How to divide fractions

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zach9414's profile pic

zach9414 | High School Teacher | (Level 2) Adjunct Educator

Posted on

In order to divide two fractions, we have to multiply the numerator (top of fraction), by the reciprocal of the denominator (bottom of fraction). To do this, let's look at an example:

`((2/3))/((4/3))`

If the value of 4/3 is on the denominator, and the reciprocal of that fraction is 3/4. Now that we know that, we can re-write the problem as the following:

`(2/3)*(3/4)`

Then if we multiply across (top X top, bottom X bottom) we should get the following (and simplify):

`6/12 = 1/2`

So, this is the value of the original problem:

`((2/3))/((4/3))=1/2`

Multiplying by the reciprocal works because by doing so it becomes the opposite, so for example if we have the following:

`3/2`  Then we can multiply the numerator by the reciprocal of the denominator the same way that we did before then we will be left with the following:

`3*(1/2)`

If we multiply across the same way we did before, then we should be left with:

`3/2`

Which is the same value we started with.

hmalcolm525's profile pic

hmalcolm525 | Student, Grade 8 | (Level 1) Honors

Posted on

Take the first number and divide the fraction from it.

mcshean's profile pic

Nolan McShea | Student, Grade 11 | (Level 2) Honors

Posted on

Dividing two fractions is easy.

It's just like multiplying fractions. In case you don't know how to multiply fractions, you just line up the two fractions, and multiply the numerators (top of the fraction) together, as well as the denominators (bottom of the fraction). The result numerator and denominator is your new product, and may or may not be simplified further.

For dividing, it's just a LITTLE bit different. All you must do is take the SECOND fraction, and switch the numerator and denominator values. In other words, if you have this fraction for the second fraction:

All you have to do is flip the values. So the new fraction would be:

`5/3`

Now you just need to multiply the first fraction with this new second fraction the regular way, and you get your quotient!~

The flipping thing is called finding the reciprocal, by the way.

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