Question

The numerator of the fraction is 4 less than the denominator.if the numerator is decreased by 2 and denominator is increased by 1,then the denominator becomes 8 times the numerator.find the fraction.

Answer 1

Let the numerator be x and the denominator be y
=> rational number = x/y
given that, the numerator is 4 less than the denominator
=> x = y-4
=> fraction = (y-4)/y
if the numerator is decreased by 2 and denominator is increased by 1,
new numerator = y-4-2 = y-6
new denominator = y+1
=> new fraction = (y-6)/(y+1)
also given that, new denominator becomes 8 times the new numerator
=> y+1 = 8(y-6)
=> y+1 = 8y-48
=> 8y-48-y-1=0
=> 7y-49=0
=> 7y=49
=> y= 49/7 = 7
therefore,
numerator  = y-4 = 7-4 = 3
denominator = y = 7
fraction = 3/7

Answer 2

Given :

→ The numerator of a fraction is 4 less than denominator.if the numerator is decreased by 2 and denominator is increased by 1 then denominator is eight times numerator.

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Find :

→ The fractional form.

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Solution :

→ Let "x/y" be fractional form.

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→ x = y - 4

→ x - y = - 4 -----(1)

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→ 8(x - 2) = y + 1

→ 8x - 16 = y + 1

→ 8x - y = 17 -----(2)

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Subtract the equations:

→ 8x - y = 17

→ -7x = -21

→ x = 21/7 = 3

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Adding "x = 3" in equation (1):

→ 3 - y = - 4

→ y = 3 + 4 = 7

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Therefore ,

→ x = 3

→ y = 7

→ Fractional form = (3/7).