Question

By what percent will a fraction change if its numerator is decreased by 30% and its denominator is decreased by 20%?

Answer 1

Decreased 12.5%

Explanation:

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Answer 2

Answer: 12.5%

Explanation:

Let the original fraction is
`(x)/(y)`

After decreasing its numerator by 30% and denominator by 20%,

New fraction =
`\frac{x-30\%\text{ of} x}{y-20\%\text{ of} y}`

=
`(x-(30x)/(100))/(y-(20x)/(100))`

=
`((100x)/(100)-(30x)/(100))/((100y)/(100)-(20x)/(100))`

=
`((100x-30x)/(100))/((100y-20y)/(100))`

=
`((70x)/(100))/((80y)/(100))`

=
`(70x)/(80y)`

=
`(7x)/(8y)`

Thus, the total percentage change in the original fraction,

=
`\frac{\text{original fraction-new fraction}}{\text{original fraction}} * 100`

=
`((x)/(y) -(7x)/(8y) )/((x)/(y) ) * 100`

=
`(1 -(7)/(8) )/(1 ) * 100`

=
`(8-7)/(8)* 100`

=
`(100)/(8) = 12.5\%`