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.
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