Question

The numerator of a fraction is 2 less than the denominator.The sum of the two is 8.What is the fraction?

Answer 1

$\bf{\huge{\boxed{\underline{\tt{\blue{Answer:}}}}}}$

Given:-

• the numerator of a fraction is 2 less than the denominator
• the sum of the two is 8

To find :-

• The fraction.

Solution :-

Let the denominator of the fraction be x

As per the first given statement,

• the numerator of a fraction is 2 less than the denominator,

Numerator = x - 2

Denominator = Numerator - 2

x = x - 2 -----> 1

As per the second condition,

• the sum of the numerator and denominator is 8

Numerator + Denominator = 8

x - 2 + x = 8

x + x - 2 = 8

2x - 2 = 8

2x = 8 + 2

2x = 10

x = $\bf\large\frac{10}{2}$

x = 5

Denominator = x = 5

Numerator = x - 2 = 5 - 2 = 3

Fraction = $\bf\large\frac{3}{5}$

$\bf{\huge{\underline{\boxed{\tt{\purple{Verification:}}}}}}$

For first case :-

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

Numerator = 3

Denominator = 5

Denominator - Numerator = 2 [As per the given condition in the question]

5 - 3 = 2

LHS = RHS!

For second case :-

• the sum of numerator and denominator is 8

Numerator + Denominator = 8 [As per the given condition in the question]

3 + 5 = 8

LHS = RHS.

Hence both the required conditions are satisfied.

Hence verification is complete.