Question

The numerator of a fraction is four less than its denominator.If 1 is added to both, its numerator and denominator , the fraction becomes ½ find the fraction

Answer 1

$<b>Heya !$

Here's your answer !!

______________________________

Let the numerator be x

Denominator = x + 4

( Since, numerator is 4 less than the denominator. Therefore, it means that denominator is 4 more than the numerator )

A.T.Q.

$\mathbb {\bf {\frac{x}{x \: + \: 4}}}$

Adding 1 to both of them,

$= > \mathcal \: \bf \: \frac{x \: + \: 1}{x \: + \: 4 \: + \: 1} \: = \: \frac{1}{2} \\ \\ = > \bf \: \frac{x \: + \: 1}{x \: + \: 5} \: = \: \frac{1}{2} \\ \\ = > \bf \: 2 \: ( \: x \: + \: 1 \: ) \: = \: x \: + \: 5 \\ \\ = > \bf \: 2x \: + \: 2 \: = \: x \: + \: 5 \\ \\ = > \bf \: 2x \: - \: x \: = \: 5 \: - \: 2 \\ \\ = > \bf \: x \: = \: 3$

ANS )

Numerator = 3

Denominator = 3 + 4 = 7

$\bf {Fraction \: = \:{\frac{3}{7}}}$

_____________________________

Thanks !!

Answer 2

$hey \: mate \: here \: is \: your \: answer \:$

GIVEN THAT IN A FRACTION NUMERATOR IS 4 LESS THAN ITS DENOMINATOR. AND IF WE ADD 1 TO BOTH

ITS NUMERATOR AND DENOMINATOR . SO WE NEED TO FIND THE FRACTION

SOLUTION ➡️

LET THE DENOMINATOR = X

NOW ACCORDING TO QUESTIONS NUMERATOR IS 4 LESS THAN DENOMINATOR

THEREFORE

THE NUMERATOR IS = X - 4

SO THE OBTAINED FRACTION IS


$\frac{x - 4}{x} \: \: \: \: \: let \: this \: be \: eq. \: (1)$


NOW IN QUESTION ITS GIVEN THA PT IF WE ADD ONE TWO BOTH NUMERATOR AND DENOMINATOR THAN

THE FRACTION BECOMES 1/2

THAT IS


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


SO WE HAVE

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


SO NOW CROSS MULTIPLYING LHS AND RHS WE HAVE



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



THAT IS



$2x - 6 = x + 1$


THAT IS



$2x - x = 1 + 6$



THEREFORE WE HAVE

$x = 7$
NOW PUTTING VALUE OF X = 7 IN EQUATION ( 1 )


WE HAVE

$\frac{x - 4}{x} \: = \: \frac{7 - 4}{7}$


THAT IS EQUAL TO



$\frac{3}{7}$


THEREFORE THE FRACTION IS

$\frac{3}{7}$


$hope \: its \: helpful \:$



BE BRAINLY ☯️