How do you divide fractions?

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baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

In order to divide fractions, you must multiply by the reciprocal.

For example,  `2/3-: 7/8`

1) Take the reciprocal of the second fraction. To find the reciprocal, "flip" the fraction.

The reciprocal of `7/8`  is `8/7.`

2) Multiply `2/3* 8/7.`

3)  `(2*8)/(3*7)`

4)  This equals `16/21.`

Finally, always simplify if necessary.

Sources:
steveschoen's profile pic

steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

I assume you mean divide fractions.

There are a couple of ways to remember how to do this.  I like to remember it by a definition:


"Dividing by a number" is the same as "multiplying by its reciprocal"

So, given this, every division problem you have ever gotten could be rewritten as a multiplication problem, like we will do with fractions.

First, we need to make sure what reciprocals are.  It is probably easier to show how to get them than define them.  Such as:


reciprocal of 3/4 is 4/3

reciprocal of 5/2 is 2/5

reciprocal is -3/7 is -7/3 (negative sign can be top number or bottom number, it doesn't make a difference)


So, to get the reciprocal, you flip the number.

So, for fractions, for example:

"4/3         `-:`               2/7"      is     "4/3      *                7/2"
       "Dividing by a number"           "Multiplying by its reciprocal"


So, change the division to multiplication, and flip the second fraction.  Then, we multiply the fractions straight across:

4/3 * 7/2 = 28/6 = 14/3

queen1598's profile pic

queen1598 | Student, Grade 9 | (Level 1) eNoter

Posted on

To divide fractions, multiply the first fraction to the reciprocal of the divisor.

 Example: 3/4 / 2/5 = 3/4 * 5/2 = 15/8

Rule to ponder: "Dividing numbers by 0 is a sin."

alysha_w13's profile pic

alysha_w13 | Student, Undergraduate | (Level 1) Honors

Posted on

If you are talking about dividing fractions then there are 3 very simple steps.

1. Find the reciprocal of the second fraction. This basically means flip it over. For example, if you want to find 3/4 / 1/2.

Change 1/2 to 2/1

This become 3/4 / 2/1.

2. Multiply the first fraction with the reciprocal.

3/4 * 2/1

To do this you just multiply the numerators and the denominators together.

This would make the numerator 3*2=6

and the denominator 4*1=4

so the fraction would be 6/4

3. The final step is to simplify. 

You can present it as a simplified fraction of a mixed number.

This, for example, would be 3/2 or 1 1/2

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

Dividing fractions is simple all you need to do is change the division sign to multiplication by changing the second fraction to it's reciprocal. Take this as an example, divide 2/4 by 8/10,

`2/4-:8/10`

You can start by changing the second fraction to 10/8, which will result in division becoming multiplication,

`2/4*8/10`

Now cross multiply them and check if the numerators are being divided by the denominators,

`1/1*2/5`

After that multiply the numerators and the denominators,

`(1*2)/(1*5)`

`2/5` 

Now if you want you can further turn this into a decimal, then the answer will be 0.4.    

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