Question

In a fraction, denominator is 3 less than the twice the numerator. If 1/ 2 is subtracted from numerator and 3/ 5 is added to the denominator, then the new fraction becomes 45/ 76. Find the original fraction.

Answer 1

Let the numerator of the fraction be x

By data denominator

$2 \times x - 3$

The fraction

$= ( x \div (2 \times x - 3))$

1 ÷ 2 is subtracted from the numerator fraction

$= ((x - 0.5) \div (2 \times x - 3))$

3 ÷ 5 is added to the denominator

$= ((x - 0.5) \div (2 \times x - 3 + (3 \div 5))$

New fraction

$= 45 \div 76$

$((x - 0.5) \div (2x - (12 \div 5))) = 45 \div 76$

$76(x - 0.5) = 45(2x - (12 \div 5))$

$76x - 38 = 90x - 108$

$14x = 70$

$x = 5$

Therefore the numerator = 5

Denominator = 2x - 3 = 7

The fraction = 5/7