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SSAT Upper Level Math : Number Concepts and Operations

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 #3 : How To Divide Fractions

$\frac{12}{7}\div\frac{3}{4}=?$

Possible Answers:

$\frac{18}{7}$

$\frac{7}{16}$

$\frac{16}{7}$

$\frac{9}{7}$

Correct answer:

$\frac{16}{7}$

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.

$\frac{12}{7}\div\frac{3}{4}=\frac{12}{7}\times\frac{4}{3}$

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

$\frac{12}{7}\times\frac{4}{3}=\frac{4}{7}\times\frac{4}{1}=\frac{16}{7}$

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Example Question #5 : How To Divide Fractions

$\frac{9}{10}\div\frac{4}{5}=?$

Possible Answers:

$\frac{8}{9}$

$\frac{13}{15}$

$\frac{9}{8}$

$\frac{18}{25}$

Correct answer:

$\frac{9}{8}$

Explanation:

$\frac{9}{10}\div\frac{4}{5}=\frac{9}{10}\times\frac{5}{4}$

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

$\frac{9}{10}\times\frac{5}{4}=\frac{9}{2}\times\frac{1}{4}=\frac{9}{8}$

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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:

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

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 #201 : Number Concepts And Operations

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

Possible Answers:

$\frac{5}{84}$

$\frac{60}{7}$

$\frac{6}{19}$

$\frac{7}{60}$

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 #11 : How To Divide Fractions

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

Possible Answers:

$\frac{140}{9}$

$\frac{36}{13}$

$\frac{9}{140}$

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 #12 : How To Divide Fractions

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

Possible Answers:

$\frac{16}{55}$

$\frac{75}{11}$

$\frac{11}{75}$

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 #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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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Number Concepts and Operations

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

All SSAT Upper Level Math Resources

Example Questions

Example Question #3 : How To Divide Fractions

Example Question #5 : How To Divide Fractions

Example Question #6 : How To Divide Fractions

Example Question #7 : How To Divide Fractions

Example Question #201 : Number Concepts And Operations

Example Question #9 : How To Divide Fractions

Example Question #11 : How To Divide Fractions

Example Question #12 : How To Divide Fractions

Example Question #1 : How To Multiply Fractions

Example Question #2 : How To Multiply Fractions

All SSAT Upper Level Math Resources

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