Question

the numera the numerator of a fraction is 6 less than the denominator if 3 is added to the numerator the fraction becomes equal to 2 by 3 find the original fraction​

Answer 1

Answer:

$\frac{1}{3}$

Given:

Numerator of a fraction is 6 is less than the denominator

3 added to numerator the fraction becomes 2/3

To find:

The original fraction

Solution:-

Let the denominator be x

Then numerator be x-6

3 added to it becomes 2/3

Now

According to the question

$(x - 6) + \frac{3}{x} = \frac{2}{3}$

$\frac{(x - 6 + 3)}{x} = \frac{2}{3}$

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

$3(x - 3) = 2x$

$3x - 9 = 2x$

$x = 9$

Denominator=9

Numberator=x-6

=9-6

=3

___________________

$The \: fraction = \frac{3}{9}$

=1/3

Answer 2

Answer:

$\huge{\pink{\green{\sf{\therefore Fraction=\frac{1}{3}}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

• In the given question information given about relation between numerator and denominator.

• So, we have to find the fraction.

$\underline \bold{Given : } \\ \implies Let \: Denominator = x \\ \implies Numerator = x - 6 \\ \\ \\ \underline \bold{To \: Find : }\\ \implies fraction = ?$

• According to given question :

$\implies \frac{x - 6 + 3}{x} = \frac{2}{3} \\ \implies \frac{x - 3}{x} = \frac{2}{3} \\ \implies 3x - 9 = 2x \\ \implies3x - 2x = 9 \\ \bold{\implies x = 9} \\ \\ \bold { \therefore Numerator = x - 6 = 9 - 6 = 3} \\ \bold{ \therefore Denominator = x = 9} \\ \\ \bold{\therefore Fraction = \frac{3}{9} = \frac{1}{3} }$