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SSAT Upper Level Math : Operations with Fractions

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

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Example Questions

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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Example Question #151 : Fractions

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?

Possible Answers:

$\frac{1}{6}$

$\frac{3}{10}$

$\frac{5}{11}$

$\frac{2}{5}$

Correct answer:

$\frac{1}{6}$

Explanation:

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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Example Question #32 : Operations With Fractions

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?

Possible Answers:

$\frac{1}{21}$

$\frac{4}{13}$

$\frac{1}{14}$

$\frac{5}{42}$

Correct answer:

$\frac{1}{14}$

Explanation:

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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Example Question #161 : Rational Numbers

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?

Possible Answers:

$\frac{3}{5}$

$\frac{6}{7}$

$\frac{7}{9}$

$\frac{1}{5}$

Correct answer:

$\frac{3}{5}$

Explanation:

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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Example Question #34 : Operations With Fractions

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?

Possible Answers:

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

$\frac{5}{24}$

$\frac{3}{10}$

$\frac{1}{5}$

Correct answer:

$\frac{5}{24}$

Explanation:

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

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

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Example Question #31 : Operations With Fractions

Multiply:

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

Possible Answers:

$\frac{3}{7}$

$\frac{2}{3}$

$\frac{3}{8}$

$\frac{1}{3}$

Correct answer:

$\frac{3}{8}$

Explanation:

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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Example Question #32 : Operations With Fractions

Multiply,

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

Possible Answers:

$\frac{3}{7}$

$\frac{3}{10}$

$\frac{2}{5}$

$\frac{4}{7}$

Correct answer:

$\frac{3}{10}$

Explanation:

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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Example Question #15 : How To Multiply Fractions

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

Possible Answers:

Correct answer:

Explanation:

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:

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

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

This makes 55 the response closest to the actual product.

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Example Question #33 : Operations With Fractions

Multiply these fractions:

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

Possible Answers:

$\frac{1}{5}$

$\frac{2}{9}$

$\frac{1}{10}$

$\frac{1}{20}$

Correct answer:

$\frac{1}{10}$

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:

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

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SSAT Upper Level Math : Operations with Fractions

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #4 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

Example Question #151 : Fractions

Example Question #32 : Operations With Fractions

Example Question #161 : Rational Numbers

Example Question #34 : Operations With Fractions

Example Question #31 : Operations With Fractions

Example Question #32 : Operations With Fractions

Example Question #15 : How To Multiply Fractions

Example Question #33 : Operations With Fractions

All SSAT Upper Level Math Resources

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