**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 is an operation performed on fractions with multiple steps. Also, learn dividing fractions here.

**Parts of Fraction
**The fraction has two parts:

- Numerator
- 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, then it is a proper fraction.

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

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

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

**Mixed Fraction: **When a whole number and a proper 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.

**Also, read:**

## 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:

- Division of the whole number by a fraction.
- Division of a fraction by a whole number
- 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 of the condition as mentioned earlier 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)

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 writing 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 multiply the first term with the reciprocal of the second term.

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 at BYJU’S today!

## Frequently Asked Questions – FAQs

### What is a reciprocal of the fraction?

### How do you divide fractions with the whole numbers?

### Why do you use reciprocal when dividing fractions?

### What is the reciprocal rule of division?

### Is 1 the reciprocal of 1?

### What are the different cases involved in the division of fractions?

Dividing a fraction by a whole number

Dividing a whole number by a fraction

Dividing a fraction by another fraction (i.e. division of two fractions)