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Understanding the Division of Fractions

Today we’re going to learn how to perform a division of fractions using the very definition of division as the inverse operation of multiplication. This way we don’t need to use the more known methods that we’ve already seen in the post about Dividing fractions.

You might know how to use those methods, but without knowing what they mean. Learning how to divide fractions this way will give you a deeper mathematical understanding of the operation.

Example of division of fractions

Let’s take a look at how to solve the following division using mathematical compression:

division of fractions

Since division is the inverse operation to multiplication, we have to find a fraction that, when multiplied by 7/5 gives us a result of 2/3. Let’s see how to find it, I’m sure it’ll be easy for you.

division of fractions

Steps to find the result of the division

Making use of the simplification of fractions, let’s see how we can find the unknown term of our product, step by step.

  • Since we have a 7 as the numerator of the first term of the product and we don’t want it to appear in the result (which we already know is 2/3), if we put it in the denominator of the fraction that we’re multiplying by, it will disappear through simplification:

division of fractions

  • Since we have a 5 as the denominator and we don’t want it to appear in the result (which we already know it is 2/3), if we put it in the denominator of the fraction that we’re multiplying by, it will also disappear through simplification:

division of fractions

  • Now we need a 2 for the numerator, so we multiply this numerator by 2:

division of fractions

  • And finally, since we want a divisor of 3, we multiply this denominator by 3:

division of fractions

Result of the division

We’ve found the fraction we were looking for! So:

division of fractions

By doing the operations we get the fraction 10/21:

division of fractions

Therefore, since:

division of fractions


division of fractions

See how easy it is when you use simplification? And more importantly, when you understand mathematically what we’re doing.

If you found this post useful, you can read more about fractions on our blog. Some related posts are:

And if you want to learn more about mathematics, register with Smartick and try it for free.

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