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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 #231 : Number Concepts And Operations

Multiply these fractions:

$\frac{1}{8}\cdot \frac{2}{3}$

Possible Answers:

$\frac{1}{12}$

$\frac{1}{24}$

$\frac{2}{27}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{12}$

Explanation:

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

$\frac{1}{8}\cdot \frac{2}{3}=\frac{1\cdot 2}{8\cdot 3}=\frac{2}{24}$

Then simplify the fraction accordingly:

$\frac{2\div 2}{24\div 2}=\frac{1}{12}$

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Example Question #232 : Number Concepts And Operations

Multiply these fractions:

$\frac{4}{9}\cdot \frac{6}{8}$

Possible Answers:

$\frac{2}{3}$

$\frac{1}{8}$

$\frac{1}{4}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{3}$

Explanation:

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

$\frac{4}{9}\cdot \frac{6}{8}=\frac{4\cdot 6}{9\cdot 8}=\frac{24}{72}$

Then simplify the fraction accordingly:

$\frac{24\div 3}{72\div 3}=\frac{8}{24}$

But we are not done simplifying yet:

$\frac{8\div 8}{24\div 8}=\frac{1}{3}$

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Example Question #233 : Number Concepts And Operations

Multiply these fractions:

$\frac{3}{5}\cdot \frac{4}{6}$

Possible Answers:

$\frac{2}{11}$

$\frac{2}{5}$

$\frac{1}{10}$

$\frac{1}{5}$

Correct answer:

$\frac{2}{5}$

Explanation:

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

$\frac{3}{5}\cdot \frac{4}{6}=\frac{3\cdot 4}{5\cdot 6}=\frac{12}{30}$

Then simplify the fraction accordingly:

$\frac{12\div 3}{30\div 3}=\frac{4}{10}$

But we are not done simplifying yet:

$\frac{4\div 2}{10\div 2}=\frac{2}{5}$

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Example Question #232 : Number Concepts And Operations

Multiply these fractions:

$\frac{6}{7}\cdot \frac{5}{8}$

Possible Answers:

$\frac{17}{28}$

$\frac{15}{28}$

$\frac{11}{28}$

$\frac{5}{28}$

Correct answer:

$\frac{15}{28}$

Explanation:

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

$\frac{6}{7}\cdot \frac{5}{8}=\frac{6\cdot 5}{7\cdot 8}=\frac{30}{56}$

Then simplify the fraction accordingly:

$\frac{30\div 2}{56\div 2}=\frac{15}{28}$

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Example Question #233 : Number Concepts And Operations

Multiply these fractions:

$\frac{9}{10}\cdot \frac{3}{7}$

Possible Answers:

$\frac{12}{17}$

$\frac{12}{70}$

$\frac{27}{70}$

$\frac{26}{70}$

Correct answer:

$\frac{27}{70}$

Explanation:

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

$\frac{9}{10}\cdot \frac{3}{7}=\frac{9\cdot 3}{10\cdot 7}=\frac{27}{70}$

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

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Example Question #234 : Number Concepts And Operations

Multiply these fractions:

$\frac{5}{17}\cdot \frac{6}{7}$

Possible Answers:

$\frac{11}{119}$

$\frac{11}{24}$

$\frac{30}{117}$

$\frac{30}{119}$

Correct answer:

$\frac{30}{119}$

Explanation:

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

$\frac{5}{17}\cdot \frac{6}{7}=\frac{5\cdot 6}{17\cdot 7}=\frac{30}{119}$

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

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Example Question #235 : Number Concepts And Operations

Multiple these fractions:

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

Possible Answers:

$\frac{8}{35}$

$\frac{1}{2}$

$\frac{8}{12}$

$\frac{6}{35}$

Correct answer:

$\frac{8}{35}$

Explanation:

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

$\frac{4}{5}\cdot \frac{2}{7}=\frac{4\cdot 2}{5\cdot 7}=\frac{8}{35}$

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

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Example Question #236 : Number Concepts And Operations

Find the arithmetic mean of the following five numbers.

$\frac{2}{5}, \frac{1}{5},\frac{1}{2},\frac{3}{10}, \frac{2}{5}$

Possible Answers:

$\frac{6}{25}$

$\frac{2}{5}$

$\frac{3}{5}$

$\frac{9}{25}$

$\frac{7}{25}$

Correct answer:

$\frac{9}{25}$

Explanation:

Add the numbers, then divide by or, equivalently, multiply by $\frac{1}{5}$ .

$\frac{\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}}{5}$

$\frac{1}{5} \left(\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}\right )$

Find the common denominator of the terms we are adding.

$\frac{1}{5} \left(\frac{4}{10}+ \frac{2}{10}+\frac{5}{10}+\frac{3}{10}+ \frac{4}{10}\right )$

$\frac{1}{5} \left(\frac{4+2+5+3+4}{10} \right)$

Multiply and simplify.

$\frac{1}{5} \left(\frac{18}{10} \right)= \frac{1}{5} \left(\frac{9}{5} \right) = \frac{9}{25}$

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Example Question #2 : How To Add Fractions

Scott gave $\frac{1}{4}$ of the chocolate chip cookies he made to Cindy, and he gave $\frac{1}{6}$ of the cookies to Stephanie. What fraction of his chocolate chip cookies did he give away?

Possible Answers:

$\frac{1}{5}$

$\frac{1}{2}$

$\frac{5}{12}$

$\frac{7}{12}$

Correct answer:

$\frac{5}{12}$

Explanation:

This question wants you to add $\frac{1}{4}$ and $\frac{1}{6}$ . First, convert both fractions so that they share the same denominator.

$\frac{1}{4}=\frac{3}{12}$

$\frac{1}{6}=\frac{2}{12}$

$\frac{1}{4}+\frac{1}{6}=\frac{3}{12}+\frac{2}{12}=\frac{5}{12}$

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Example Question #1302 : Ssat Upper Level Quantitative (Math)

A poll was conducted in a class to see what fraction of the class plays sports. $\frac{3}{7}$ of the class plays basketball, and $\frac{1}{4}$ of the class plays soccer. The rest of the class do not play any sports. What fraction of the class plays a sport?

Possible Answers:

$\frac{11}{28}$

$\frac{4}{11}$

$\frac{5}{28}$

$\frac{19}{28}$

Correct answer:

$\frac{19}{28}$

Explanation:

To find what fraction of the class plays a sport, add together $\frac{3}{7}$ and $\frac{1}{4}$ .

First, convert both fractions so that the denominators are the same.

$\frac{3}{7}=\frac{12}{28}$

$\frac{1}{4}=\frac{7}{28}$

Now, you can add them together.

$\frac{3}{7}+\frac{1}{4}=\frac{12}{28}+\frac{7}{28}=\frac{19}{28}$

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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 #231 : Number Concepts And Operations

Example Question #232 : Number Concepts And Operations

Example Question #233 : Number Concepts And Operations

Example Question #232 : Number Concepts And Operations

Example Question #233 : Number Concepts And Operations

Example Question #234 : Number Concepts And Operations

Example Question #235 : Number Concepts And Operations

Example Question #236 : Number Concepts And Operations

Example Question #2 : How To Add Fractions

Example Question #1302 : Ssat Upper Level Quantitative (Math)

All SSAT Upper Level Math Resources

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