Question

The numerator of a fraction is 4 less than the denominator. If 1 is added to both its numerator and denominator it becomes 1/2. find the fraction

Answer 1

Given :-

• The numerator of a fraction is 4 less than the denominator.
• If 1 is added to both its numerator and denominator, it becomes 1/2.

To Find :-

• Find the original fraction.

Solution :-

• Let us assume the denominator as "x".

$\qquad$☀️It's given the numerator of a fraction is 4 less than the denominator.If 1 is added to both its numerator and denominator, it becomes 1/2

$\qquad$$\sf \pink{ { Original \: Fraction = \dfrac{x-4}{x} }}$

$\small\underline{\pmb{\sf \:According \: to \: the \: question :-}}$

$\sf { :\implies New \: Fraction = \dfrac{x-4+1}{x+1} }$

$\qquad\leadsto\quad \sf \dfrac{x-4+1}{x+1} = \dfrac{1}{2}$

$\qquad\leadsto\quad \sf \dfrac{x-3}{x+1} = \dfrac{1}{2}$

$\qquad\leadsto\quad \sf 2(x-3) = 1(x+1)$

$\qquad\leadsto\quad \sf 2x - 6= x + 1$

$\qquad\leadsto\quad \sf 2x - x= 1 + 6$

$\qquad\leadsto\quad \sf \pink{ x= 7}$

Substituting value of x:-

$\sf {: \implies Original \: Fraction = \dfrac{x-4}{x} }$

$\qquad\leadsto\quad \sf \dfrac{7-4}{7}$

$\qquad\leadsto\quad \sf \dfrac{3}{7}$

$\therefore\:\underline{\textsf{Original fraction is \textbf{ 3/7 }}}.$

Answer 2

Given that :—

→ The numerator of a fraction is 4 less than the denominator

→ 1 is added to both its numerator and denominator, it becomes 1/2.

So,

Let the fraction to be predicted a/b

As per the given condition :—

Numerator = denominator - 4

→ a = b − 4

→ =b − a

→. = 4

As per the given data:—

if 1 added to both numerator and denominator then fraction becomes 1/2

→ a+1 / b+1 = 1/2

On cross multiplying the above equation we get:—

→ 2a + 2 = b + 1

→ 2a − b = −1

→ (2a − b) + (b − a)

→ = 4 − 1

a = 3,

and b = 7

Fraction = 3/7

Hence we get the answer → 3/7

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: @vikramjeeth$