If one be added to the numerator of a fraction it reduces to 1/5 if one be taken from the denomenator it reduces to 1/7 require the fraction
n = the numerator
d = the denomenator
the fraction = n / d
If one be added to the numerator of a fraction it reduces to 1 / 5 mean:
( n + 1 ) / d = 1 / 5
If one be taken from the denomenator it reduces to 1 / 7 mean:
n / ( d - 1 ) = 1 / 7
Now:
( n + 1 ) / d = 1 / 5 Multiply both sides by d
n + 1 = d / 5 Multiply both sides by 5
5 n + 5 = d
d = 5 n + 5
Replace this value in equation
n / ( d - 1 ) = 1 / 7
n / ( 5 n + 5 - 1 ) = 1 / 7
n / ( 5 n + 4 ) = 1 / 7 Multiply both sides by 5 n + 4
n = ( 5 n + 4 ) / 7 Multiply both sides by 7
7 n = 5 n + 4 Subtract 5 n to both sides
7 n - 5 n = 5 n + 4 - 5 n
2 n = 4 Divide both sides by 2
n = 4 / 2
n = 2
Replace this value in equation
d = 5 n + 5
d = 5 * 2 + 5
d = 10 + 5
d = 15
The fraction = 2 / 15
Proof:
( n + 1 ) / d = ( 2 + 1 ) / 15 = 3 / 15 = 3 / ( 3 * 5 ) = 1 / 5
n / ( d - 1 ) = 2 / ( 15 - 1 ) = 2 / 14 = 2 / ( 2 * 7 ) = 1 / 7