Student Question

# How do you divide fractions?

You divide fractions by inverting the divisor and multiplying. Take, for example, 3/8 divided by 1/4. Invert the divisor, 1/4, to make it 4/1, then multiply it times 3/8. Remember that to multiply fractions you multiply the two numerators times each other and the two denominators times each other. In...

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this example, the two numerators are 3 and 4, and the two denominators are 1 and 8. The product of the numerators is 12, which we put over the product of the denominators, 8, giving us 12/8. Because the numerator is larger in this case (it won't always be), we generally want to change it to a mixed number. Do this by dividing 12 by 8 and writing the remainder over 8, giving 1 4/8. Reduce 4/8 to get 1 1/2.

If you start with a mixed number, you will need to change it into an improper fraction before inverting and multiplying.

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A fraction is made up of two parts, the numerator and the denominator. The numerator is the upper number of the fraction, while the denominator is its lower part. For example, in \frac{2}{5}

   2 is the numerator, while 5 is the denominator. 

In order to divide two fractions, we change the division sign into a multiplication sign. We then multiply the first fraction by the reciprocal of the second fraction.

In order to find the reciprocal of the second fraction, we turn it upside down. In other words, its numerator now becomes the denominator, and its denominator becomes the numerator.

Here is an example:

Evaluate  \frac{2}{7} \div \frac{5}{42}

This becomes  \frac{2}{7} \times \frac{42}{5}

This gives us \frac{12}{5}

This can be written as 2 \frac{2}{5}

In order to divide more than two fractions, we work from left to right and start with the first two fractions. We then follow the same steps as above.

Here is an example:

Evaluate \frac{2}{15} \div \frac{3}{5} \div \frac{2}{3}

Working from left to right, this becomes \frac{2}{15} \times \frac{5}{3} \times \frac{3}{2}

When simplified, this gives us \frac{1}{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.

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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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