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How to Divide Fractions (Mathematics Lesson)

Dividing Fractions

Fractions can be divided.

Imagine you wanted to divide 1/5 (one-fifth) by 2/3 (two-thirds).

How to Divide Fractions

An Example Question

What is the answer to dividing the fractions below?

Dividing by a fraction can be changed to multiplying by a fraction (which is much easier!). Flip the fraction you are dividing by upside down, then change the ÷ to a ×.

Step 1
Flip the fraction you after the ÷ sign upside-down (so the top number becomes the bottom number and the bottom number becomes the top number.)



Step 2
Change the ÷ sign to a × sign.



Now we are multiplying fractions. Multiply 1/5 (one-fifth) by 3/2.



Step 3
Multiply the top numbers (called the numerators) of the fractions together
1 × 3 = 3
Step 4
Multiply the bottom numbers (called the denominators) of the fractions together.
5 × 2 = 10
Step 5
The answer from Step 3 is the numerator of our answer. The answer from Step 4 is the denominator of our answer.



Step 6
Simplify the fraction if possible. (The fraction in our example is already as simple as possible.)

A Real Example of How to Divide Fractions

The slider below gives a real example of how to divide fractions.
Quick Test
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Here's a second test on dividing fractions.
Here's a third test on dividing fractions.
Top Tip

Dividing by a Fraction = Multiplying by the Upside-Down Fraction

Dividing by a fraction is equivalent to multiplying by the reciprocal of the fraction (i.e the fraction turned upside-down).

For example, to divide by two-thirds:


Change the ÷ sign to a × sign and flip the fraction upside-down:


The operation becomes:



which is just the same as multiplying fractions.

Flip the Fraction You Are Dividing by - Not Into

When dividing one fraction by another, it is very important that the fraction after the ÷ sign is flipped over, not before it.

For example, to divide the following fractions:


The ÷ sign must be changed to a × sign. But it would be wrong to flip the first fraction upside-down:


It would be right to flip the second fraction over:



Note
What Is a Fraction?

A fraction is a part of a whole number.

Fractions consist of a numerator and a denominator.

There are three different types of fractions: