Question

The value of a certain fraction becomes 1/5 if one is added to its numerator. If one is taken away from its denominator, its value becomes 1/7. Find the fraction.

Use an algebraic equation. Thanks!

Answer 1

`(2)/(15)`

Explanation:

Let the original fraction be
`(x)/(y)`

Then adding 1 to the numerator gives

`(x+1)/(y)` =
`(1)/(5)` ( cross- multiply )

⇒ y = 5x + 5 → (1)

Subtracting 1 from the denominator gives

`(x)/(y-1)` =
`(1)/(7)` (cross- multiply )

y - 1 = 7x → (2)

Substitute y = 5x + 5 into (2)

5x + 5 - 1 = 7x ← subtract 5x from both sides

4 = 2x ⇒ x = 2

Substitute x = 2 into (1)

y = (5 × 2) + 5 = 10 + 5 = 15

Hence original fraction =
`(2)/(15)`