Question

the number of a fraction is 3 less than its denominator if the numerator is increased by 1 and the denominator is increased by 3 the fraction becomes 1/2 find the original fraction​

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

The Original Fraction is $\tt{\dfrac{4}{7}}$

$\mathfrak{\large{\underline{\underline{Explanation :- }}}}$

Given :

Numerator of the Fraction = 3 less than its denominator

If numerator is increased by 1 & the denominator is increased by 3 new Fraction = $\tt{\dfrac{1}{2}}$

To Find :

The Original Fraction

Solution :

◆ $\textbf{\small{\underline{Consider the -}}}$

• Denominator as x
• Numerator as (x - 3)

◆ $\textbf{\small{\underline{According to the Question -}}}$

If numerator is increased by 1 & the denominator is increased by 3 new Fraction = $\tt{\dfrac{1}{2}}$

★ $\boxed{\tt{\dfrac{(x - 3) + 1}{x + 3} = \frac{1}{2} }}$

$\tt{\longrightarrow} \: \dfrac{(x - 3) + 1}{x + 3} = \dfrac{1}{2}$

$\tt{\longrightarrow} \: \dfrac{x - 3+ 1}{x + 3} = \dfrac{1}{2}$

$\tt{\longrightarrow} \: \dfrac{x - 2}{x + 3} = \dfrac{1}{2}$

$\tt{\longrightarrow} \:2(x - 2) = 1(x + 3)$

$\tt{\longrightarrow} \:2x - 4= x + 3$

$\tt{\longrightarrow} \:2x - x= 3 + 4$

$\tt{\longrightarrow} \: x= 7$

Denominator = 7

$\rule{300}{1.5}$

★ Value of (x - 3)

$\tt{\longrightarrow} \:7 - 3$

$\tt{\longrightarrow} \:4$

Numerator = 4

$\therefore$ The Original Fraction is $\tt{\dfrac{4}{7}}$

$\rule{300}{1.5}$

$\mathfrak{\large{\underline{\underline{Verification :-}}}}$

As the Original Fraction is $\tt{\dfrac{4}{7}}$ add 1 to Numerator and 3 to Denominator and check if the new Fraction is $\tt{\dfrac{1}{2}}$ or not.

$\tt{\longrightarrow} \: \dfrac{4 + 1}{7 + 3} = \dfrac{1}{2}$

$\tt{\longrightarrow} \: \dfrac{5}{10} = \dfrac{1}{2}$

$\tt{\longrightarrow} \: \dfrac{1}{2} = \dfrac{1}{2}$

$\therefore$ The Original Fraction is $\tt{\dfrac{4}{7}}$

Answer 2

Given :-

The numerator of a fraction is 3 less than its denominator.

When numerator increased by 1 the denominator is increased by 3.

Therefore, the fraction becomes 1/2

To Find :- The original fraction

Solution :-

Let the denominator be x and numerator be (x - 3) respectively.

According to the given condition we get,

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

x - 3 + 1/ x + 3 = 1/2

x - 2/ x + 3 = 1/2

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

2x - 4 = x + 3

2x - x = 3 + 4

x = 7

Therefore, denominator is 7

The value of numerator is = (x - 3)

Substituting the value of x = 7 We get,

7 - 3

4

Therefore, the numerator is 4

Therefore, the original required fraction is 4/7 respectively.