Question

The numerator of a fraction is 5 less than the denominator. if 1 is added to both its neumerator and denominator, it becomes 1/2 find the fraction

Answer 1

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

✴ The numerator of a fraction is 5 less than the denominator. if 1 is added to both its neumerator and denominator, it becomes 1/2 .find the fraction.

$\mathtt{\huge{\underline{\green{Answer:-}}}}$

➡ The Fraction obtained is 4/9.

$\mathtt{\huge{\underline{\pink{Solution:-}}}}$

Given :-

• The numerator of a fraction is 5 less than its denominator.

• If 1 is added to the numerator and denominator both , the fraction becomes 1/2.

To Find :-

• The Fraction obtained.

Calculation :-

Let denominator of the fraction be = x

And then numerator be (x – 5)

Original fraction = (x – 5)/x

According to the Question,

⇒ (x – 5 + 1)/(x + 1) = 1/2

⇒ (x – 4)/(x + 1) = 1/2

⇒ 2(x – 4) = (x + 1)

⇒ 2x-8 = x + 1

⇒ 2x-x = 1 + 8

⇒ x = 9

⇒ x = 9.

Original fraction = (x – 5)/x

Original fraction = ( 9 - 5 ) / 9

Original fraction = 4/9

Hence, the original Faction obtained is 4/9.

Answer 2

$\large\mathcal\pink{\underbrace{QUESTION:-}}$

The numerator of a fraction is 5 less than the denominator. If 1 is added to both its numerator and denominator, it becomes 1/2. Find the fraction.

$\large\mathcal\red{\underbrace{SOLUTION:-}}$

Let the denominator be "x."

And, Numerator be "x-5."

According To The Question,

The Equation :-

(x-5+1)/(x+1) = 1/2

➠ (x-4)/(x+1) = 1/2.

➠ x+1 = 2(x-4).

➠ x+1 = 2x-8.

➠ x-2x = -8-1

➠ -x = -9.

➠ x = 9.

If the value of x = 9, then the fraction :-

(x-5)/x = 4/9.

Hence, The Fraction = 4/9.