Question

8. The numerator of a fraction is 4 less than the denominator. If 1 is added to both its
numerator and denominator, it becomes ½
Find the fraction.

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Answer 1

Answer: Let the denominator be' x'

and the numerator be 'x-4'

∴ According to the given condition, after adding 1 to both the

denominator becomes 'x+1'

and the numerator becomes 'x-4+1' = ' x-3'

and the fraction becomes 1/2

∴ x-3/x+1 = 1/2  ( cross multiplication)

∴2 ( x-3) = 1 (x+1)

∴2x-6= x+ 1

∴2x-x=1+6

∴x = 7

the fraction is x-4/ x

the numerator = 7-4 =3

and the denominator = x= 7

∴hence fraction is 3/7

Answer 2

✿AnSwer:

The fraction is 3/7.

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☯GiVen:

Here in the above question it is given that the fraction is 4 times less than that of it's denominator.

☯To Find:

We have to find the original fraction.

☯SoluTion:

Let us we assume that the denominator be x.

So, numerator becomes x - 4.

ATQ,

† If 1 is added to both its numerator and denominator, it becomes ½ ,

$\sf \longmapsto \: \: \dfrac{x - 4 + 1}{x + 1} = \dfrac{1}{2} \\ \\ \sf \longmapsto \: \: \frac{x - 3}{x + 1} = \frac{1}{2} \\ \\ \sf \longmapsto \: \: 2(x - 3) = x + 1 \\ \\ \sf \longmapsto \: \: 2x - 6 = x + 1 \\ \\ \sf \longmapsto \: \: 2x - x = 1 + 6 \\ \\ \sf \longmapsto \: \: { \underline{ \boxed{ \bf{ \purple{ \: x = 7 \: }}}}} \: \bigstar$

As we have considered denominator is x so the value of denominator is 7.

Now,

★ Fraction :

$\sf \longmapsto \: \: \dfrac{x - 4}{x} \\ \\ \sf \longmapsto \: \: \dfrac{7 - 4}{7} \\ \\ \sf \longmapsto \: \: { \underline{ \boxed{ \bf{ \pink{ \: \: \dfrac{3}{7} \: }}}}} \: \bigstar$

So, the fraction is 3/7.

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