Question

the numerator of a fraction is 6 less than the denominator.If 3 is added to the numerator the fraction is equal to 2/3.what is the original fraction equal to?​

Answer 1

Given :

• The numerator of a fraction is 6 less than the denominator .
• If 3 is added to the numerator the fraction is equal to 2/3.

To Find :

• Original Fraction.

Solution :

$\longmapsto\tt{Let\:Denominator\:be=x}$

As Given that Numerator of fraction is 6 less than the Denominator. So ,

$\longmapsto\tt{Numerator=x-6}$

Now ,

• If 3 is added to the numerator the fraction is equal to 2/3 .

$\longmapsto\tt{Numerator=x-6+3}$

$\longmapsto\tt{x-3}$

A.T.Q :

$\longmapsto\tt{\dfrac{x-3}{x}=\dfrac{2}{3}}$

$\longmapsto\tt{2(x)=3(x-3)}$

$\longmapsto\tt{2x=3x-9}$

$\longmapsto\tt{2x-3x=-9}$

$\longmapsto\tt{-1x=-9}$

$\longmapsto\tt\bf{x=9}$

Value of x is 9 ....

Therefore :

$\longmapsto\tt{Numerator=9-6}$

$\longmapsto\tt\bf{3}$

$\longmapsto\tt\bf{Denominator=9}$

So , The Original Fraction is 3/9 ...

Answer 2

Given :-

• The numerator of fraction = 6 less than the denominator.

• The fraction by adding 3 to numerator = 2/3.

To Find :-

• The original fraction.

Solution :-

$: \implies\sf{Let, \: the \: denominator = \: }{\textsf{\textbf{x}}} \\ \\ : \implies\sf{Let, \: the \: numerator = \: }{\textsf{\textbf{x - 6}}} \\ \\ \sf{Now,} \\ \\ : \implies\sf{numerator = \: }{\textsf{\textbf{x - 6 + 3}}} \\ \\ : \implies\sf{x - 3} \\ \\ : \implies\sf{ \frac{x - 3}{x} = \frac{2}{3} } \\ \\ : \implies\sf{2(x) = 3(x - 3)} \\ \\ : \implies\sf{2x = 3x - 9} \\ \\ : \implies\sf{2x - 3x = -9} \\ \\ : \implies\sf{ -1x = -9} \\ \\ : \implies\sf{x = \: }{\textsf{\textbf{9.}}}$

Value of x = 9.

Therefore,

• Numerator = 9 - 6 = 3.

• Denominator = 9.