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

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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Lyla 1 month 2021-08-13T13:47:17+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-13T13:48:29+00:00

    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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    0
    2021-08-13T13:48:29+00:00

    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

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