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SSAT Middle Level Math : Numbers and Operations

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

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10 Diagnostic Tests 225 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #14 : How To Subtract Fractions

The time is now 1:32 PM. What time was it three hours and seventeen minutes ago?

Possible Answers:

$10:05\textrm{ AM}$ $\displaystyle 10:05\textrm{ AM}$

$10:15\textrm{ AM}$ $\displaystyle 10:15\textrm{ AM}$

$11:15\textrm{ AM}$ $\displaystyle 11:15\textrm{ AM}$

The correct answer is not given among the other choices.

$11:05 \textrm{ AM}$ $\displaystyle 11:05 \textrm{ AM}$

Correct answer:

$10:15\textrm{ AM}$ $\displaystyle 10:15\textrm{ AM}$

Explanation:

One hour and thirty-two minutes have elapsed since midnight. Since three hours and seventeen minutes make a greater quantity, we need to look at this as thirteen hours and thirty-two minutes having elapsed since noon.

We can subtract hours, then subtract minutes:

$13\textrm{ hr }32\textrm{ min}$ $\displaystyle 13\textrm{ hr }32\textrm{ min}$

$\underline{- 3\textrm{ hr }17\textrm{ min}}$ $\displaystyle \underline{- 3\textrm{ hr }17\textrm{ min}}$

$10 \textrm{ hr }15 \textrm{ min}$ $\displaystyle 10 \textrm{ hr }15 \textrm{ min}$

The time was 10:15 AM.

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Example Question #13 : How To Subtract Fractions

Which of the following is the difference of seven tenths and seventeen hundredths?

Possible Answers:

0.053 $\displaystyle 0.053$

0.5983 $\displaystyle 0.5983$

0.53 $\displaystyle 0.53$

0.683 $\displaystyle 0.683$

0.6983 $\displaystyle 0.6983$

Correct answer:

0.53 $\displaystyle 0.53$

Explanation:

Seven tenths is equal to 0.7; seventeen hundredths is equal to 0.17. Subtract them, rewriting 0.7 as 0.70;

0.70 $\displaystyle 0.70$

$\underline{- \; 0.17 }$ $\displaystyle \underline{- \; 0.17 }$

0.53 $\displaystyle 0.53$

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Example Question #51 : How To Subtract Fractions

$\frac{3}{4}-\frac{2}{3}$ $\displaystyle \frac{3}{4}-\frac{2}{3}$

Possible Answers:

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{1}{24}$ $\displaystyle \frac{1}{24}$

$\frac{1}{0}$ $\displaystyle \frac{1}{0}$

$\frac{1}{12}$ $\displaystyle \frac{1}{12}$

$\frac{1}{1}$ $\displaystyle \frac{1}{1}$

Correct answer:

$\frac{1}{12}$ $\displaystyle \frac{1}{12}$

Explanation:

$\frac{3}{4}-\frac{2}{3}$ $\displaystyle \frac{3}{4}-\frac{2}{3}$

In order to solve this problem, we first have to find common denominators.

$\frac{3}{4}\times\frac{3}{3}=\frac{9}{12}$ $\displaystyle \frac{3}{4}\times\frac{3}{3}=\frac{9}{12}$

$\frac{2}{3\time}\times\frac{4}{4}=\frac{8}{12}$ $\displaystyle \frac{2}{3\time}\times\frac{4}{4}=\frac{8}{12}$

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{9}{12}-\frac{8}{12}=\frac{1}{12}$ $\displaystyle \frac{9}{12}-\frac{8}{12}=\frac{1}{12}$

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Example Question #141 : Numbers And Operations

$\frac{8}{12}-\frac{1}4{}$ $\displaystyle \frac{8}{12}-\frac{1}4{}$

Possible Answers:

$\frac{5}{12}$ $\displaystyle \frac{5}{12}$

$\frac{5}{0}$ $\displaystyle \frac{5}{0}$

$\frac{7}{16}$ $\displaystyle \frac{7}{16}$

$\frac{7}{8}$ $\displaystyle \frac{7}{8}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

Correct answer:

$\frac{5}{12}$ $\displaystyle \frac{5}{12}$

Explanation:

$\frac{8}{12}-\frac{1}4{}$ $\displaystyle \frac{8}{12}-\frac{1}4{}$

In order to solve this problem, we first have to find common denominators.

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

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{8}{12}-\frac{3}{12}=\frac{5}{12}$ $\displaystyle \frac{8}{12}-\frac{3}{12}=\frac{5}{12}$

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Example Question #151 : Numbers And Operations

Solve:

$\frac{2}{3}-\frac{3}{5}$ $\displaystyle \frac{2}{3}-\frac{3}{5}$

Possible Answers:

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\frac{1}{30}$ $\displaystyle \frac{1}{30}$

$\frac{5}{15}$ $\displaystyle \frac{5}{15}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{1}{15}$ $\displaystyle \frac{1}{15}$

Correct answer:

$\frac{1}{15}$ $\displaystyle \frac{1}{15}$

Explanation:

$\frac{2}{3}-\frac{3}{5}$ $\displaystyle \frac{2}{3}-\frac{3}{5}$

In order to solve this problem, we first have to find common denominators.

$\frac{2}{3}\times\frac{5}{5}=\frac{10}{15}$ $\displaystyle \frac{2}{3}\times\frac{5}{5}=\frac{10}{15}$

$\frac{3}{5}\times \frac{3}{3}=\frac{9}{15}$ $\displaystyle \frac{3}{5}\times \frac{3}{3}=\frac{9}{15}$

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{10}{15}-\frac{9}{15}=\frac{1}{15}$ $\displaystyle \frac{10}{15}-\frac{9}{15}=\frac{1}{15}$

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Example Question #152 : Numbers And Operations

Solve:

$\frac{7}{8}-\frac{3}{16}$ $\displaystyle \frac{7}{8}-\frac{3}{16}$

Possible Answers:

$\frac{1}{4}$ $\displaystyle \frac{1}{4}$

$\frac{4}{16}$ $\displaystyle \frac{4}{16}$

$\frac{13}{16}$ $\displaystyle \frac{13}{16}$

$\frac{4}{8}$ $\displaystyle \frac{4}{8}$

$\frac{11}{16}$ $\displaystyle \frac{11}{16}$

Correct answer:

$\frac{11}{16}$ $\displaystyle \frac{11}{16}$

Explanation:

$\frac{7}{8}-\frac{3}{16}$ $\displaystyle \frac{7}{8}-\frac{3}{16}$

In order to solve this problem, we first have to find common denominators.

$\frac{7}{8}\times\frac{2}{2}=\frac{14}{16}$ $\displaystyle \frac{7}{8}\times\frac{2}{2}=\frac{14}{16}$

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{14}{16}-\frac{3}{16}=\frac{11}{16}$ $\displaystyle \frac{14}{16}-\frac{3}{16}=\frac{11}{16}$

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Example Question #22 : How To Subtract Fractions

$\frac{5}{6}-\frac{1}{4}$ $\displaystyle \frac{5}{6}-\frac{1}{4}$

Possible Answers:

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

$\frac{4}{2}$ $\displaystyle \frac{4}{2}$

$\frac{8}{13}$ $\displaystyle \frac{8}{13}$

$\frac{7}{0}$ $\displaystyle \frac{7}{0}$

Correct answer:

$\frac{7}{12}$ $\displaystyle \frac{7}{12}$

Explanation:

$\frac{5}{6}-\frac{1}{4}$ $\displaystyle \frac{5}{6}-\frac{1}{4}$

In order to solve this problem, we first have to find common denominators.

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

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

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{10}{12}-\frac{3}{12}=\frac{7}{12}$ $\displaystyle \frac{10}{12}-\frac{3}{12}=\frac{7}{12}$

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Example Question #141 : Fractions

$\frac{9}{10}-\frac{3}{5}$ $\displaystyle \frac{9}{10}-\frac{3}{5}$

Possible Answers:

$\frac{6}{5}$ $\displaystyle \frac{6}{5}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

$\frac{5}{7}$ $\displaystyle \frac{5}{7}$

$\frac{3}{0}$ $\displaystyle \frac{3}{0}$

Correct answer:

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

Explanation:

$\frac{9}{10}-\frac{3}{5}$ $\displaystyle \frac{9}{10}-\frac{3}{5}$

In order to solve this problem, we first have to find common denominators.

$\frac{3}{5}\times\frac{2}{2}=\frac{6}{10}$ $\displaystyle \frac{3}{5}\times\frac{2}{2}=\frac{6}{10}$

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{9}{10}-\frac{6}{10}=\frac{3}{10}$ $\displaystyle \frac{9}{10}-\frac{6}{10}=\frac{3}{10}$

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Example Question #23 : How To Subtract Fractions

$\frac{1}{2}-\frac{1}{3}$ $\displaystyle \frac{1}{2}-\frac{1}{3}$

Possible Answers:

$\frac{0}{6}$ $\displaystyle \frac{0}{6}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

$\frac{3}{4}$ $\displaystyle \frac{3}{4}$

$\frac{2}{6}$ $\displaystyle \frac{2}{6}$

Correct answer:

$\frac{1}{6}$ $\displaystyle \frac{1}{6}$

Explanation:

$\frac{1}{2}-\frac{1}{3}$ $\displaystyle \frac{1}{2}-\frac{1}{3}$

In order to solve this problem, we first have to find common denominators.

$\frac{1}{2}\times\frac{3}{3}=\frac{3}{6}$ $\displaystyle \frac{1}{2}\times\frac{3}{3}=\frac{3}{6}$

$\frac{1}{3}\times\frac{2}{2}=\frac{2}{6}$ $\displaystyle \frac{1}{3}\times\frac{2}{2}=\frac{2}{6}$

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{3}{6}-\frac{2}{6}=\frac{1}{6}$ $\displaystyle \frac{3}{6}-\frac{2}{6}=\frac{1}{6}$

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Example Question #6 : Subtract Fractions With Unlike Denominators

$\frac{3}{4}-\frac{5}{8}$ $\displaystyle \frac{3}{4}-\frac{5}{8}$

Possible Answers:

$\frac{1}2{}$ $\displaystyle \frac{1}2{}$

$\frac{2}{4}$ $\displaystyle \frac{2}{4}$

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

$\frac{3}{8}$ $\displaystyle \frac{3}{8}$

$\frac{11}{16}$ $\displaystyle \frac{11}{16}$

Correct answer:

$\frac{1}{8}$ $\displaystyle \frac{1}{8}$

Explanation:

$\frac{3}{4}-\frac{5}{8}$ $\displaystyle \frac{3}{4}-\frac{5}{8}$

In order to solve this problem, we first have to find common denominators.

$\frac{3}{4}\times\frac{2}{2}=\frac{6}{8}$ $\displaystyle \frac{3}{4}\times\frac{2}{2}=\frac{6}{8}$

Now that we have common denominators, we can subtract the fractions. Remember, when we add and subtract fractions, we only add or subtract the numerator.

$\frac{6}{8}-\frac{5}{8}=\frac{1}{8}$ $\displaystyle \frac{6}{8}-\frac{5}{8}=\frac{1}{8}$

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SSAT Middle Level Math : Numbers and Operations

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #14 : How To Subtract Fractions

Example Question #13 : How To Subtract Fractions

Example Question #51 : How To Subtract Fractions

Example Question #141 : Numbers And Operations

Example Question #151 : Numbers And Operations

Example Question #152 : Numbers And Operations

Example Question #22 : How To Subtract Fractions

Example Question #141 : Fractions

Example Question #23 : How To Subtract Fractions

Example Question #6 : Subtract Fractions With Unlike Denominators

All SSAT Middle Level Math Resources

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