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If \(\frac{a}{b}\) and \(\frac{c}{d}\) are two fractions, where \(\frac{c}{d}\) is not equal to zero, then **\(\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} X \frac{d}{c}\)** i.e., **the dividend is multiplied by the reciprocal of the divisor**.

## Reciprocal (or) Multiplicative inverse of a Fraction:

When the **product of two fractions is 1**, each of the fractions is called the reciprocal of the other. We can obtain the reciprocal of a given fraction by interchanging the numerator and denominator of the fraction.

Reciprocal of any non-zero fraction \(\frac{a}{b} = \frac{b}{a}\) { a,b not equal to zero }

### Dividing Fractions Example 1:

Find 1) \(\frac{2}{5} \div \frac{1}{2}\)

2) \(2\frac{3}{4} \div \frac{4}{5}\)

**Solution:** 1) \(\frac{2}{5} \div \frac{1}{2}\) = \(\frac{2}{5} X \frac{2}{1} = \frac{4}{5}\)

2) \(2\frac{3}{4} \div \frac{4}{5}\) = \(\frac{11}{4} \div \frac{4}{5}\)

= \(2\frac{11}{4} X \frac{5}{4}\) = \(\frac{55}{16} = 3\frac{7}{16}\).

### Dividing Fractions Example 2:

A company can repair \(2\frac{1}{5}\) km of road in a day. How many days will it take to repair a road \(24\frac{3}{5}\) km.

**Solution:** Number of days taken to repair \(2\frac{1}{5}\) km of road = 1 day

Therefore, Number of days taken to repair \(24\frac{3}{5}\) km of road

= \(24\frac{3}{5} \div 2\frac{1}{5}\) days = \(\frac{123}{5} \div 2\frac{11}{5}\) days

= \(\frac{123}{5} X \frac{5}{11}\) days = \(\frac{123}{11}\) days

= \(11\frac{2}{11}\) days.

### Dividing Fractions Example 3:

Simplify \(2\frac{1}{4} X \frac{3}{14} \div 1\frac{2}{7}\).

**Solution:**