Question

the numerator fraction is 1 less than its denominator. if the numerator is increase bi fore and the denominator is increased by 5 the new fraction becomes equivalent to 4 by 5 what is the the original fraction?​

Answer 1

Question :-

• The numerator of a fraction is 1 less than its denominator. If the numerator is increased by 4 and the denominator is increased by 5, the new fraction becomes equivalent to 4 by 5. What is the original fraction?​

Answer :-

• The original fraction is 4/5.

To find :-

• The original fraction.

Solution :-

Let the denominator of the original fraction be "x".

It is given that :-

• The numerator of the fraction is 1 less than it's denominator.

Hence :-

• The numerator of the original fraction will be "x - 1."

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Increasing the numerator by 4,

• We get "x - 1 + 4".

Increasing the denominator by 5,

• We get "x + 5".

Now, it is given that :-

• When the numerator is increased by 4 and the denominator is increased by 5, the new fraction becomes equivalent to 4/5.

Therefore,

$\implies \sf \dfrac{x - 1 + 4}{x + 5} = \dfrac{4}{5}$

$\sf \implies 5 \: (x - 1 + 4) = x + 5 \: (4)$

$\sf \implies 5x - 5 + 20 = 4x + 20$

$\sf \implies 5x + 15 = 4x + 20$

$\implies \sf 5x - 4x = 20 - 15$

$\implies \underline{\boxed{\sf x = 5}}$

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Hence :-

$\rm Numerator = x - 1 = 5 - 1 = 4.$

$\rm Denominator = x = 5.$

Thus, the original fraction is :-

$\underline{\boxed{\bf \dfrac{4}{5}}}$