Question

The numerator of a fraction is 4 less than its denominator if 2 is added to both the numerator and the denominator the fraction becomes 7/11 find the original fraction

Answer 1

The original fraction is $<strong>\frac{5}{9}</strong>$

EXPLAINATION

GIVEN

• Numerator of a fraction is 4 less than the denominator.
• If 2 is added to both numerator and denominator, the fraction becomes 7/11

CALCULATION

Let

• x be the denominator
• x-4 be the numerator

The original fraction is $\frac{x-4}{x}$.

Using the given condition, the new fraction

$\frac{(x-4)+2}{x+2}=\frac{7}{11}$

$\frac{x-2}{x+2}=\frac{7}{11}$

$11(x-2)=7(x+2)$

$11x-22=7x+14$

$11x-7x=22+14$

$4x=36$

$x=9$

Substituting value of x in the expression of original fraction, we get

The original fraction =$\frac{5}{9}$