Question

The denominator of a fraction is 4 more than its numerator .On subtracting 1 from each numerator and the denominator,the fraction becomes 1/2 .Find the original fraction.​

Answer 1

Answer:

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Answer 2

FIND THE FRACTION

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Solve:

• Let n be the numerator.

$\sf original\implies \sf \large \frac{n}{n + 4 }$

$\:$

$\implies \sf \large \frac{n - 1}{(n + 4) - 1} = \frac{1}{2}$

$\implies \sf \large \frac{n - 1}{n + 4 - 1} = \frac{1}{2}$

$\implies \sf \large \frac{n - 1}{n + 3} = \frac{1}{2}$

$\:$

Cross Multiplication Method:

$\implies \sf \large \frac{ \blue{n - 1}}{ \green{n + 3}} = \frac{ \: \green1 \: }{ \blue2}$

$\implies \sf \large \blue{2n - 2} = \green{n + 3}$

$\:$

Transpose:

$\implies \sf \large2n - 2 = n + 3$

$\implies \sf \large2n - n = 3 + 2$

$\implies \sf \large \therefore \: n = 5$

$\:$

Back to the original fraction, substitute n as 5 or the numerator.

$\sf original\implies \sf \large \frac{5}{5 + 4 }$

$\sf \orange{original}\implies \orange{ \sf \large \frac{5}{9} }$

$\:$

Final Answer:

$\: \sf \huge \orange{ \frac{ \: 5 \: }{9} }$

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