# Division of a Fractional Number

We will discuss here about division of a fractional number by a fractional number.

Now, let us consider the division $$\frac{2}{3}$$ ÷ $$\frac{1}{3}$$

= $$\frac{\frac{2}{3}}{\frac{1}{3}}$$

= $$\frac{2}{3}$$ × $$\frac{1}{\frac{1}{3}}$$

= $$\frac{2}{3}$$ × $$\frac{3}{1}$$

= $$\frac{2}{3}$$ × 3

= $$\frac{6}{3}$$

= 2

Therefore, $$\frac{2}{3}$$ ÷ $$\frac{1}{3}$$ = $$\frac{2}{3}$$ × 3 = 2

Therefore, the rules for the division of a fraction by a fraction is

A Fraction ÷ Another Fraction = First Fraction × Reciprocal of the Second Fraction.

Hence, we conclude that to divide a fractional number by another fractional number, we multiply the first fractional number by the multiplicative inverse of the second fraction number.

1. $$\frac{1}{3}$$ ÷ $$\frac{2}{5}$$

[First Fraction × Reciprocal of the Second Fraction]

= $$\frac{1}{3}$$ × $$\frac{5}{2}$$

= $$\frac{1 × 5}{3 × 2}$$

= $$\frac{5}{6}$$

2. $$\frac{6}{19}$$ ÷ $$\frac{12}{38}$$

= $$\frac{6}{19}$$ × $$\frac{38}{12}$$

= 1

3. 2$$\frac{1}{7}$$ ÷ $$\frac{7}{2}$$

= $$\frac{2 × 7 + 1}{7}$$ ÷ $$\frac{7}{2}$$

= $$\frac{15}{7}$$ ÷ $$\frac{7}{2}$$

= $$\frac{15}{7}$$ × $$\frac{2}{7}$$

= $$\frac{15 × 2}{7 × 7}$$

= $$\frac{30}{49}$$

4. 6 2/3 ÷ 4 1/5

= (6 × 3 + 2)/3 ÷ (4 × 5 + 1)/5

= 20/3 ÷ 21/5

= 20/3 × 5/21

= (20 × 5)/(3 × 21)

= 100/63

5. 12/11 ÷ 144/121

= 12/11 × 121/144

= 11/12

6. 5 1/8 ÷ 8 2/16

= (5 × 8 + 1)/8 ÷ (8 × 16 + 2)/16

= 41/8 ÷ 130/16

= 41/8 × 16/130

= 41/65

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