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 eaten of the whole pizza, such as one-half (½), three-quarters (¾) etc.

**Parts of Fraction- **

- Numerator
- Denominator.

**Types of Fraction- **

**(i) Proper Fraction- **

If both the numerator and denominator are positive, and numerator is less than the denominator, then such fractions are called **proper fraction. **

Ex: \(\small \frac{2}{5}\).

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

Ex: \(\small \frac{8}{3}\).

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

Ex: \(\small \frac{8}{3}\).

**Reciprocal- **

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

For example, a reciprocal of 5 is \(\small \frac{1}{5}\). , a reciprocal of \(\small \frac{8}{3}\). is \(\small \frac{3}{8}\).

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: \(\small \frac{7}{3}\) and \(\small \frac{3}{7}\), where \(\small \frac{3}{7}\) is called reciprocal of \(\small \frac{7}{3}\) or \(\small 2\frac{1}{3}\).

*Note***:** The product of a fraction and its 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 ×

**Step 2:** Find the reciprocal of the second term (number after sign) in the question.

**Step 3: **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 for each condition are explained below.

**Division of Whole Number by a Fraction**

**Evaluate: \(\small 16\div \frac{4}{3}\)**

**Solution:** \(\small 16\div \frac{4}{3} \Rightarrow \frac{16}{1}\times \frac{4}{3}\)

Here second term is \(\small \frac{4}{3}\) ; take the reciprocal of \(\small \frac{4}{3}\)

\(\small \Rightarrow 16 \div \frac{16}{1}\times \frac{3}{4}=\frac{16\times 3}{1\times 4}=\frac{48}{4}=12\)

Alternatively, here \(\small \frac{16}{1}\times \frac{3}{4}\) ; 16 and 4 can be simplified to get \(\small \frac{4}{1}\times \frac{3}{1}=\frac{4\times 3}{1\times 1} = 12\)

**Division of a Fraction by a Whole Number**

**Evaluate: \(\small \frac{8}{3}\div 3\)**

**Solution:** \(\small \frac{8}{3}\div3 \Rightarrow \frac{8}{3}\times 3\)

Here the second term is \(\small 3 = \frac{3}{1}\) ; take the reciprocal of \(\small \frac{3}{1}\)

\(\small \Rightarrow \frac{8}{3}\times \frac{1}{3}=\frac{8\times 1}{3\times 3}=\frac{8}{9}\)

**Division of a Fraction by another Fraction**

**Evaluate: \(\small \frac{8}{3} \div \frac{4}{3}\)**

**Solution:** Here the second term is \(\small \frac{4}{3}\) , take the reciprocal of \(\small \frac{4}{3}\)

Hence,

\(\small \Rightarrow \frac{8}{3}\times \frac{3}{4} = \frac{8\times 3}{3\times 4}=\frac{8}{4}=\frac{2}{1}=2\)

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.