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Nov23

Two Ways of Dividing Fractions and Some Examples

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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

 dividing fractions

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

 dividing fractions

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 from the division is 5/4

 dividing fractions

Method 2 fo 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:

 dividing fractions

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:

 dividing fractions

We hope you liked this post.

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

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