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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #6 : How To Divide Fractions

$\frac{11}{12}\div\frac{4}{9}=?$

Possible Answers:

$\frac{5}{6}$

$\frac{44}{108}$

$\frac{33}{16}$

$\frac{48}{99}$

Correct answer:

$\frac{33}{16}$

Explanation:

Turn the second fraction upside down to find its reciprocal, and then multiply the first fraction by the reciprocal of the second fraction to divide the two fractions. When multiplying fractions, you can multiply across, finding the products of the numbers being multiplied in the numerator and in the denominator.

$\frac{11}{12}\div\frac{4}{9}=\frac{11}{12}\times\frac{9}{4}$

In this case, you can reduce the fractions being multiplied by cross-canceling before multiplying them together.

$\frac{11}{12}\times\frac{9}{4}==\frac{11}{4}\times\frac{3}{4}=\frac{33}{16}$

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Example Question #7 : How To Divide Fractions

$\frac{1}{12}\div\frac{5}{6}=?$

Possible Answers:

$\frac{1}{3}$

$\frac{1}{10}$

$\frac{5}{72}$

Correct answer:

$\frac{1}{10}$

Explanation:

$\frac{1}{12}\div\frac{5}{6}=\frac{1}{12}\times\frac{6}{5}$

In this case, you can reduce the fractions being multiplied by cross-canceling before multiplying them together.

$\frac{1}{12}\times\frac{6}{5}=\frac{1}{2}\times\frac{1}{5}=\frac{1}{10}$

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Example Question #1271 : Ssat Upper Level Quantitative (Math)

$\frac{5}{7}\div\frac{1}{12}=?$

Possible Answers:

$\frac{60}{7}$

$\frac{7}{60}$

$\frac{6}{19}$

$\frac{5}{84}$

Correct answer:

$\frac{60}{7}$

Explanation:

$\frac{5}{7}\div\frac{1}{12}==\frac{5}{7}\times\frac{12}{1}=\frac{60}{7}$

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Example Question #9 : How To Divide Fractions

$\frac{6}{7}\div\frac{10}{3}=?$

Possible Answers:

$\frac{60}{21}$

$\frac{16}{21}$

$\frac{9}{35}$

$\frac{8}{5}$

Correct answer:

$\frac{9}{35}$

Explanation:

$\frac{6}{7}\div\frac{10}{3}=\frac{6}{7}\times\frac{3}{10}$

In this case, you can reduce the fractions being multiplied by cross-canceling before multiplying them together.

$\frac{6}{7}\times\frac{3}{10}=\frac{3}{7}\times\frac{3}{5}=\frac{9}{35}$

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Example Question #21 : Operations With Fractions

$\frac{35}{9}\div\frac{1}{4}=?$

Possible Answers:

$\frac{140}{9}$

$\frac{9}{140}$

$\frac{36}{13}$

Correct answer:

$\frac{140}{9}$

Explanation:

$\frac{35}{9}\div\frac{1}{4}=\frac{35}{9}\times\frac{4}{1}=\frac{140}{9}$

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Example Question #22 : Operations With Fractions

$\frac{15}{11}\div\frac{1}{5}=?$

Possible Answers:

$\frac{11}{75}$

$\frac{16}{55}$

$\frac{75}{11}$

Correct answer:

$\frac{75}{11}$

Explanation:

$\frac{15}{11}\div\frac{1}{5}=\frac{15}{11}\times\frac{5}{1}=\frac{75}{11}$

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Example Question #1272 : Ssat Upper Level Quantitative (Math)

Simplify the expression.

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

Possible Answers:

$\frac{3}{16}$

$\frac{1}{8}$

$\frac{5}{16}$

$\frac{5}{12}$

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 #23 : Operations With Fractions

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

Possible Answers:

$\frac{16}{9}$

$\frac{9}{16}$

$-\frac{16}{9}$

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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SSAT Upper Level Math : SSAT Upper Level Quantitative (Math)

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #6 : How To Divide Fractions

Example Question #7 : How To Divide Fractions

Example Question #1271 : Ssat Upper Level Quantitative (Math)

Example Question #9 : How To Divide Fractions

Example Question #21 : Operations With Fractions

Example Question #22 : Operations With Fractions

Example Question #1272 : Ssat Upper Level Quantitative (Math)

Example Question #2 : How To Multiply Fractions

Example Question #23 : Operations With Fractions

Example Question #3 : How To Multiply Fractions

All SSAT Upper Level Math Resources

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