Example 1: Convert the decimal   into vulgar fraction.

Sol: Let x = 0.737373 …..(i)
Multiplying both sides by 100 we get
100x = 73.737373……(ii)
Subtract equation (i) from (ii) we get
99x = 73 ⇒ x = 73/99.

Example 2: Convert  into vulgar fraction.

Sol: Let x = …..(i)
Multiplying both sides by 100 we get
100x = 21.3333…(ii)
Multiplying both sides of equation (ii) by 10 we get
1000x = 213.3333…(iii )
Subtract equation (ii) from (i) we get
900x = 192 ⇒ x = 192/900.

Example 3: Find the fractional equivalent of 

Sol: As it is case of pure recurring

Example 4: Find the fractional equivalent of 

Sol: As it is case of mixed recurring

Example 5: Find the fractional equivalent of 

Sol: As it is case of mixed recurring

Example 6: Find the fractional equivalent of 

Sol: As it is case of mixed recurring
 = (57934 – 5)/99990 = 57929/99990.

Example 7: Akshay spends 20% of his income, and then he spends 30% of his income, if he still has Rs. 900 with him. Find his total income.

Sol: In this case, the second expenditure is 30% of his income. Thus in total he spends 50% of his income, means he is left with 50% of his income, which is given to be Rs. 900. Thus his income is 900 × 100/50 = Rs. 1800

Example 8: Raj spends 4/9^th of his income, then he spends 4/5 of the remaining. If he still has Rs. 2000 with him. Find his total income.

Sol: Let total income = K. Firstly he spend 4/9^th of his income, thus he is left with 5/9^th of the same. Then he spends 4/5^th of the remaining, means he is left with 1/5^th of the remaining.
Hence K x 5/9 x 1/5 = 2000
So K = 2000 x 9 = 18000.