How to multiply fractions - SSAT Upper Level Quantitative

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Question

Simplify the expression.

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

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Answer

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

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

$\left ( {\frac{1* 2}{2* 2} + \frac{1}{4}}\right ) \left ({\frac{1 2}{22} - \frac{1}{4}}\right )$

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

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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Question

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

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Answer

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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Question

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

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Answer

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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Question

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

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Answer

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

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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Question

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?

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Answer

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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Question

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?

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Answer

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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Question

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?

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Answer

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

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

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Question

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?

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Answer

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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Question

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?

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Answer

To find what fraction of the games are Japanese fighting ones, multiply $\frac{1}{6}$ by $\frac{3}{7}$ .

$\frac{1}{6}\times \frac{3}{7}=\frac{1\times3}{6\times7}=\frac{3}{42}=\frac{1}{14}$

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Question

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?

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Answer

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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Question

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?

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Answer

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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Question

$\frac{1}{3}$ 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?

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Answer

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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Question

Of the students in Hannah's high school band, ${}\frac{4}{5}$ play a woodwind instrument. Of the woodwind players, ${}\frac{3}{4}$ plays the clarinet. What fraction of the band plays the clarinet?

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Answer

Multiply $\frac{4}{5}$ by ${}\frac{3}{4}$ to find out what fraction of the students play the clarinet.

$\frac{4}{5}\times\frac{3}{4}=\frac{3\times4}{5\times4}=\frac{12}{20}=\frac{3}{5}$

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Question

In Timothy's 3rd grade class, $\frac{1}{5}$ of the students enjoy eating vegetables. Of the ones who enjoy eating vegetables, $\frac{5}{6}$ say that spinach is their favorite vegetable. What fraction of the class say spinach is their favorite vegetable?

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Answer

Multiply $\frac{1}{5}$ by $\frac{5}{6}$ to find out what fraction of the students say spinach is their favorite vegetable.

$\frac{1}{5}\times \frac{5}{6}=\frac{1\times5}{5\times6}=\frac{5}{30}=\frac{1}{6}$

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Question

Multiply:

$\frac{3}{7}\times\frac{7}{8}$

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Answer

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

After the multiplication is complete simply the fraction to get the final answer.

$\frac{3}{7}\times\frac{7}{8}=\frac{3\times7}{7\times8}=\frac{21}{56}=\frac{3}{8}$

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Question

Multiply,

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

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Answer

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

$\frac{3}{5}\times\frac{1}{2}=\frac{3\times1}{5\times2}=\frac{3}{10}$

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Question

Which of the following is closest to the product of $6\frac{1}{2}$ and $8\frac{2}{3}$ ?

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Answer

First convert the mix fractions into improper fractions by multiplying the whole number with the numerator and then adding that number to the numerator while all keeping it over the denominator.

$6\frac{1}{2} \times 8\frac{2}{3}$

$= \frac{6 \times 2 + 1}{2} \times \frac{8 \times 3+ 2}{3}$

$= \frac{13}{2} \times \frac{26}{3}$

When multiplying two fractions, multiply the numerators together and the denominators together.

$= \frac{13 \times 26 }{2 \times 3}$

$= \frac{338}{6}$

$= \frac{338 \div 2}{6 \div 2}$

$= \frac{169}{3}$

Divide:

$169 \div 3 = 56 \textup{ R }1$ ,

so

$6\frac{1}{2} \times 8\frac{2}{3} = \frac{169}{3} = 56 \frac{1}{3}$ .

This makes 55 the response closest to the actual product.

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Question

Multiply these fractions:

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

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Answer

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:

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

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Question

Multiply these fractions:

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

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Answer

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.

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Question

Multiply these fractions:

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

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Answer

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:

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

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