4}=\frac{9\times3}{10\times4}=\frac{27}{40}$

Simplify the expression $\frac{9}{10}\times \frac{2}{3}$ .

$\frac{3}{5}$

CORRECT

$\frac{11}{13}$

$\frac{18}{13}$

$\frac{9}{7}$

$\frac{3}{7}$

Explanation

Beginning with $\frac{9}{10}\times \frac{2}{3}$ , we multiply across both numerators and denominators for both terms:

$=\frac{9\times 2}{10\times 3}$

$=\frac{18}{30}$

Reducing the fraction to its simplest form by dividing by the Greatest Common Factor:

$\frac{18}{30}$

$=\frac{18\div 6}{30\div 6}$

$=\frac{3}{5}$

Multiply these fractions:

$\frac{4}{7}\cdot \frac{2}{5}$

$\frac{8}{35}$

CORRECT

$\frac{8}{17}$

$\frac{1}{2}$

$\frac{6}{35}$

Explanation

To multiply the fractions, simply multiply the numerators together and the denominators together.

$\frac{4}{7}\cdot \frac{2}{5}=\frac{4\cdot 2}{7\cdot 5}=\frac{8}{35}$

Since this fraction is in its simplest form, that is the final answer.

At an arcade, $\frac{1}{6}$ of the games are fighting games. Of those games, $\frac{3}{7}$ are Japanese games. What fraction of the games at the arcade are Japanese fighting games?