Question

The denominator of a fraction is greater than its numerator by 7. If

the numerator is increased by 1 and the denominator is increased by
4, the fraction becomes 1/3

. Find the original fraction.

Answer 1

4/11

Explanation:

Let :

x = numerator

x + 7 = denominator
`(x)/(x + 7)`

`(x)/(x+7) + (1)/(4) = (1)/(3)`

`(x + 1)/(x + 11) = (1)/(3)`

cross multiply

3(x + 1) = x + 11

3x + 3 = x + 11

combine like terms

3x - x = 11 - 3

2x = 8

x = 4

x + 7 = 4 + 7 = 11

original fraction = 4/11