Dividing Fractions

Dividing Fractions

Dividing fractions is a straightforward process that relies on the concept of reciprocals and converts the division problem into a multiplication problem. The popular mnemonic for remembering the steps is “Keep, Change, Flip”

The following diagram shows how to divide fractions using the Keep-Change-Flip method. Scroll down the page for more examples and solutions on dividing fractions by fractions.

 

Fraction Worksheets
Practice with the following worksheets.
Printable & Online Fractions Worksheets

The Basic Rule (“Keep, Change, Flip”)
To divide one fraction by another:

1. Keep the first fraction as it is.
2. Change the division sign (÷) to a multiplication sign (×).
3. Flip the second fraction (find its reciprocal).
4. Then, multiply the fractions as usual (numerator by numerator, denominator by denominator).
5. Simplify the resulting fraction if possible.

What is a Reciprocal?
The reciprocal of a fraction is obtained by swapping its numerator and denominator.

The reciprocal of \(\frac{a}{b}\) is \(\frac{b}{a}\).
The reciprocal of a whole number (like 5) is found by first writing it as a fraction \(\frac{5}{1}\), then flipping it \(\frac{1}{5}\).

Step-by-Step Example:
Problem: \(\frac{1}{2} \div \frac{3}{4}\)

1. Keep the first fraction: \(\frac{1}{2}\)
2. Change the division sign to multiplication: ×
3. Flip the second fraction (find its reciprocal): \(\frac{3}{4}\) becomes \(\frac{4}{3}\)
4. Now you have a multiplication problem: \(\frac{1}{2} × \frac{4}{3}\)
   \(\frac{1}{2} × \frac{4}{3} = \frac{4}{6} = \frac{2}{3}\)

Videos

Dividing fractions
Examples:
3/4 ÷ 2/7
15/16 ÷ 9/22
2/3 ÷ 3/5

• Show Step-by-step Solutions

Dividing fractions
Examples:
2/3 ÷ 5/6
2/3 ÷ 5/2
5/7 ÷ 10/3
2 ÷ 1/3

• Show Step-by-step Solutions

GMAT Prep Math - Arithmetic - Dividing Fractions
Examples:
1/2 ÷ 3/5
3 3/5 ÷ 1 2/3

• Show Step-by-step Solutions

Dividing Fractions with Keep, Change, Flip
Fractions Rap Song

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Check out this lesson on types of fractions:
Types of Fractions
Check out this lesson on equivalent fractions:
Equivalent Fractions
Check out this lesson on how to convert between mixed numbers and improper fractions:
Mixed Numbers & Improper Fractions
Check out this lesson on how to convert between fractions and decimals:
Fractions & Decimals

Check out these lessons on adding, subtracting, multiplying, and dividing fractions:
Adding Fractions
Subtracting Fractions
Multiplying Fractions
Dividing Fractions

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