Question

the denominator of a fraction is two more than the numerator. if both numerator and denominator are increased by ten, the simplified is 9/10. find the original fraction. (Do not simplify).

Answer 1

Give to each part of the fraction a variable (a letter)

Numerator: n

Denominator: d

the denominator of a fraction is two more than the numerator:

`d=n+2`
`(n)/(d)=(n)/(n+2)`

both numerator and denominator are increased by ten, the simplified is 9/10:

`(n+10)/(n+2+10)=(9)/(10)`

Use the equation above to find the value of n:

`\begin{gathered} 10(n+10)=9(n+12) \\ 10n+100=9n+108 \\ 10n-9n=108-100 \\ n=8 \end{gathered}`

As n is equal to 8 find the value of d:

`\begin{gathered} d=n+2 \\ d=8+2 \\ d=10 \end{gathered}`

The original fraction is:

`(8)/(10)`