In a rational number, twice the numerator is 2 more than the denominat

1.	In a rational number, twice the numerator is 2 more than the denominator If 3 is added to each, the numerator and the denominator. The new fraction is 2/3. Find the original number.
Answer» Le the numerator be x and the denominator be (2x – 2) By using the formula Fraction = numerator/denominator = x / (2x – 2) So, the numerator and denominator are increased by 3, then fraction is 2/3 (x + 3)/(2x – 2 + 3) = 2/3 (x + 3)/(2x + 1) = 2/3 By cross-multiplying we get, 3(x + 3) = 2(2x + 1) 3x + 9 = 4x + 2 3x – 4x = 2 – 9 -x = -7 x = 7 ∴ The numerator is x = 7, denominator is (2x – 2) = (2(7) – 2) = 14-2 = 12 And the fraction is numerator/denominator = 7/12

In a rational number, twice the numerator is 2 more than the denominator If 3 is added to each, the numerator and the denominator. The new fraction is 2/3. Find the original number.

Answer»

Le the numerator be x and the denominator be (2x – 2)

By using the formula

Fraction = numerator/denominator

= x / (2x – 2)

So, the numerator and denominator are increased by 3, then fraction is 2/3

(x + 3)/(2x – 2 + 3) = 2/3

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

By cross-multiplying we get,

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

3x + 9 = 4x + 2

3x – 4x = 2 – 9

-x = -7

x = 7

∴ The numerator is x = 7, denominator is (2x – 2) = (2(7) – 2) = 14-2 = 12

And the fraction is numerator/denominator = 7/12