Question

The numerator of a fraction is 4 less than the denpminator.if one is added to both its numetator and denomenator,the fraction become 1/2. find the fraction​

Answer 1

Answer:

This is the answer for your question

Answer 2

Given :

• Numerator of a fraction is 4 less than the denominator.

• One added to numerator amd denominator the fraction becomes 1/2.

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To find :

• Find the fraction.

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Concept :

Formation of a fraction - $\bf\:\frac{numerator}{denominator}$

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Assumption :

Let the denominator be x

According to the question ,

$\sf\therefore\:Numerator~=~4~less~than~denominator$

$\sf\therefore\:Numerator~=~(x-4)$

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Solution :

So from assumption we got our fraction to be -

$\bf\:Fraction~=~\frac{x-4}{x}$

Now according to the question -

➻ 1 is to be added to both numerator and denominator to make the fraction 1/2.

$\sf\to\:\frac{x-4+1}{x+1}=\frac{1}{2}$

$\sf\to\:\frac{x-3}{x+1}=\frac{1}{2}$

$\sf\to\:2(x-3)=1(x+1)$

$\sf\to\:2x-6=x+1$

$\sf\to\:2x-x-6=1$

$\sf\to\:x-6=1$

$\sf\to\:x=1+6$

$\small{\mathfrak{\to\:x=7}}$

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So fraction will be -

Numerator of the fraction = $\tt\:x-4~=7-4~=3$

Denominator of the fraction = $\tt\:x~=7$

$\small{\underline{\boxed{\mathrm{\therefore\:Original~fraction~=~\frac{3}{7}}}}}$ $\sf\color{red}{⋆}$

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Verification :

We got the original fraction as 3/7.

Now according to the question, adding 1 to both numerator and denominator we would get 1/2.

$\sf\:\frac{3+1}{7+1}=\frac{1}{2}$

$\sf\twoheadrightarrow\frac{4}{8}=\frac{1}{2}$

$\sf\twoheadrightarrow\cancel{\frac{4}{8}}=\frac{1}{2}$

$\sf\twoheadrightarrow\frac{1}{2}=\frac{1}{2}$

Hence Verified !~

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