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

Answer:

$\frac{2}{15}$

Step-by-step explanation:

Let the original fraction be $\frac{x}{y}$

Then adding 1 to the numerator gives

$\frac{x+1}{y}$ = $\frac{1}{5}$ ( cross-  multiply )

⇒ y = 5x + 5 → (1)

Subtracting 1 from the denominator gives

$\frac{x}{y-1}$ = $\frac{1}{7}$ (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 = $\frac{2}{15}$