Question

The numerator of a fraction is 3 less than its denominator. If we add 1 to both numerator and denominator, it becomes equal to 5/8. Find the fraction.

Please give full explanation and write it on a paper

Answer 1

Step-by-step explanation:

Let,

Numerator of a fraction = x

Denominator of a fraction = x + 3

If we add 1 to both numerator and denominator, it becomes equal to 5/8.

Numerator of a fraction = x + 1

Denominator of a fraction = x + 3 + 1 = x + 4

★ According to the Question :

⇒ $\dfrac{x \: + \: 1}{x \: + \: 4} \: = \: \dfrac{5}{8}$

⇒ 8 (x + 1) = 5 (x + 4)

⇒ 8x + 8 = 5x + 20

⇒ 8x - 5x = 20 - 8

⇒ 3x = 12

⇒ x = 12/3

⇒ x = 4

Numerator of a fraction = 4

• Denominator of a fraction = x + 3

⇒ 4 + 3

⇒ 7

Denominator of a fraction = 7

Therefore, the fraction is $\dfrac{4}{7}$

Answer 2

Answer:

Given :-

• The numerator of a fraction is 3 less than its denominator.
• If we added 1 to both numerator and denominator, it becomes equal to 5/8.

To Find :-

• What is the original fraction.

Solution :-

Let,

$\mapsto \bf{Denominator =\: x}$

$\mapsto \bf{Numerator =\: x - 3}$

Hence, the required original fraction will be :

$\leadsto \sf \dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\green{\dfrac{x - 3}{x}}}$

According to the question,

$\implies \sf \dfrac{Numerator + 1}{Denominator + 1} =\: \dfrac{5}{8}$

$\implies \sf \dfrac{x - 3 + 1}{x + 1} =\: \dfrac{5}{8}$

$\implies \sf \dfrac{x - 2}{x + 1} =\: \dfrac{5}{8}$

By doing cross multiplication we get,

$\implies \sf 8(x - 2) =\: 5(x + 1)$

$\implies \sf 8x - 16 =\: 5x + 5$

$\implies \sf 8x - 5x =\: 5 + 16$

$\implies \sf 3x =\: 21$

$\implies \sf x =\: \dfrac{\cancel{21}}{\cancel{3}}$

$\implies \sf x =\: \dfrac{7}{1}$

$\implies \sf\bold{\purple{x =\: 7}}$

Hence, the required original fraction is :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{x - 3}{x}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{7 - 3}{7}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{4}{7}}}$

${\small{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{4}{7}\: .}}}}$

▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃

$\bigstar\: \: \sf\bold{\purple{VERIFICATION\: :-}}$

$\implies \sf \dfrac{x - 3 + 1}{x + 1} =\: \dfrac{5}{8}$

By putting x = 7 we get,

$\implies \sf \dfrac{7 - 3 + 1}{7 + 1} =\: \dfrac{5}{8}$

$\implies \sf \dfrac{7 - 2}{8} =\: \dfrac{5}{8}$

$\implies \bf \dfrac{5}{8} =\: \dfrac{5}{8}$

Hence, Verified.