Question

The numerator of a fraction is 8 less than the denominator of a fraction. The value of the fraction is 3/5, find the value of the fraction.

Answer 1

`\LARGE{ \boxed{ \rm{ \orange{ Solution:}}}}`

Let the numerator be x

It is given that,

• Denominator - 8 = Numerator

Then,

⇛ Denominator- 8 = x

⇛ Denominator = x + 8

According to condition -2)

⇛ Fraction = 3/5

⇛ x/x + 8 = 3/5

Cross multiplying,

⇛ 3(x + 8) = 5x

⇛ 3x + 24 = 5x

⇛ 24 = 5x - 3x

⇛ 24 = 24

Flipping it out,

⇛ 2x = 24

⇛ x = 24/2 = 12

Then,

⇛ x + 8 = 12 + 8 = 20

• Numerator = 12
• Denominator = 20

`\large{ \therefore{ \boxed{ \rm{ \pink{Then, \: the \: fraction = (12)/(20) }}}}}`

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Answer 2

Hello!

Answer:

`\huge\boxed{(12)/(20)}`

To find the numerator and denominator, we can set up a proportion where:

x = denominator

x -8 = numerator

`(3)/(5) = (x-8)/(x)`

Cross multiply:

`3(x) = 5(x - 8)`

`3x = 5x - 40`

Simplify:

`3x - 5x = -40\\\\-2x = -40\\\\x = 20`

Substitute in this value of x to find the numerator and denominator:

`((20) - 8)/((20)) = (12)/(20)`

Hope this helped you! :)