(ii) When the divisor is a fraction.
In the operation 24 ÷ 3, we have to find the number which, when multiplied by 3, will give 24. Similarly, to find the value of 3⁄7 ÷ 5⁄9 we have to find the fraction which, when multiplied by 5⁄9, will give 3⁄7.
But 3 × 97 × 5 is the fraction which gives 3⁄7 when multiplied by 5⁄9. Therefore, 37 ÷ 59 = 3 × 97 × 5.
Hence, to divide by a fraction, invert the divisor and multiply.
As in multiplication, mixed numbers must first be reduced to improper fractions.
Example 3: Divide 31⁄14 by 55⁄42.
3114 ÷ 5542 = 4314 ÷ 21542 = 4314 × 3 42 215 5 = 35 Ans.
DECIMAL FRACTIONS
Differ in form from common fractions, in not having a written denominator; and from whole numbers, by having the decimal point (.) prefixed; which also separates the integral part from the decimal. The word decimal is derived from the Latin word decem, which signifies ten. The denominator of a decimal is always 10, or some power of 10, as 100, 1000, etc.