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SSAT Upper Level Math : Rational Numbers

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

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All SSAT Upper Level Math Resources

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Example Questions

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 #161 : Rational Numbers

Multiply:

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

Possible Answers:

$\frac{3}{8}$

$\frac{1}{3}$

$\frac{2}{3}$

$\frac{3}{7}$

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 #162 : Rational Numbers

Multiply,

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

Possible Answers:

$\frac{4}{7}$

$\frac{2}{5}$

$\frac{3}{10}$

$\frac{3}{7}$

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 #163 : Rational Numbers

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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Example Question #164 : Rational Numbers

Multiply these fractions:

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

Possible Answers:

$\frac{2}{23}$

$\frac{2}{21}$

$\frac{3}{11}$

$\frac{2}{11}$

Correct answer:

$\frac{2}{21}$

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.

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Example Question #165 : Rational Numbers

Multiply these fractions:

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

Possible Answers:

$\frac{5}{84}$

$\frac{5}{42}$

$\frac{10}{42}$

$\frac{10}{19}$

Correct answer:

$\frac{5}{42}$

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:

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

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Example Question #166 : Rational Numbers

Multiply these fractions:

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

Possible Answers:

$\frac{6}{35}$

$\frac{8}{35}$

$\frac{1}{2}$

$\frac{8}{17}$

Correct answer:

$\frac{8}{35}$

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.

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Example Question #167 : Rational Numbers

Multiply these fractions:

$\frac{1}{6}\cdot \frac{1}{5}$

Possible Answers:

$\frac{2}{11}$

$\frac{1}{15}$

$\frac{1}{11}$

$\frac{1}{30}$

Correct answer:

$\frac{1}{30}$

Explanation:

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

$\frac{1}{6}\cdot \frac{1}{5}=\frac{1\cdot 1}{6\cdot 5}=\frac{1}{30}$

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

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Rational Numbers

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #161 : Rational Numbers

Example Question #34 : Operations With Fractions

Example Question #161 : Rational Numbers

Example Question #162 : Rational Numbers

Example Question #15 : How To Multiply Fractions

Example Question #163 : Rational Numbers

Example Question #164 : Rational Numbers

Example Question #165 : Rational Numbers

Example Question #166 : Rational Numbers

Example Question #167 : Rational Numbers

All SSAT Upper Level Math Resources

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