Question

the numertor of fraction is 4 less than the denominator. if 1 is added to both it's numertor and denominator, it becomes 1/2.find the fraction

Answer 1

$\textbf {Hey there, here is the solution.}$

.............................................................................................

STEP 1: Define x:

Let the denominator be x.

The numerator is 4 less than the denominator:

$\text{Fraction = }\dfrac{x - 4}{x}$

.............................................................................................

STEP 2: Form equation:

1 is added to the numerator and denominator, the fraction is 1/2:

$\dfrac{x - 4 + 1}{x + 1} = \dfrac{1}{2}$

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

.............................................................................................

STEP 3: Solve x:

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

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

$2x - 6 = x + 1$

$x = 7$

.............................................................................................

STEP 4: Find the fraction:

$\text{Fraction = }\dfrac{7 - 4}{7} = \dfrac{3}{7}$

.............................................................................................

$\textbf {Cheers}$

Answer 2

Let Denominator of fraction be X .

Numerator = ( X - 4 ).

Fraction = Numerator/Denominator = ( X - 4 )/ X.

Given : If 1 is added to both the numerator and denominator then fraction is equal to 1/2.

X - 4 + 1 / X + 1 = 1/2

X - 3 / X + 1 = 1/2

2 ( X - 3 ) = X + 1

2X - 6 = X + 1

2X - X = 1 + 6

X = 7

Denominator of fraction = X = 7.

and,

Numerator of fraction = X - 4 = 7-4 = 3.

Fraction = Numerator/Denominator = 3/7