# Reciprocal and Division of Fractions

Reciprocal and division of fractions are two different methods. When the numerator and denominator of a fraction are interchanged then it is said to be it’s reciprocal. Suppose a fraction is a/b, then it’s reciprocal will be b/a. A fraction is a numerical quantity that is not a whole number. Rather it represents a part of the whole. For example, it tells how many slices of a pizza are remaining or eating of the whole pizza, such as one-half (½), three-quarters (¾)  etc. Division of fractions involve is an operation performed on fractions with multiple steps included.  Also, learn dividing fractions here.

Parts of Fraction
The fraction has two parts:

1. Numerator
2. Denominator.

Types of Fraction: Fractions are basically of three types, proper, improper and mixed. Learn the definitions below.

Proper Fraction: If both the numerator and denominator are positive, and the numerator is less than the denominator.

Example: 2/5, 1/3, 3/6, 7/8. 9/11, etc.

Improper Fractions: Whereas fractions having numerator greater than the denominator are called Improper fraction.

Example: 8/3, 3/2, 6/3, 11/9, etc

Mixed Fraction: When a whole number and a fraction are combined it is known as a mixed fraction.

All these details were the basics of fractions. Now let us learn reciprocal of fractions along with its division.

## Reciprocal of Fractions

The fraction obtained by swapping or interchanging Numerator and Denominator with each other is known as Reciprocal of the given fraction.

For example, a reciprocal of 5 is 1/5 , a reciprocal of 8/3 is 3/8.

The reciprocal of a mixed fraction can be obtained by converting it into an improper fraction and then swap the numerator and denominator.

For example, to find the reciprocal of $\small 2\frac{1}{3}$;

• Convert the mixed fraction into improper fraction:$\small 2\frac{1}{3}=\frac{7}{3}$
• Now invert the fraction: 7/3 and 3/7, where 3/7 is called reciprocal of 7/3 or $\small 2\frac{1}{3}$.

Note: The product of a fraction and it’s reciprocal is always 1.

## Division of Fractions

Division involving a fraction follows certain rules. To perform any division involving fraction just multiply the first number with the reciprocal of the second number. Steps are as follows:

Step 1: First change the division sign (÷) to multiplication sign (×)

Step 2: If we change the sign of division to multiplication, at the same time we have to write the reciprocal of the second term or fraction.

Step 3: Now, multiply the numbers and simplify the result.

These rules are common for:

1. Division of the whole number by a fraction.
2. Division of a fraction by a whole number
3. Division of a fraction by another fraction.

Note: It is to be noted that division of fractions is basically the multiplication of fraction obtained by reciprocal of the denominator (i.e. divisor).

### Examples of Divisions of Fractions

Examples for each condition are explained below.

Division of the Whole Number by a Fraction

Example 1: 16 ÷ 4/3

Solution: 16 ÷ 4/3 = 16/1 × 3/4

3/4 is the reciprocal of 4/3

Hence, (16 × 3)/(1×4)

× 3 = 12

Therefore,

16 ÷ 4/3 = 12

Division of a Fraction by a Whole Number

Example 2: Divide 8/3 by 3

Solution: We need to simplify, 8/3 ÷ 3

The reciprocal of 3 is 1/3.

Now write the given expression into multiplication form,

8/3 × 1/3 = 8 /9

Therefore,

8/3 ÷ 3 = 8/9

Division of a Fraction by another Fraction

Example 3: 8/3 ÷ 4/3

Solution: 8/3 ÷ 4/3

Reciprocal of second term 4/3 is 3/4.

Now multiplying first term with the reciprocal of the second term we get;

8/3 × 3/4 = 8/4 = 2

Hence,

8/3 ÷ 4/3 = 2

To perform division involving mixed fraction, convert the mixed fraction into an improper fraction and follow the above steps.

Study more on the related topics such as representing fractions on a number line, visit our Byju’s page.’