Question

The numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator, the fraction becomes 3/4. Find the fraction.

Answer 1

Given

The numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator, the fraction becomes 3/4.

To find

Find the fraction

Solution

✞ Let the denominator be x and numerator be (x - 2)

According to the given condition

✒Numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator then fraction becomes 3/4

➨ x - 2+3/x+3 = 3/4

➨ x + 1/x + 3 = 3/4

➨ 4(x + 1) = 3(x + 3)

➨ 4x + 4 = 3x + 9

➨ 4x - 3x = 9 - 4

∴ x = 5

Hence,

${\boxed{\bf{Denominator = x = 5}}}$

${\boxed{\bf{Numerator = x - 2 = 5 - 2 = 3}}}$

${\underline{\boxed{\bf{Required\:fraction=\dfrac{3}{5}}}}}$

Answer 2

Given :-

• Numerator of a fraction is 2 less than the denominator.

• If 3 is added to both numerator and denominator, fraction becomes 3/4

To Find :-

• The fraction

Solution :-

Let the denominator be 'x'

then,

Numerator = ( x - 2)

Now,

According to question :-

If 3 is added to both then, we get 3/4

$\implies \: \frac{(x - 2) + 3}{x + 3} = \frac{3}{4} \\ \\ \implies \: \frac{x + 1}{x + 3} = \frac{3}{4} \\ \\ \implies \: 4(x + 1) = 3(x + 3) \\ \\ \implies \: 4x + 4 = 3x + 9 \\ \\ \implies \: 4x - 3x = 9 - 4 \\ \\ \implies \: x = 5$

Hence,

x = 5

So,

Numerator = ( x - 2) = ( 5 - 2) = 3

Denominator = x = 5

Fraction = Numerator / Denominator = 3/5