Question

the numerator of a fraction is 4 less then its denomenator. if the numerator is decreased by 1, the fraction is equal to 2/3 , find the fraction​

Answer 1

EXPLANATION.

Let the numerator of a fraction be = x

Let the denominator of a fraction be = y

To find the fraction.

According to the question,

The numerator of a fraction is 4 less than it's

denominator.

=> x = y - 4

=> x - y = -4 ......(1)

if the numerator is decreased by 1 , the fraction

is equal to 2/3

=> x - 1 / y = 2/3

=> 3 ( x - 1 ) = 2y

=> 3x - 3 = 2y

=> 3x - 2y = 3 .....(2)

From equation (1) and (2)

multiply equation (1) by 2

multiply equation (2) by 1

we get,

=> 2x - 2y = -8

=> 3x - 2y = 3

we get,

=> -x = -11

=> x = 11

put the value of x = 11 in equation (1) we get,

=> 11 - y = -4

=> -y = -15

=> y = 15

Therefore,

fraction = x/y = 11/15

Answer 2

Answer:

3/7 is a required fraction.

Step-by-step explanation:

Let the numerator be x and denominator be y.

Then,

The required fraction will be x/y.

_____________________

$\underline{\boldsymbol{According\: to \:the\: Question\:now :}} </p><p>$

☯ Condition 1 :

$:\implies\sf x = y - 4$

$: \implies \sf \: x - y = -4 \: \: \: \bigg \lgroup \bf{Equation \: 1} \bigg \rgroup$

☯ Condition 2 :

$:\implies\sf 8(x - 2) \: = \: y + 1$

$:\implies\sf 8x - 16\: = \: y + 1$

$:\implies\sf 8x - y \: = \: 1 \: \: \: \bigg \lgroup \bf{Equation \: 2} \bigg \rgroup$

Substracting equation (2) from (1) we get,

$:\implies\sf - 7x \: = \: - 21$

$:\implies\sf x \: = \: \dfrac{21}{7}$

$:\implies \underline{ \boxed{\sf x \: = \: 3}}$

Putting the value of x in equation (2) :

$:\implies\sf x - y \: = \: - 4$

$:\implies\sf 3 - y \: = \: - 4$

$:\implies\sf y \: = \: 3 + 4$

$:\implies \underline{ \boxed{\sf y \: = \: 7}}$

$\therefore\:\underline{\textsf{The required fraction is \textbf{3/7}}}.</p><p></p><p>$