The sum of the numerator and denominator of a fraction is 3 less than

1.	The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.
Answer» Let the numerator be ‘a’ and denominator be ‘b’. Given, Sum of the numerator and denominator of a fraction is 3 less than twice the denominator. ⇒ a + b = 2b – 3 ⇒ a = b – 3 ------ (1) Also, If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. ⇒ a – 1 = (b – 1)/2 ⇒ b = 2a - 1 ------ (2) Substituting value of b in eq1. ⇒ a = 2a – 1 – 3 ⇒ a = 4. Thus, b = 2 × 4 – 1 = 7

The sum of the numerator and denominator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator becomes half the denominator. Determine the fraction.

Answer»

Let the numerator be ‘a’ and denominator be ‘b’.

Given,

Sum of the numerator and denominator of a fraction is 3 less than twice the denominator.

⇒ a + b = 2b – 3

⇒ a = b – 3 ------ (1)

Also,

If the numerator and denominator are decreased by 1, the numerator becomes half the denominator.

⇒ a – 1 = (b – 1)/2

⇒ b = 2a - 1 ------ (2)

Substituting value of b in eq1.

⇒ a = 2a – 1 – 3

⇒ a = 4.

Thus,

b = 2 × 4 – 1 = 7