Dividing Fractions

This lesson is all about dividing fractions.

Before diving into division of fractions you need to know some definitions of words that will be used going further. So if you are all set to learn these new words move on.

Reciprocals

The reciprocal of a fraction is a fraction that has the numerator and the denominator exchanging places.

For example let’s consider the fraction ¾.

Here the numerator is 3 and the denominator is 4. In order to find the reciprocal the numerator and the denominator must swap places. Thus the numerator of the reciprocal is 4 which was the denominator in the original fraction. The denominator of the reciprocal is 3 which happened to be the numerator in the original number.

Some more examples for you with fraction to the left and their reciprocal to the right.

• 1/3 3/1
• 2/5 5/2
• 7/9 9/7
• 8/6 6/8

The reciprocals are also known as inverse.

Division Elements

Have a look at the elements that participate in the division process.

Dividend /Divisor = Quotient

Dividend: The fraction that is divided is called the dividend. Divisor: The fraction with which the dividend is divided is called divisor. Quotient: The fraction that is the resultant of the division is called the quotient.

Steps to Dividing Fractions

Let’s take a division example to explain the process.

(3/5)/(10/15)

Here we will divide 3/5 by 10/15.

Step #1)

Reduce the numerator and the denominator to its simplest form.

As we can see the dividend is already in its simplest form. Therefore there is no further simplification necessary. The divisor can be reduced by dividing the numerator and the denominator by 5. The fraction becomes 2/3.

Step #2)

Find the reciprocal of the simplified divisor.

Here the divisor is 2/3. Following the reciprocal conversion technique mentioned above the reciprocal of the fraction is 3/2

Step #3)

Multiply the dividend by the reciprocal of the divisor.

For the example we have, multiply 3/5 and 3/2.

(3/5) X (3/2) = (3 X 3)/(5 X 2) = 9/10

Step #4)

The resultant obtained in step 3 is the quotient of the division carried out between the given fractions.

Dividing Mixed Fractions

Dividing mixed fractions is more like any other fraction division. The only thing that you need to take care of is the fact that you must convert the mixed fractions into improper fractions before going ahead with the division process.

Once this is accomplished then you may follow the steps mentioned earlier for the division process.


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