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# How do you divide fractions?

How do you divide fractions?

Posted by user1676262 on October 29, 2013 at 1:11 AM via web and tagged with frations, math

College Teacher

(Level 2) Assistant Educator

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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

Posted by steveschoen on October 29, 2013 at 1:27 AM (Answer #1)

Student

eNoter, TA

eNoter

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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

Posted by alysha_w13 on October 29, 2013 at 1:31 AM (Answer #2)

High School Teacher

(Level 2) Associate Educator

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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.

Posted by baxthum8 on October 29, 2013 at 9:08 AM (Answer #3)

Student

eNoter

eNoter

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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."

Posted by queen1598 on October 29, 2013 at 9:39 AM (Answer #4)