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The ratio of the numerator to the denominator of a certain fraction is 5 to 8 If 5 is subtracted from the numerator and 4 is added to the denominator the new fraction reduces to one half Find fraction?
Wiki User
∙ 12y ago
The fraction is 35/56.
The way to find it is as follows:
1) n/d = 5/8
2) (n-5) / (d+4) = 1/2
3) n = (5/8)*d [rearrange (1)]
4) 2*(n-5) = (d+4) [rearrange (2)]
5) 2*n - 10 = d + 4 [rearrange (4)]
6) 2*n = d + 14 [rearrange (5)]
7) 2*((5/8)*d) = d + 14 [substitue (3) into (6)]
8) (10/8)*d = d+14 [rearrange (7)]
9) (10/8)*d - d = 14 [rearrange (8)]
10) (10/8)*d - (8/8)*d = 14 [rearrange (9)]
11) (2/8)*d = 14 [rearrange (10)]
12) d = 14 / (2/8) = 14 * 8/2 [rearrange (11)]
13) d = 112/2 = 56 [simplify (12)]
14) n = (5/8)*56 [substitute (13) into (3)]
15) n = 280/8 = 35 [simplify (14)]
16) THE ANSWER IS n/d = 35/56 [substitute (13) and (15) into the definition of the fraction]
Wiki User
∙ 12y ago
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