Question

the numerator of a fraction is 1 less than the denominator . if numerator is decreased by 2 and denominator is increased by 3 the fraction becomes 1/4 find the fraction

Answer 1

HEY MATE HERE IS UR ANSWER

GIVEN THAT ➡️ THE NUMERATOR OF A FRACTION IS 1 LESS THAN DENOMINATOR AND IF NUMERATOR IS

DECREASED BY 2 AND DENOMINATOR IS INCREASED BY 3 DIFFRACTION BECOMES 1/4 . AND NOW WE

NEED TO FIND THE FRACTION.



SOLUTION ➡️

LET THE DENOMINATOR OF FRACTION = X

SO ACCORDING TO QUESTION NUMERATOR IS 1 LESS THAN DENOMINATOR .

THEREFORE

NUMERATOR OF FRACTION IS = X - 1

SO THE FRACTION OBTAINED NOW IS EQUAL TO


$\frac{(x - 1)}{x} \: - - - - - - \: eq \: \:( 1)$


SO NOW IN QUESTION IT'S GIVEN THAT

IF WE DECREASE 2 FROM NUMERATOR AND INCREASE 3 TO DENOMINATOR THEN THE FRACTION

BECOMES 1/4 .


THAT IS


$\frac{(x - 1) - 2}{x + 3} = \frac{1}{4}$


THIS IS EQUAL TO

$\frac{x - 3}{x + 3} = \frac{1}{4}$

SO NOW CROSS MULTIPLYING LHS AND RHS WE HAVE

$4(x - 3) = 1(x + 3)$


THAT IS


$4x - 12 = x + 3$


THAT IS


$4x - x = 3 + 12$


THIS IS EQUAL TO

$3x = 15$


SO WE HAVE


$x = \frac{15}{3} = 5$


SO NOW PUTTING VALUE OF X = 5 IN EQ. (1) WE HAVE


$\frac{x - 1}{x} = \frac{5 - 1}{5}$

THAT IS EQUAL TO

$\frac{4}{5}$




SO THE FRACTION IS

$\frac{4}{5}$


HENCE THE REQUIRED ANSWER = 4/5


HOPE IT'S HELPFUL !!!!!


BE BRAINLY ☯️

Answer 2

Define x:

Let the denominator be x

The numerator is x - 1

$\text {Fraction = } \dfrac{x-1}{x}$

Number is decreased by 2 and denominator is increased by 3:

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

The fraction becomes 1/4:

$\dfrac{x - 3}{x + 3} = \dfrac{1}{4}$

Cross multiply:

$x + 3 = 4(x - 3)$

Distribute 4:

$x + 3 = 4x - 12$

Rearrange with x on the LHS:

$4x - x = 3 + 12$

Solve x:

$3x = 15$

$x = 5$

Find the fraction:

$\text {Fraction = } \dfrac{x-1}{x} = \dfrac{5-1}{5} = \dfrac{4}{5}$

Answer: 4/5