Question

The numerator of a fraction is 4 less than its denominator. If the numerator is decreased by 1, the fraction becomes ⅔ . Find the fraction.​

Answer 1

Given : The numerator of a fraction is 4 less than its denominator. Numerator is decreased by 1, the fraction becomes ⅔.

Need to find : The fraction.

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Lets form the equation :

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Let denominator of the fraction be x , then numerator will be (x - 4). When 1 decreased from the numerator, then numerator will be (x - 3).

• Final equation = (x - 3)/x

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It's also given that :

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When numerator is decreased by 1 , the fraction becomes ⅔.

• So, (x - 3)/x = ⅔

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

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

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$\sf : \implies \: 3x - 9 = 2x$

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$\sf : \implies \: 3x - 2x = 9$

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$\sf : \implies \: \bold{ x = 9}$

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Put the value of x in the equation.

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$\sf : \implies \: \dfrac{(x - 4)}{x}$

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$\sf : \implies \: \dfrac{9 - 4}{9}$

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$\sf : \implies \: \dfrac{5}{9}$

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$\sf\therefore{\underline{Hence, \: the \: fraction \: is \: \bold{ \dfrac{5}{9}}. }}$