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SSAT Upper Level Math : How to multiply fractions

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Example Questions

Example Question #1 : How To Multiply Fractions

Simplify the expression.

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

Possible Answers:

$\frac{5}{12}$

$\frac{3}{16}$

$\frac{5}{16}$

$\frac{1}{8}$

Correct answer:

$\frac{3}{16}$

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.

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

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Example Question #2 : How To Multiply Fractions

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

Possible Answers:

$\frac{11}{13}$

$\frac{3}{7}$

$\frac{9}{7}$

$\frac{18}{13}$

$\frac{3}{5}$

Correct answer:

$\frac{3}{5}$

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:

$\frac{18}{30}$

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

$=\frac{3}{5}$

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Example Question #2 : How To Multiply Fractions

Simplify the expression $\frac{4}{3}\times(-\frac{3}{4})$ .

Possible Answers:

$\frac{9}{16}$

$-\frac{16}{9}$

$\frac{16}{9}$

Correct answer:

Explanation:

Multiplying across the numerators and denominators of both terms and simplifying:

$\frac{4}{3}\times(-\frac{3}{4})=-\frac{12}{12}=-1$

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Example Question #3 : How To Multiply Fractions

Simplify the expression $\frac{12}{5}\times\frac{10}{20}$ .

Possible Answers:

$\frac{6}{5}$

$\frac{22}{25}$

$-\frac{5}{6}$

$-\frac{6}{5}$

$\frac{5}{6}$

Correct answer:

$\frac{6}{5}$

Explanation:

$\frac{12}{5}\times\frac{10}{20}$

First, multiply straight across. Multiply the numerators together and then multiply the denominators together.

$=\frac{12\times 10}{5\times 20}$

$=\frac{120}{100}$

From here, simplify the expression by factoring out the Greatest Common Factor.

In this case the Greatest Common Factor is 20.

$=\frac{120\div 20}{100\div 20}$

$=\frac{6}{5}$

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Example Question #4 : How To Multiply Fractions

Steven runs a pizza shop. On Monday, he used $\frac{4}{5}$ of a bag of flour. On Tuesday, he used $\frac{1}{6}$ the amount he used on Monday. How much of a bag of flour did he use on Tuesday?

Possible Answers:

$\frac{2}{15}$

$\frac{4}{10}$

$\frac{1}{10}$

$\frac{4}{15}$

Correct answer:

$\frac{2}{15}$

Explanation:

To find how many bags of flour he used on Tuesday, multiply $\frac{4}{5}$ by $\frac{1}{6}$ .

To multiply fractions, multiply the numerators together, then multiply the denominators together.

$\frac{4}{5}\times \frac{1}{6}=\frac{4\times1}{5\times6}=\frac{4}{30}=\frac{2}{15}$

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Example Question #5 : How To Multiply Fractions

In Mary's class, $\frac{1}{12}$ of the class owns a dog, and of those in the class that own a dog, $\frac{2}{7}$ also owns a cat. What fraction of the class owns both a dog and a cat?

Possible Answers:

$\frac{3}{19}$

$\frac{1}{10}$

$\frac{1}{47}$

$\frac{1}{42}$

Correct answer:

$\frac{1}{42}$

Explanation:

Multiply $\frac{1}{12}$ by $\frac{2}{7}$ to find out how much of the class have both a cat and a dog.

$\frac{1}{12}\times \frac{2}{7}=\frac{1\times2}{12\times7}=\frac{2}{84}=\frac{1}{42}$

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Example Question #3 : How To Multiply Fractions

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?

Possible Answers:

$\frac{27}{40}$

$\frac{9}{10}$

$\frac{6}{7}$

$\frac{1}{9}$

Correct answer:

$\frac{27}{40}$

Explanation:

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

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

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Example Question #6 : How To Multiply Fractions

A poll was conducted at a high school. The poll found that $\frac{2}{3}$ of the students at the school had siblings, and that $\frac{4}{5}$ of the students who had siblings also had a dog at home. What fraction of the students have siblings and a dog?

Possible Answers:

$\frac{9}{14}$

$\frac{1}{5}$

$\frac{2}{5}$

$\frac{8}{15}$

Correct answer:

$\frac{8}{15}$

Explanation:

To find what fraction of the students have siblings and a dog, multiply $\frac{2}{3}$ by $\frac{4}{5}$ .

$\frac{2}{3}\times \frac{4}{5}=\frac{2\times4}{3\times5}=\frac{8}{15}$

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Example Question #4 : How To Multiply Fractions

Louis gave away $\frac{7}{8}$ of his comic books to his sister. Of the ones he gave to his sister, $\frac{1}{8}$ were Superman comics. What fraction of the comics that Louis gave away are Superman comics?

Possible Answers:

$\frac{1}{8}$

$\frac{7}{64}$

$\frac{3}{16}$

$\frac{2}{5}$

Correct answer:

$\frac{7}{64}$

Explanation:

Multiply $\frac{7}{8}$ by $\frac{1}{8}$ to figure out what fraction of the comics are Superman comics.

$\frac{7}{8}\times \frac{1}{8}=\frac{7\times1}{8\times8}=\frac{7}{64}$

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Example Question #2 : How To Multiply Fractions

$\frac{1}{3}$ of the students in an elementary school owns their own computer. Of those that own their own computer, $\frac{2}{5}$ also owned their own cell phone. What fraction of the students owned both a computer and a cell phone?

Possible Answers:

$\frac{4}{15}$

$\frac{2}{15}$

$\frac{3}{8}$

$\frac{2}{3}$

Correct answer:

$\frac{2}{15}$

Explanation:

Multiply $\frac{1}{3}$ by $\frac{2}{5}$ to find what fraction of the students own a computer and a cell phone.

$\frac{1}{3}\times\frac{2}{5}=\frac{1\times2}{3\times5}=\frac{2}{15}$

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : How to multiply fractions

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #1 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

Example Question #3 : How To Multiply Fractions

Example Question #4 : How To Multiply Fractions

Example Question #5 : How To Multiply Fractions

Example Question #3 : How To Multiply Fractions

Example Question #6 : How To Multiply Fractions

Example Question #4 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

All SSAT Upper Level Math Resources

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