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ISEE Middle Level Math : How to divide fractions

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Example Questions

Example Question #41 : How To Divide Fractions

Divide the following:

$10 \div \frac{1}{2}$

Possible Answers:

$\frac{2}{10}$

$\frac{1}{2}$

$\frac{1}{10}$

Correct answer:

Explanation:

To divide fractions, follow these steps:

Leave the first fraction alone.
Change the division sign to a multiplication sign.
Replace the second fraction with it's reciprocal.
Multiply.

So, given the problem

$10 \div \frac{1}{2}$

we will follow the steps.

Leave the first fraction alone. In this case, we need to write 10 as a fraction. We know that whole numbers can be written as fractions over 1. So, we get

$\frac{10}{1} \div \frac{1}{2}$
Change the division sign to a multiplication sign.

$\frac{10}{1} \cdot \frac{1}{2}$
Replace the second fraction with it's reciprocal. To write the reciprocal, the numerator becomes the denominator, and the denominator becomes the numerator. In other words, we will flip the second fraction.

$\frac{10}{1} \cdot \frac{2}{1}$
Multiply. We will multiply straight across.

$\frac{10 \cdot 2}{1 \cdot 1}$

$\frac{20}{1}$

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Example Question #42 : How To Divide Fractions

Divide the following:

$\frac{3}{4} \div \frac{1}{2}$

Possible Answers:

$\frac{3}{8}$

$\frac{1}{2}$

$\frac{1}{6}$

$\frac{3}{2}$

$\frac{1}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

To divide fractions, we will use the following steps:

Leave the first fraction alone.
Change the division sign to a multiplication sign.
Replace the second fraction with it's reciprocal.
Multiply.

So, given the problem

$\frac{3}{4} \div \frac{1}{2}$

we will follow the steps:

Leave the first fraction alone.

$\frac{3}{4} \div \frac{1}{2}$
Change the division sign to a multiplication sign.

$\frac{3}{4} \cdot \frac{1}{2}$
Replace the second fraction with it's reciprocal. To find the reciprocal, the numerator becomes the denominator, and the denominator becomes the numerator. In other words, we will flip the fraction.

$\frac{3}{4} \cdot \frac{2}{1}$
Multiply.

$\frac{3 \cdot 2}{4 \cdot 1}$

$\frac{6}{4}$

$\frac{3}{2}$

Report an Error

Example Question #43 : How To Divide Fractions

Divide the following:

$\frac{2}{3} \div \frac{1}{4}$

Possible Answers:

$\frac{1}{4}$

$\frac{8}{3}$

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{3}{8}$

Correct answer:

$\frac{8}{3}$

Explanation:

To divide fractions, we will use the following steps:

Keep the first fraction the same.
Change the multiplication sign to a division sign.
Replace the second fraction with it's reciprocal.
Multiply.

So, given the problem

$\frac{2}{3} \div \frac{1}{4}$

we will follow the steps.

Keep the first fraction the same.

$\frac{2}{3} \div \frac{1}{4}$
Change the multiplication sign to a division sign.

$\frac{2}{3} \cdot \frac{1}{4}$
Replace the second fraction with it's reciprocal. To write the reciprocal, the numerator will become the denominator, and the denominator will become the numerator. In other words, we will flip the fraction.

$\frac{2}{3} \cdot \frac{4}{1}$
Multiply.

$\frac{2}{3} \cdot \frac{4}{1}$

$\frac{2 \cdot 4}{3 \cdot 1}$

$\frac{8}{3}$

Report an Error

Example Question #404 : Fractions

Divide the following:

$\frac{4}{8} \div \frac{1}{2}$

Possible Answers:

$\frac{1}{2}$

$\frac{4}{6}$

$\frac{1}{4}$

Correct answer:

Explanation:

To divide fractions, we will use the following steps:

Leave the first fraction alone.
Change the division sign to a multiplication sign.
Replace the second fraction with it’s reciprocal.
Multiply.

So, given the problem

$\frac{4}{8} \div \frac{1}{2}$

We will follow the steps.

Leave the first fraction alone.

$\frac{4}{8} \div \frac{1}{2}$

Change the division sign to a multiplication sign.

$\frac{4}{8} \cdot \frac{1}{2}$

Replace the second fraction with it’s reciprocal. To find the reciprocal of a fraction, the numerator becomes the denominator, and the denominator becomes the numerator. In other words, we will flip the fraction.

$\frac{4}{8} \cdot \frac{2}{1}$

Multiply.

$\frac{4 \cdot 2}{8 \cdot 1}$

$\frac{8}{8}$

Report an Error

Example Question #411 : Fractions

Divide the following:

$\frac{8}{9} \div 12$

Possible Answers:

$\frac{4}{5}$

$\frac{7}{8}$

$\frac{2}{27}$

$\frac{3}{5}$

Correct answer:

$\frac{2}{27}$

Explanation:

To divide fractions, we will take the first fraction and multiply by the reciprocal of the second fraction. So, we get

$\frac{8}{9} \cdot \frac{1}{12}$

We will simplify before we multiply to make things easier. The 8 and the 12 can both be divided by 4. We get

$\frac{2}{9} \cdot \frac{1}{3}$

$\frac{2 \cdot 1}{9 \cdot 3}$

$\frac{2}{27}$

Report an Error

Example Question #412 : Fractions

Divide the following:

$\frac{8}{9} \div \frac{1}{4}$

Possible Answers:

$\frac{32}{9}$

$\frac{8}{3}$

$\frac{4}{9}$

$\frac{2}{3}$

Correct answer:

$\frac{32}{9}$

Explanation:

To divide, we will multiply the first fraction by the reciprocal of the second fraction. To find the reciprocal, the numerator becomes the denominator, and the denominator becomes the numerator (in other words, we will flip the fraction).

We get

$\frac{8}{9} \div \frac{1}{4}$

$\frac{8}{9} \cdot \frac{4}{1}$

$\frac{8 \cdot 4}{9 \cdot 1}$

$\frac{32}{9}$

Report an Error

Example Question #413 : Fractions

Divide the following:

$\frac{4}{5} \div \frac{1}{2}$

Possible Answers:

$\frac{2}{10}$

$\frac{5}{8}$

$\frac{4}{10}$

$\frac{8}{5}$

$\frac{2}{5}$

Correct answer:

$\frac{8}{5}$

Explanation:

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction.

To find the reciprocal, the numerator will become the denominator, and the denominator will become the numerator. In other words, we will flip the fraction.

So, we get

$\frac{4}{5} \div \frac{1}{2}$

$\frac{4}{5} \cdot \frac{2}{1}$

$\frac{4 \cdot 2}{5 \cdot 1}$

$\frac{8}{5}$

Report an Error

Example Question #414 : Fractions

Divide the following:

$\frac{8}{9} \div \frac{1}{2}$

Possible Answers:

$\frac{8}{4.5}$

$\frac{4}{9}$

$\frac{1}{2}$

$\frac{16}{9}$

$\frac{8}{18}$

Correct answer:

$\frac{16}{9}$

Explanation:

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction. To find the reciprocal, the numerator will become the denominator, and the denominator will become the numerator. In other words, we will flip the fraction. So, we get

$\frac{8}{9} \div \frac{1}{2}$

$\frac{8}{9} \cdot \frac{2}{1}$

$\frac{8 \cdot 2}{9 \cdot 1}$

$\frac{16}{9}$

Report an Error

Example Question #415 : Fractions

Divide the following:

$\frac{9}{10} \div \frac{1}{2}$

Possible Answers:

$\frac{3}{5}$

$\frac{9}{20}$

$\frac{4}{5}$

$\frac{9}{5}$

Correct answer:

$\frac{9}{5}$

Explanation:

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction. To find the reciprocal of a fraction, the numerator will become the denominator, and the denominator will become the numerator. In other words, we will flip the fraction.

So, we get

$\frac{9}{10} \div \frac{1}{2}$

$\frac{9}{10} \cdot \frac{2}{1}$

$\frac{9 \cdot 2}{10 \cdot 1}$

$\frac{18}{10}$

$\frac{9}{5}$

Report an Error

Example Question #416 : Fractions

Divide the following:

$\frac{6}{8} \div \frac{1}{2}$

Possible Answers:

$\frac{6}{8}$

$\frac{3}{2}$

$\frac{3}{4}$

$\frac{1}{2}$

$\frac{3}{8}$

Correct answer:

$\frac{3}{2}$

Explanation:

So, we get

$\frac{6}{8} \div \frac{1}{2}$

$\frac{6}{8} \cdot \frac{2}{1}$

$\frac{6 \cdot 2}{8 \cdot 1}$

$\frac{12}{8}$

$\frac{6}{4}$

$\frac{3}{2}$

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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 #41 : How To Divide Fractions

Example Question #42 : How To Divide Fractions

Example Question #43 : How To Divide Fractions

Example Question #404 : Fractions

Example Question #411 : Fractions

Example Question #412 : Fractions

Example Question #413 : Fractions

Example Question #414 : Fractions

Example Question #415 : Fractions

Example Question #416 : Fractions

All ISEE Middle Level Math Resources

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