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How do you divide fractions?

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user1676262 | eNotes Newbie

Posted October 29, 2013 at 1:11 AM via web

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How do you divide fractions?

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steveschoen | College Teacher | (Level 2) Assistant Educator

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

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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

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alysha_w13 | Student , Undergraduate | eNoter

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

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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

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

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

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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.

Sources:

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queen1598 | Student , Grade 9 | eNoter

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

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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."

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