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SSAT Middle Level Math : Fractions

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Example Questions

Example Question #372 : Concepts

How many times does $\frac{1}{4}$ $\displaystyle \frac{1}{4}$ go into $\displaystyle 16$ $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ ?

Possible Answers:

$\displaystyle 7$

$\displaystyle 65$

121 $\displaystyle 121$

$\displaystyle 67$

$\displaystyle 55$

Correct answer:

$\displaystyle 67$

Explanation:

This problem can be solved by dividing $\displaystyle 16$ $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ by $\frac{1}{4}$ $\displaystyle \frac{1}{4}$. First, simplify $\displaystyle 16$ $\frac{3}{4}$ $\displaystyle \frac{3}{4}$ into $\frac{67}{4}$ $\displaystyle \frac{67}{4}$, then divide by $\frac{1}{4}$ $\displaystyle \frac{1}{4}$.

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Example Question #502 : Numbers And Operations

Solve:

$\frac{3}{7}\div \frac{1}{5}$ $\displaystyle \frac{3}{7}\div \frac{1}{5}$

Possible Answers:

$\frac{3}{35}$ $\displaystyle \frac{3}{35}$

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

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

$\frac{15}{7}$ $\displaystyle \frac{15}{7}$

Correct answer:

$\frac{15}{7}$ $\displaystyle \frac{15}{7}$

Explanation:

$\frac{3}{7}\div \frac{1}{5}=\frac{3}{7}\times \frac{5}{1}=\frac{15}{7}$ $\displaystyle \frac{3}{7}\div \frac{1}{5}=\frac{3}{7}\times \frac{5}{1}=\frac{15}{7}$

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Example Question #16 : How To Divide Fractions

Solve:

$\frac{9}{10}\div \frac{3}{5}=$ $\displaystyle \frac{9}{10}\div \frac{3}{5}=$

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

$\small \frac{9}{10}\div \frac{3}{5}=\frac{9}{10}\times\frac{5}{3}=\frac{45}{30}=\frac{3}{2}$ $\displaystyle \small \frac{9}{10}\div \frac{3}{5}=\frac{9}{10}\times\frac{5}{3}=\frac{45}{30}=\frac{3}{2}$

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Example Question #21 : How To Divide Fractions

$\frac{7}{49}\div \frac{2}{14}=$ $\displaystyle \frac{7}{49}\div \frac{2}{14}=$

Possible Answers:

$1\frac{3}{4}$ $\displaystyle 1\frac{3}{4}$

$\frac{2}{94}$ $\displaystyle \frac{2}{94}$

$\displaystyle 1$

196 $\displaystyle 196$

$\displaystyle 49$

Correct answer:

$\displaystyle 1$

Explanation:

Change division to multiplication by flipping the second fraction. Then, simplify and perform the multiplication.

$\frac{7}{49}\div \frac{2}{14}=$ $\displaystyle \frac{7}{49}\div \frac{2}{14}=$

$\frac{7}{49}\times \frac{14}{2}= \frac{1}{7}\times \frac{7}{1}=\frac{7}{7}=1$ $\displaystyle \frac{7}{49}\times \frac{14}{2}= \frac{1}{7}\times \frac{7}{1}=\frac{7}{7}=1$

The answer is 1.

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Example Question #503 : Numbers And Operations

$12 \frac{4}{6} \div 4\frac{2}{4}=$ $\displaystyle 12 \frac{4}{6} \div 4\frac{2}{4}=$

Possible Answers:

$2\frac{20}{27}$ $\displaystyle 2\frac{20}{27}$

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

$2\frac{7}{9}$ $\displaystyle 2\frac{7}{9}$

$2\frac{22}{27}$ $\displaystyle 2\frac{22}{27}$

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

Correct answer:

$2\frac{22}{27}$ $\displaystyle 2\frac{22}{27}$

Explanation:

First convert each fraction into an improper fraction.

$\frac{76}{6}\div \frac{18}{4}=$ $\displaystyle \frac{76}{6}\div \frac{18}{4}=$

Then flip the second fraction, reduce and multiply:

$\frac{76}{6}\ast \frac{4}{18}=$ $\displaystyle \frac{76}{6}\ast \frac{4}{18}=$

The answer is $2\frac{22}{27}$ $\displaystyle 2\frac{22}{27}$.

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Example Question #504 : Numbers And Operations

Divide:

$\frac{4}{9}\div \frac{2}{3}$ $\displaystyle \frac{4}{9}\div \frac{2}{3}$

Possible Answers:

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

$\frac{7}{}9$ $\displaystyle \frac{7}{}9$

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

$\frac{4}{}9$ $\displaystyle \frac{4}{}9$

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

Correct answer:

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

Explanation:

The first step in dividing fractions is to make the second fraction a reciprocal (flip it) and then rewrite the problem as a multiplication problem: $\left(\frac{4}{9}\times \frac{3}{2}\right)$ $\displaystyle \left(\frac{4}{9}\times \frac{3}{2}\right)$.

You can cross-reduce so that the problem now becomes $\left(\frac{2}{3}\times \frac{1}{1}\right)$ $\displaystyle \left(\frac{2}{3}\times \frac{1}{1}\right)$. Then, mulitply straight across so that your answer is $\frac{2}{3}$ $\displaystyle \frac{2}{3}$.

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Example Question #23 : How To Divide Fractions

What is the below expression equal to?

$\frac{3}{5}\div \frac{2}{7}$ $\displaystyle \frac{3}{5}\div \frac{2}{7}$

Possible Answers:

$\frac{10}{21}$ $\displaystyle \frac{10}{21}$

$\frac{21}{10}$ $\displaystyle \frac{21}{10}$

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

$\displaystyle 2$

Correct answer:

$\frac{21}{10}$ $\displaystyle \frac{21}{10}$

Explanation:

When one fraction is being divided by another, the latter fraction must be inverted. The numerators are then multiplied by each other, and the denominators are also multiplied by each other.

$\frac{3}{5}\div \frac{2}{7}$ $\displaystyle \frac{3}{5}\div \frac{2}{7}$

$\frac{3}{5}\cdot \frac{7}{2}=\frac{21}{10}$ $\displaystyle \frac{3}{5}\cdot \frac{7}{2}=\frac{21}{10}$

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Example Question #24 : How To Divide Fractions

What is the value of $\displaystyle x$ in this equation?

$\frac{9}{5}\div \frac{5}{7}=x$ $\displaystyle \frac{9}{5}\div \frac{5}{7}=x$

Possible Answers:

$\frac{25}{63}$ $\displaystyle \frac{25}{63}$

$\frac{7}{9}$ $\displaystyle \frac{7}{9}$

$\frac{9}{7}$ $\displaystyle \frac{9}{7}$

$\frac{63}{25}$ $\displaystyle \frac{63}{25}$

Correct answer:

$\frac{63}{25}$ $\displaystyle \frac{63}{25}$

Explanation:

In order to solve $\frac{9}{5}\div \frac{5}{7}$ $\displaystyle \frac{9}{5}\div \frac{5}{7}$, the latter fraction must be inverted and then multiplied by the first fraction, as shown below:

$\frac{9}{5}\cdot \frac{7}{5} = \frac{63}{25}$ $\displaystyle \frac{9}{5}\cdot \frac{7}{5} = \frac{63}{25}$

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Example Question #21 : How To Divide Fractions

What is the solution to the expression below?

$\frac{1}{4}\div \frac{9}{17}$ $\displaystyle \frac{1}{4}\div \frac{9}{17}$

Possible Answers:

$\frac{17}{36}$ $\displaystyle \frac{17}{36}$

$\frac{36}{17}$ $\displaystyle \frac{36}{17}$

$\frac{3}{12}$ $\displaystyle \frac{3}{12}$

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

Correct answer:

$\frac{17}{36}$ $\displaystyle \frac{17}{36}$

Explanation:

When one fraction is being divided by another, the latter fraction must be inverted. The numerators are then multiplied together, and the denominators are also multiplied by each other.

$\frac{1}{4}\div \frac{9}{17}$ $\displaystyle \frac{1}{4}\div \frac{9}{17}$

$\frac{1}{4}\div \frac{17}{9}$ $\displaystyle \frac{1}{4}\div \frac{17}{9}$

$\frac{17}{36}$ $\displaystyle \frac{17}{36}$

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Example Question #162 : Operations With Fractions And Whole Numbers

$\small \frac{1}{7}\div\frac{2}{3}$ $\displaystyle \small \frac{1}{7}\div\frac{2}{3}$

Possible Answers:

$\small \frac{14}{3}$ $\displaystyle \small \frac{14}{3}$

$\small \frac{2}{21}$ $\displaystyle \small \frac{2}{21}$

$\small \frac{3}{14}$ $\displaystyle \small \frac{3}{14}$

$\small \frac{21}{2}$ $\displaystyle \small \frac{21}{2}$

$\small \frac{3}{11}$ $\displaystyle \small \frac{3}{11}$

Correct answer:

$\small \frac{3}{14}$ $\displaystyle \small \frac{3}{14}$

Explanation:

$\small \frac{1}{7}\div\frac{2}{3}$ $\displaystyle \small \frac{1}{7}\div\frac{2}{3}$

To divide fractions, we multiply by the reciprocal. In order to find the reciprocal, we simply flip the fraction over. The numerator becomes the denominator and the denominator becomes the numerator.

$\small \frac{1}{7}\times\frac{3}{2}=\frac{3}{14}$ $\displaystyle \small \frac{1}{7}\times\frac{3}{2}=\frac{3}{14}$

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SSAT Middle Level Math : Fractions

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #372 : Concepts

Example Question #502 : Numbers And Operations

Example Question #16 : How To Divide Fractions

Example Question #21 : How To Divide Fractions

Example Question #503 : Numbers And Operations

Example Question #504 : Numbers And Operations

Example Question #23 : How To Divide Fractions

Example Question #24 : How To Divide Fractions

Example Question #21 : How To Divide Fractions

Example Question #162 : Operations With Fractions And Whole Numbers

All SSAT Middle Level Math Resources

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