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Division of rational numbers is same as division of fractions. Division of fractions is the **inverse of multiplication**. In case of rational number also, division is the inverse of multiplication.

### Division:

If x and y are two rational numbers such that y is not equal to 0, then the result of dividing x by y is the rational number obtained on multiplying x by the reciprocal of y. When x is divided by y, we write **x ÷y = x X \(\frac{1}{y}\)**

**Some important terms to be noted in case of division are:**

**Dividend:** The number to be divided is called the dividend.

**Divisor:** The number which divides the dividend is called the divisor.

**Quotient:** When dividend is divided by the divisor, the result of the division is called the quotient.

**Example:**

If \(\frac{a}{b}\) is divided by \(\frac{c}{d}\), then \(\frac{a}{b}\) is the dividend, \(\frac{c}{d}\) is the divisor, and is the quotient.

Division by 0 is not defined.

### Division of Rational Numbers Example 1:

Divide \(\frac{3}{5}\) by \(\frac{4}{25}\)

**Solution:**

\(\frac{3}{5}\) ÷ \(\frac{4}{25}\) = \(\frac{3}{5}\) X \(\frac{25}{4}\)

= \(\frac{(3 X 25)}{(5 X 4)}\) = \(\frac{(3 X 5)}{(1 X 4)}\) = \(\frac{15}{4}\)

### Division of Rational Numbers Example 2:

Divide \(\frac{-8}{9}\) by \(\frac{4}{3}\)

**Solution:**

\(\frac{-8}{9}\) **÷ **\(\frac{4}{3}\) = \(\frac{-8}{9}\) X \(\frac{3}{4}\)

= \(\frac{(-8 X 3)}{(9 X 4)}\) = \(\frac{(-2 X 1)}{(3 X 1)}\) = \(\frac{-2}{3}\)

### Division of Rational Numbers Example 3:

Divide \(\frac{-16}{21}\) by \(\frac{-4}{3}\)

**Solution:**

\(\frac{-16}{21}\) ÷ \(\frac{-4}{3}\) = \(\frac{-16}{21}\) X \(\frac{3}{-4}\)

= \(\frac{(-16 X 3)}{(21 X -4)}\) = \(\frac{(4 X 1)}{(7 X 1)}\) = \(\frac{4}{7}\)

### Division of Rational Numbers Example 4:

Divide \(\frac{-8}{13}\) by \(\frac{3}{-26}\)

**Solution:**

\(\frac{-8}{13}\) ÷ \(\frac{3}{-26}\) = \(\frac{-8}{13}\) X \(\frac{-26}{3}\)

= \(\frac{(-8 X -26)}{(13 X 3)}\) = \(\frac{(8 X 2)}{(1 X 3)}\) = \(\frac{16}{3}\)