Question

numerator of fraction is 4 less than denominator. if 1 is added to both numerator and denominator, it becomes 1/2 . find the frraction

Answer 1

Answer:

The fraction is 3/7

Explanation:

Given,

Numerator of a fraction is 4 less than denominator.

If we assume denominator as x

Then, numerator = (x - 4)

Now, 1 added to both the numerator and denominator,

∴ New numerator = (x - 4) + 1 = (x - 3)

And also, new denominator = (x + 1)

According to the question,

The fraction becomes ½

∴ (x - 3)/(x + 1) = ½

On solving further,

⇒ 2(x - 3) = 1(x + 1)

⇒ 2x - 6 = x + 1

⇒ 2x - x = 6 + 1

⇒ x = 7

∴ x = 7

∴ The denominator is 7

So, the numerator will be :-

→ (x - 4)

→ (7 - 4)

→ 3

Hence, the fraction :-

→ Numerator/Denominator

→ 3/7

∴ Required fraction :- 3/7

_____________________

Verification :

If we add 1 to both the numerator and denominator of 3/7 we must get ½

Let's check

→ (3 + 1)/(7 + 1)

→ 4/8

→ 1/2

So we are getting ½ as a result.

Hence verified!!