Question

the numerator of a fraction is 2 less than the denominator if 3 is added to both the numerator and denominator the fraction becomes 3 by 4 find the fraction

Answer 1

let the original fraction be x/x+2
x+3/x+2+3=3/4
x+3/x+5=3/4
4 (x+3)=3 (x+5)
4x+12=3x+15
4x-3x=15-12
x=3

so the original fraction is
x/x+2=3/5

Answer 2

Given,

The numerator of a fraction is 2 less than the denominator.

If 3 is added to both the numerator and denominator the fraction becomes 3/4.

To find,

The fraction.

Solution,

The fraction will be 3/5.

We can easily solve this problem by following the given steps.

According to the question,

The numerator of a fraction is 2 less than the denominator.

Now, let's take the denominator of the fraction to be x.

Then,

Numerator = (x-2)

So, the fraction is (x-2)/x.

Now,

If 3 is added to both the numerator and denominator the fraction becomes 3/4.

(x-2+3)/(x+3) = 3/4

(x+1)/(x+3) = 3/4

Using the cross multiplication method,

4(x+1) = 3(x+3)

4x+4 = 3x+9

4x-3x+4 = 9

x+4 = 9

x = 9-4

x = 5

So, the denominator of the fraction = 5

Therefore,

Numerator = (x-2)

Numerator = (5-2)

Numerator = 3

Hence, the fraction is 3/5.