Question

The numerator of a fraction &
a fraction & 2 less
than the denominator. If one is
added to its denominator, it becomes 1/2
I find the fraction​

Answer 1

$\dag$$\boxed{\sf\: fraction\:is\:\frac{3}{5}}$

GIVEN :

• The numerator of a fraction is 2 less than the denominator.
• If one is added to its denominator it becomes $\sf \: \frac{1}{2}$

TO FIND : The fraction.

SOLUTION :

• Let the numerator be x.
• Then, the fraction is $\sf\: \frac{x}{x+2}$

$\underline{\sf\:According\:to\:the\:question}$

$\longrightarrow \sf\: \frac{x}{x+2+1}= \frac{1}{2} \\ \\ \longrightarrow \sf\: \frac{x}{x+3}=\frac{1}{2} \\ \\ \longrightarrow \sf\: 2x=x+3 \\ \\ \longrightarrow \sf\:x = 3$

$\bold{Fraction}$$\longrightarrow \sf\: \frac{x}{x+2}=\boxed{\frac{3}{5}}$

Answer 2

Given :

• The numerator of a fraction & a fraction & 2 less than the denominator. If one is added to its denominator, it becomes 1/2.

To Find :

• The fraction = ?

Procedure :

Let the denominator of the fraction be x.

Therefore,

• The numerator = x - 2
• The fraction = x - 2/x

Since, it becomes 1/2 when 1 is added to it's denominator.

➩ x - 2/ x + 1 = 1/2

➩ 2(x - 2) = x + 1

➩ 2x - 4 = x + 1

➩ 2x - x = 1 + 4

➩ x = 5

Therefore,

Fraction = 5 - 2/5 = 3/5