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# Learning The Methods of Dividing Fractions

Dividing fraction involves multiplying one fraction with the reciprocal of another given fraction. In this article, we will learn the meaning and different methods of dividing fractions. But before we dive into the main concept, it is essential to know the meaning of fractions.

### What do you Mean by Fractions?

In mathematics, fractions can be defined as the parts of a whole number. The word fraction is derived from the Latin word “fractio”, the meaning of which is “break”. Fractions are represented in the form of p/q or a/b or m/n. In a fraction, the upper part (p, a, or m) is called the numerator and the lower part (q, b, or n) is called the denominator. For example, 2/3, 4/7, 1/2, and so on.

All the arithmetic operations such as addition, subtraction, multiplication, and division can be performed on the fractional numbers.

### What do you mean by Dividing Fractions?

Division simply implies sharing an item in different parts. In mathematics, dividing fractions is nothing but multiplying the fractions by writing the reciprocal of one of the two fractions. When one fraction is divided by another fraction, then any one of them is reversed and thus, both the fractions are multiplied. By reversing we mean that, if a fraction, say p/q is given, then the reverse or reciprocal of it will be q/p. Thus, writing reciprocal or reversing a fraction is nothing but interchanging the position of numerator and denominator.

p/q ÷ a/b = p/q × b/a

For example, 2/3 ÷ 4/6 = 2/3 × 6/4 = 1

### How Fractions Can be Divided?

The division of fraction is categorized into three basic ways and these are as follows:

#### Dividing Fraction by Fraction

We just discussed above how to divide fractions by reversing or writing reciprocal of one of the two given fractions. Follow the below-given steps to compute the result for the division of fractions by fractions:

• The first step is to reverse or write the reciprocal of the second fraction and then multiply it with the first one.
• Multiply the numerator of the first fraction with the numerator of the reciprocal fraction. Do the same with denominators of both fractions.
• Now in the end simplify the calculated result into the smallest fraction or whole number.

For example, 2/3 ÷ 4/6 = 2/3 × 6/4 = 1

### Dividing Fraction by Whole Number

The procedure of dividing a fraction by a whole number is very simple. Follow the below-given steps to compute the result for the division of a fraction by the whole number:

• Firstly the given whole number is transformed into a fraction by putting 1 as the denominator.
• Now reverse or write the reciprocal of the given number.
• Multiply the reversed number with a given fraction
• Now in the end simplify the calculated result into the smallest fraction or whole number.

For example, dividing 3/4 by 6 = 3/4 × 1/6 = 1/8

### Dividing Fraction by Mixed Fraction

The procedure of dividing a fraction by a fixed fraction is almost the same as a dividing fraction by fraction. Follow the below-given steps:

Firstly, convert the given mixed fraction into an improper fraction.
Now reverse or write the reciprocal of the improper fraction.
Multiply the numerator of the first fraction with the numerator of the reciprocal fraction. Do the same with denominators of both fractions.
Now in the end simplify the calculated result into the smallest fraction or whole number.

For example, dividing 3/4 by 3½ = 3/4 × 2/7 = 3/14

#### Bottom Line

Before one learns about dividing fractions, it is important for one to know different types of fractions such as proper, improper, or equivalent fraction. Cuemath being an educational platform provides live online classes so that students can understand basic concepts of maths.