Division of a Fraction by a Whole Number
We will discuss here about division of a fraction by a whole number.
| If |
 |
represent 1 |
| The shaded |
 |
portion represents
1 ÷ 2 or ½ of 1 |
| 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