Question

The numerator of a fraction is 3 less than the denominator If 3 is added to the numerator and 2 subtracted from the denominator the new fraction is (5)/(3) .Find the fraction.​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

Given :-

• The numerator of a fraction is 3 less than the denominator.
• If 3 is added to the numerator and 2 is subtracted from the denominator the new fraction will be 5/3.

To Find :-

• What is the fraction.

Solution :-

Let,

$\mapsto$ The denominator be x

$\mapsto$ The numerator will be x - 3

Then, the required fraction is :

$\leadsto \sf \dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\green{\dfrac{x - 3}{x}}}$

According to the question,

$\implies \sf \dfrac{Numerator + 3}{Denominator - 2} =\: New\: fraction$

$\implies \sf \dfrac{x \cancel{- 3} \cancel{+ 3}}{x - 2} =\: \dfrac{5}{3}$

$\implies \sf \dfrac{x}{x - 2} =\: \dfrac{5}{3}$

By doing cross multiplication we get,

$\implies \sf 5(x - 2) =\: 3(x)$

$\implies \sf 5x - 10 =\: 3x$

$\implies \sf 5x - 3x =\: 10$

$\implies \sf 2x =\: 10$

$\implies \sf x =\: \dfrac{\cancel{10}}{\cancel{2}}$

$\implies \sf x =\: \dfrac{5}{1}$

$\implies \sf\bold{\purple{x =\: 5}}$

Hence, the required fraction are :

$\longrightarrow \sf \dfrac{x - 3}{x}$

$\longrightarrow \sf \dfrac{5 - 3}{5}$

$\longrightarrow \sf\bold{\red{\dfrac{2}{5}}}$

${\normalsize{\bold{\underline{\therefore\: The\: required\: fraction\: is\: \dfrac{2}{5}\: .}}}}$

VERIFICATION :-

$\implies \sf \dfrac{x - 3 + 3}{x - 2} =\: \dfrac{5}{3}$

By putting x = 5 we get,

$\implies \sf \dfrac{5 - 3 + 3}{5 - 2} =\: \dfrac{5}{3}$

$\implies \sf \dfrac{2 + 3}{3} =\: \dfrac{5}{3}$

$\implies \sf\bold{\pink{\dfrac{5}{3} =\: \dfrac{5}{3}}}$

Hence Verified.