# Division of a Fraction by a Whole Number

We will discuss here about division of a fraction by a whole number.

 The shaded portion represents 1 ÷ 2 or ½ of 1 or 1 × ½ = ½
 and represents ½ ÷ 3 or ½ of 1/3 = 1/3 × ½ = 1/6

Therefore, the rules for the division of a fractional number by a whole number is Fraction ÷ Whole number = Fraction × Reciprocal of whole number.

Hence, we conclude that to divide a fractional number by a whole number, we multiply the fractional number by the multiplicative inverse or reciprocal of the given whole number.

For Example:

1. 1/3 ÷ 3

Here 1/3 is the fraction and 3 is the whole number.

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘3’ by its reciprocal ‘1/3’].

= 1/3 × 1/3

= (1 × 1)/(3 × 3)

= 1/9

2. 4/7 ÷ 9

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘9’ by its reciprocal ‘1/9’].

= 4/7 × 1/9

= (4 × 1)/(7 × 9)

= 4/63

3. 1 2/5 ÷ 2

= (1 × 5 + 2)/5 ÷ 2

= 7/5 ÷ 2

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘2’ by its reciprocal ‘1/2’].

= 7/5 × 1/2

= (7 × 1)/(5 × 2)

= 7/10

4. 2 1/7 ÷ 15

= (2 × 7 + 1)/7 ÷ 15

= 15/7 ÷ 15

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘15’ by its reciprocal ‘1/15’].

= 15/7 × 1/15

= 1/7

5. 19/5 ÷ 37

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘37’ by its reciprocal ‘1/37’].

= 19/5 × 1/37

= (19 × 1)/(5 × 37)

= 19/185

6. 212/8 ÷ 4

= (21 × 8 + 2)/8 ÷ 4

= 170/8 ÷ 4

[Replace ‘÷’ by ‘×’ sign.

Replace the whole number ‘4’ by its reciprocal ‘1/4’].

= 170/8 × 1/4

= (170 × 1)/(8 × 4)

= 170/32