Question

Find the fraction which has reduced value,2/3.If the numerator is increased by 4 and the denominator is decreased by 2,then the resulting fraction has the value 2.

Answer 1

n = numerator

d = denominator

n / d = 2 / 3

Cross multiply.

3 n = 2 d

n = 2 d / 3

New fraction:

( n + 4 ) / ( d - 2 ) = 2

( 2 d / 3 + 4 ) / ( d - 2 ) = 2

Multiply both sides by d - 2

2 d / 3 + 4 = 2 ( d - 2 )

2 d / 3 + 4 = 2 d - 4

Subtract 4 to both sides.

2 d / 3 = 2 d - 8

Subtract 2d to both sides.

2 d / 3 - 2 d = - 8

2 d / 3 - 6 d / 3 = - 8

- 4 d / 3 = - 8

Multiply both sides by 3

- 4 d = - 24

d = - 24 / - 4

d = 6

n = 2 d / 3 = 2 ∙ 6 / 3 = 12 / 3

n = 4

The non-reduced fraction:

n / d = 4 / 6

Check result:

( n + 4 ) / ( d - 2 ) = ( 4 + 4 ) / ( 6 - 2 ) = 8 / 4 = 2