Question

The numerator of a fraction is 3 less than its denominator. When both the numerator and the
denominator are increased by 1 the fraction becomes 2/3. Find the fraction.
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Answer 1

EXPLANATION.

• GIVEN

The numerator of a fraction is 3 less than it's

denominator.

when both the numerator and the denominator

are increased by 1

fraction becomes = 2/3

FIND THE FRACTION.

Let,

denominator of fraction be x

numerator of fraction be = x - 3

if 1 is added the both denominator and

numerator

$\frac{x - 3 + 1}{x + 1} = \frac{2}{3}$

$\frac{x - 2}{x + 1} = \frac{2}{3}$

3(x - 2 ) = 2 ( x + 1 )

3x - 6 = 2x + 2

x = 8

Therefore,

fraction will be =

$\frac{x - 3}{x} = \frac{8 - 3}{8} = \frac{5}{8}$

Therefore,

fraction will be = 5/8

Answer 2

Solution :

Given that , If numerator of the fraction is 3 less than the denominator when both the numerator and denominator are increased by 1 then fraction becomes 2/3

So., Let the common factor of the fraction be x

Then the numerator becomes x-3

the denominator becomes x

So , when 1 is added to the numerator then it becomes

Actuall numerator+1 = x-3+1

the denominator becomes Actuall +1 = x+1

Then the total fraction becomes 2/3

numerator / denominator = Fraction

x-3+1/x+1=2/3

x-2/x+1=2/3

3 ( x-2 ) = 2 ( x+1 )

3x-6 = 2x +2

3x-2x= 4

x=8

numerator is 5 and denominator is 8