The ratio of the numerator to the denominator of a certain fraction is five to eight. If five is subtracted from the numerator and four is added to the denominator, the new fraction reduces to one-half. What is the original fraction?

5x-5/8x+4=1/2

On cross multiplying

2 (5x-5) = 8x+4

10x-10=8x+4

10x-8x=4+10

2x=14

Therefore x=7

The original fraction=35/56

35/56.

Step-by-step explanation

We can write the original fraction as 5x / 8x where x is some integer so our new fraction would be 5x - 5 / 8x + 4 and this equals 1/2. So we have the equation:

(5x - 5) / (8x + 4) = 1/2

10x - 10 = 8x + 4

2x = 14

x = 7

So the original fraction is 5 (7) / 8 (7)

= 35/56.

= 7/8

= 30/44