# Dividing Fractions - Divide Fractions and Whole Numbers

As with multiplying fractions, we saw that it is very easy, we just multiply the denominators and multiply the numerators. In the process of division is not much different from multiplication.

To divide two fractions, we convert the division operation into a multiplication operation. but how? There are 3 basic steps in order to perform division.

• First, we convert the division symbol ( or ) to the multiplication symbol ()

• Second: We keep the first number as it is, and flip the second fraction to its reciprocal.

• Third: We perform the multiplication process normally, as we explained in this lesson.

### Note:

Let , , and four non-zero integers.

To divide by we multiply by the reciprocal of . i.e. we multiply by

### Info!

• Note carefully that dividing two fractions has nothing to do with whether the two fractions have the same or different denominators, as in the case of addition and subtraction.

• After dividing two fractions, make sure your answer is reduced to lowest terms.

Let's take some examples of dividing two non-zero fractions.

#### Example1:

Divide the fractions below.

1)

2)

3)

4)

#### Solution:

1) Let's calculate

The reciprocal of is . Thus,

The resulting fraction is in its reduced form since the greatest common factor of 8 and 63 is 1.

2) Let's calculate

The reciprocal of is . Thus,

The resulting fraction is in its reduced form since the greatest common factor of 15 and 88 is 1.

3) Let's calculate

We can rewrite the operation using the division symbol.

The reciprocal of is . Thus,

The resulting fraction is in its reduced form since the greatest common factor of 9 and 35 is 1.

4) Let's calculate

We can rewrite the operation using the division symbol.

The reciprocal of is . Thus,

The resulting fraction is in its reduced form since the greatest common factor of 5 and 6 is 1.

## Dividing Fraction by Whole Number - Dividing Whole Number by Fraction

A whole number can be considered as a fraction so that its denominator is 1, and thus we have to do the division of a fraction by an integer, or vice versa by applying the following property:

### Note:

Let , and three non-zero integers.

Let's take some examples of dividing two non-zero fraction by whole number, and whole number by fraction.

#### Example2:

Divide the fractions below.

1)

2)

3)

4)

#### Solution:

1) To divide a whole number by a fraction, we must find the reciprocal of the fraction and then performe the multiplication of whole number by fraction.

2) By the same way as in the example above:

3) To divide a fraction by a whole number, we must find the reciprocal of the whole number and then performe the multiplication of whole number by fraction.

4) By the same way as in the example above: