Question

the denominator of a fraction is greater than its numerator by 8. if 1 is added to the numerator and 4 is subtracted from the denominator, the fraction becomes 4/7. Find the original number​

Answer 1

Answer:

3/7.

Step-by-step explanation:

★ Let,

• The numerator of a fraction = x.
• The denominator of a fraction = x + 8.

★ When 1 is added to the numerator,

• The numerator of a fraction = x + 1.
• The denominator of a fraction = x + 8.

★ When 4 is subtracted from the denominator,

• The numerator of a fraction = (x + 1)
• The numerator of a fraction = (x + 8 - 4)

We know that,

Fraction = Numerator/Denominator

= (x + 1) / (x + 8 - 4)

= (x + 1) / (x + 4).

★ According to the conditions,

(x + 1) / (x + 4) = 4/7

Cross-Multiply

➸ 7(x + 1) = 4(x + 4)

➸ 7x + 7 = 4x + 16

Subtract on both sides by like terms

➸ 7x - 4x = 16 - 7

➸ 3x = 9

➸ x = 9/3

➸ x = 3.

★ Therefore,

• The numerator of a fraction = x = 3.
• The denominator of a fraction = x + 8 = 3 + 8 = 11.

★ Hence,

Original Fraction = 3/7.

______________________________

Answer 2

✰ Given :

• The denominator of a fraction is greater than its numerator by 8. When 1 is added to the numerator and 4 is subtracted from the denominator, the fraction becomes 4/7 .

✰ Solution :

• Let's assume the numerator as x .

• As, denominator is greater than the numerator by 8, Let's assume the denominator as (x + 8) .

Now,

• 1 is added to the numerator = (x + 1)
• 4 is subtracted to the denominator = (x + 8 – 4) = (x + 4)

✰ According to the Question :

$\\ \leadsto \tt \frac{(x + 1)}{(x + 4)} = \frac{4}{7}$

By doing cross multiplication we get :

$\\ \: \: \: \tt : \implies \: 7(x + 1) = 4(x + 4) \\ \\ \\ \tt : \implies 7x + 7= 4x + 16 \\ \\ \\ \tt : \implies \: 7x - 4x = 16 - 7 \\ \\ \\ \tt : \implies \: 3x = 9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt : \implies \: x = \frac{9}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt : \implies { \mathfrak{ \pmb{x = 3}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Therefore,

• Numerator of the fraction = x = 3

• Denominator of the fraction = (x + 4) = (3 + 4) = 7

Henceforth,

$\: \: \: \: \: \: \: \: \: { \underline{ \boxed{ \mathfrak{ \pmb{The \: \: required \: \: original \: \: fraction \: \: is \: \: \dfrac{3}{7} }}}}} \: \: \bigstar$