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ISEE Middle Level Math : How to divide fractions

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Example Questions

Example Question #1401 : Isee Middle Level (Grades 7 8) Mathematics Achievement

$\frac{4^{^{2}}+\left ( 12-4 \right )}{2}$ $\displaystyle \frac{4^{^{2}}+\left ( 12-4 \right )}{2}$

Possible Answers:

$\displaystyle 12$

$\displaystyle 36$

$\displaystyle 16$

$\displaystyle 8$

$\displaystyle 0$

Correct answer:

$\displaystyle 12$

Explanation:

In order to solve:

First, solve the exponent equation within the numerator portion of the fraction:

$\small \small \frac{4^{2} + \left ( 12-4 \right )}{2}=$ $\displaystyle \small \small \frac{4^{2} + \left ( 12-4 \right )}{2}=$

Then, solve the equation within the parentheses:

$\small \small \frac{16+8}{2}=$ $\displaystyle \small \small \frac{16+8}{2}=$

Then, solve the entire equation in the numerator portion and divide the numerator by the denominator.

$\small \small \frac{24}{2}=12$ $\displaystyle \small \small \frac{24}{2}=12$

Answer: 12

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Example Question #511 : Numbers And Operations

$\small 2 \frac{1}{5} \div 1 \frac{2}{4}=$ $\displaystyle \small 2 \frac{1}{5} \div 1 \frac{2}{4}=$

Possible Answers:

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

$\small 2 \frac{1}{10}$ $\displaystyle \small 2 \frac{1}{10}$

$\small 4$ $\displaystyle \small 4$

$\small 1 \frac{7}{15}$ $\displaystyle \small 1 \frac{7}{15}$

Correct answer:

$\small 1 \frac{7}{15}$ $\displaystyle \small 1 \frac{7}{15}$

Explanation:

To solve:

First, turn the mixed fractions into improper fractions.

$\small \small \small \frac{11}{5}\div \frac{6}{4}=$ $\displaystyle \small \small \small \frac{11}{5}\div \frac{6}{4}=$

Then, change the operation to multiplication and flip the second fraction. Solve accordingly and simplify the answer if possible.

$\small \small \frac{11}{5}\cdot \frac{4}{6}=$ $\displaystyle \small \small \frac{11}{5}\cdot \frac{4}{6}=$

The answer is $\small 1\frac{7}{15}$ $\displaystyle \small 1\frac{7}{15}$.

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Example Question #511 : Numbers And Operations

What is $\frac{3}{5}$ $\displaystyle \frac{3}{5}$ divided by $\frac{3}{25}$ $\displaystyle \frac{3}{25}$?

Possible Answers:

$\displaystyle 5$

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

$\frac{1}{5}$ $\displaystyle \frac{1}{5}$

$\displaystyle 3$

$\displaystyle 15$

Correct answer:

$\displaystyle 5$

Explanation:

$\frac{3}{5}\div\frac{3}{25}=\frac{3}{5}\cdo*\frac{25}{3}=5$ $\displaystyle \frac{3}{5}\div\frac{3}{25}=\frac{3}{5}\cdo*\frac{25}{3}=5$

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Example Question #1 : How To Divide Fractions

Evaluate:

$\frac{\frac{2}{7}}{\frac{9}{14}}$ $\displaystyle \frac{\frac{2}{7}}{\frac{9}{14}}$

Possible Answers:

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

$\frac{49}{9}$ $\displaystyle \frac{49}{9}$

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

$\frac{13}{14}$ $\displaystyle \frac{13}{14}$

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

Correct answer:

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

Explanation:

Rewrite this horizontally as a division expression, rewrite as a product, cross-cancel, and multply across:

$\frac{\frac{2}{7}}{\frac{9}{14}}$ $\displaystyle \frac{\frac{2}{7}}{\frac{9}{14}}$ $= \frac{2}{7} \div \frac{9}{14} = \frac{2}{7} \cdot \frac{14}{9} = \frac{2}{1} \cdot \frac{2}{9} = \frac{2\cdot 2}{1\cdot 9} =\frac{4}{9}$ $\displaystyle = \frac{2}{7} \div \frac{9}{14} = \frac{2}{7} \cdot \frac{14}{9} = \frac{2}{1} \cdot \frac{2}{9} = \frac{2\cdot 2}{1\cdot 9} =\frac{4}{9}$

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Example Question #1 : How To Divide Fractions

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

Possible Answers:

$\frac{2}{13}$ $\displaystyle \frac{2}{13}$

$2\frac{6}{25}$ $\displaystyle 2\frac{6}{25}$

$\frac{13}{2}$ $\displaystyle \frac{13}{2}$

$1\frac{1}{25}$ $\displaystyle 1\frac{1}{25}$

Correct answer:

$\frac{2}{13}$ $\displaystyle \frac{2}{13}$

Explanation:

First, convert each fraction into an improper fraction

$\frac{2}{5}\div 2\frac{3}{5}=\frac{2}{5}\div \frac{13}{5}=$ $\displaystyle \frac{2}{5}\div 2\frac{3}{5}=\frac{2}{5}\div \frac{13}{5}=$

Then, change the operation to mulitplication and flip the second fraction:

$\frac{2}{5}*\frac{5}{13}=$ $\displaystyle \frac{2}{5}*\frac{5}{13}=$

Reduce and solve accordingly:

Answer: $\frac{2}{13}$ $\displaystyle \frac{2}{13}$

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Example Question #2 : How To Divide Fractions

$\dpi{100} 9\div \frac{1}{7}=$ $\displaystyle \dpi{100} 9\div \frac{1}{7}=$

Possible Answers:

$\dpi{100} \frac{9}{7}$ $\displaystyle \dpi{100} \frac{9}{7}$

$\dpi{100} 1$ $\displaystyle \dpi{100} 1$

$\dpi{100} \frac{7}{9}$ $\displaystyle \dpi{100} \frac{7}{9}$

$\dpi{100} 63$ $\displaystyle \dpi{100} 63$

Correct answer:

$\dpi{100} 63$ $\displaystyle \dpi{100} 63$

Explanation:

We never actually divide fractions. When given a division problem, you multiply by the reciprocal of the 2nd fraction.

So, $\dpi{100} 9\div \frac{1}{7}$ $\displaystyle \dpi{100} 9\div \frac{1}{7}$ becomes $\dpi{100} 9\times \frac{7}{1}$ $\displaystyle \dpi{100} 9\times \frac{7}{1}$.

This is the same as $\dpi{100} 9\times7=63$ $\displaystyle \dpi{100} 9\times7=63$

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Example Question #2 : How To Divide Fractions

Divide: $0.17 \div 32$ $\displaystyle 0.17 \div 32$

Possible Answers:

0.01882 $\displaystyle 0.01882$

$\displaystyle 0.001882$

$\displaystyle 0.0053125$

$\displaystyle 0.053125$

0.53125 $\displaystyle 0.53125$

Correct answer:

$\displaystyle 0.0053125$

Explanation:

Simply use the long division process. The quotient will be:

$0.17 \div 32 = 0.0053125$ $\displaystyle 0.17 \div 32 = 0.0053125$

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Example Question #3 : How To Divide Fractions

Solve:

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

Possible Answers:

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

$\displaystyle 4$

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

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

Correct answer:

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

Explanation:

$\frac{3}{4}\div\frac{1}{3}=\frac{3}{4}\times\frac{3}{1}=\frac{9}{4}$ $\displaystyle \frac{3}{4}\div\frac{1}{3}=\frac{3}{4}\times\frac{3}{1}=\frac{9}{4}$

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Example Question #4 : How To Divide Fractions

Simplify: $\frac{\frac{2}{7}}{\frac{9}{14}}$ $\displaystyle \frac{\frac{2}{7}}{\frac{9}{14}}$

Possible Answers:

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

$\frac{13}{14}$ $\displaystyle \frac{13}{14}$

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

$\frac{9}{49}$ $\displaystyle \frac{9}{49}$

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

Correct answer:

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

Explanation:

Rewrite this as a division, dividing the numerator by the denominator:

$\frac{\frac{2}{7}}{\frac{9}{14}} = \frac{2}{7} \div \frac{9}{14} = \frac{2}{7} \times \frac{14}{9}= \frac{2}{1} \times \frac{2}{9}=\frac{2 \times 2}{1 \times 9}= \frac{4}{9}$ $\displaystyle \frac{\frac{2}{7}}{\frac{9}{14}} = \frac{2}{7} \div \frac{9}{14} = \frac{2}{7} \times \frac{14}{9}= \frac{2}{1} \times \frac{2}{9}=\frac{2 \times 2}{1 \times 9}= \frac{4}{9}$

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Example Question #5 : How To Divide Fractions

Simplify:

$\frac{\frac{2}{5}}{\frac{7}{10}}$ $\displaystyle \frac{\frac{2}{5}}{\frac{7}{10}}$

Possible Answers:

$\frac{11}{10}$ $\displaystyle \frac{11}{10}$

$\frac{7}{25}$ $\displaystyle \frac{7}{25}$

$\frac{4}{7}$ $\displaystyle \frac{4}{7}$

$\frac{7}{4}$ $\displaystyle \frac{7}{4}$

$\frac{25}{7}$ $\displaystyle \frac{25}{7}$

Correct answer:

$\frac{4}{7}$ $\displaystyle \frac{4}{7}$

Explanation:

Rewrite as a division, then solve:

$\frac{\frac{2}{5}}{\frac{7}{10}} = \frac{2}{5} \div \frac{7}{10} = \frac{2}{5} \times \frac{10}{7} = \frac{2}{1} \times \frac{2}{7} = \frac{4}{7}$ $\displaystyle \frac{\frac{2}{5}}{\frac{7}{10}} = \frac{2}{5} \div \frac{7}{10} = \frac{2}{5} \times \frac{10}{7} = \frac{2}{1} \times \frac{2}{7} = \frac{4}{7}$

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ISEE Middle Level Math : How to divide fractions

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #1401 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Example Question #511 : Numbers And Operations

Example Question #511 : Numbers And Operations

Example Question #1 : How To Divide Fractions

Example Question #1 : How To Divide Fractions

Example Question #2 : How To Divide Fractions

Example Question #2 : How To Divide Fractions

Example Question #3 : How To Divide Fractions

Example Question #4 : How To Divide Fractions

Example Question #5 : How To Divide Fractions

All ISEE Middle Level Math Resources

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