Question

the numerator of a fraction is 3 less than its denominator. If we add 1 to both numerator and denominator it becomes equal to 1/2. Find the fraction​

Answer 1

The numerator of a fraction is 3 less than its denominator.

n = d – 3

:

if we add 1 to both numerator and denominator it becomes equal to 2/3.

(n+1/d+1) = 2/3

Cross multiply

3(n+1) = 2(d+1)

3n + 3 = 2d + 2

3n = 2d + 2 – 3

3n = 2d – 1

replace n with (d-3), from the 1st equation

3(d-3) = 2d – 1

3d – 9 = 2d – 1

3d – 2d = -1 + 9

d = 8

then

n = 8 – 3

n = 5

therefore

5/8 is the fraction

Answer 2

The numerator of a fraction is 3 less than its denominator.

n = d – 3

:

if we add 1 to both numerator and denominator it becomes equal to 2/3.

(n+1/d+1) = 2/3

Cross multiply

3(n+1) = 2(d+1)

3n + 3 = 2d + 2

3n = 2d + 2 – 3

3n = 2d – 1

replace n with (d-3), from the 1st equation

3(d-3) = 2d – 1

3d – 9 = 2d – 1

3d – 2d = -1 + 9

d = 8

then

n = 8 – 3

n = 5

therefore

5/8 is the fraction