Question

The numerator of a fraction is 4 less than the denominator.If 1 is added to both it's numerator and denominator,it becomes 1/2.Find the fraction



Please answer this guys

This is very important

Eighth class student​

Answer 1

Given:

• Numerator of fraction is 4 less than the denominator.
• If 1 is added to both it's numerator and denominator, it becomes ½.

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To find:

• The fraction.

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Solution:

• Let the denominator be x.
• Let the numerator be (x-4).

Original fraction = $\sf \dfrac {(x-4)}{x}$

Now, if we add 1 to both the numerator and denominator, then the fraction becomes ½.

So,

$\sf \dfrac{(x - 4) + 1}{x + 1} = \dfrac{1}{2}$

$\sf \dfrac{x - 4 + 1}{x + 1} = \dfrac{1}{2}$

$\sf \dfrac{x - 3}{x + 1} = \dfrac{1}{2}$

$\bigstar {\sf {\pink {Cross\ multiplication}}}$

2(x-3) = 1(x+1)

2x-6 = x+1

2x-x = 1+6

$\boxed {\bf {\orange {x=7}}}$

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Verification:

Substitute the value of x as 7 in the equation.

$\sf \dfrac{(7 - 4) + 1}{7 + 1} = \dfrac{1}{2}$

$\sf \dfrac{3 + 1}{8} = \dfrac{1}{2}$

$\sf \dfrac{4}{8} = \dfrac{1}{2}$

$\sf \dfrac{1}{2} = \dfrac{1}{2}$

LHS = RHS

Hence Verified!

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Final answer:

• Numerator = (x-4)

= 7-4

= 3

• Denominator = x

= 7

$\boxed {\sf {\blue {The\ original\ fraction\ is\ \dfrac {3}{7}.}}}$