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Nov23

## Two Ways of Dividing Fractions and Some Examples

In this post, we are going to learn how to divide fractions. In order to do this, we are going to take a look at two different methods:

##### Method 1 for dividing fractions: Cross-multiplication
• This method consists of multiplying the numerator of the first fraction by the denominator of the second fraction and then writing the answer in the resulting fraction’s numerator.
• Next, we multiply the denominator of the first fraction by the numerator of the second fraction, and then write the answer in the resulting fraction’s denominator*.
• Lastly, we simplify the final fraction.

For example, in order to divide the fraction

We multiply the numerator of the first fraction (3) by the denominator of the second fraction (10). This gives us the numerator for the final fraction: 3 x 10 = 30.

Next, we multiply the denominator of the first fraction (4) by the numerator of the second fraction (6). This gives us the denominator of the final fraction: 4 x 6 = 24.

The last step is to simplify the fraction. Since both numbers are multiples of 6, we can divide the numerator and denominator by 6.

30 ÷ 6 = 5

24 ÷ 6 = 4

Therefore, the result of the division is 5/4.

##### Method 2 of dividing fractions: Inverting and multiplying
• Step 1: Invert the second fraction. That is, swap the numerator for the denominator.
• Step 2: Simplify any numerator with any denominator.
• Step 3: Multiply across.

For example, we are going to divide:

Step 1: We invert the second fraction 6/4. This becomes 4/6.

Step 2: We simplify the numerators with the denominators.

Numerators are:
12 = 2 x 2 x 3
4 = 2 × 2

Denominators are:
5 = 5
6 = 2 × 3

We can simplify both from numerator and denominator a 2 and a 3. We call this process “cross canceling” if one numerator has a common factor with the other denominator.

And we multiply across:

We hope you liked this post.

If you want to see more examples, visit our previous post on word problems with division of fractions and How to Simplify Fractions: Lowest Terms Fractions.

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