Question

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

Answer 1

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