Question

By what percent will a fraction change if its numerator is decreased by 50% and its denominator is decreased by 25%?

(It's not 33%, 1/3%, or -33% btw)

Answer 1

The fractional change is
`(1)/(3)` % .

Explanation:

Given as :

The original fraction =
`(x)/(y)`

Where numerator = x

Denominator = y

According to question

The numerator decreased by 50%

Let The new numerator = x' = x - 50% of x

I,e x' = x ( 1 -
`(50)/(100)`)

Or, x' = x (
`(100-50)/(100)`)

Or, x' =
`(50)/(100)` x

or, x' =
`(x)/(2)` .........A

Again

The new denominator = y' = y - 25% of y

i.e y' = y (1 -
`(25)/(100)`)

Or, y' = y (
`(100-25)/(100)`)

Or, y' = y (
`(75)/(100)`)

Or, y' =
`(3 y)/(4)` ............B

So, The new fraction =
`(x')/(y')` =
`((x)/(2))/((3 y)/(4))`

Or,
`(x')/(y')` =
`(2 x)/(3 y)`

So, The fractional change =
`(1-(2)/(3) )/(1)` × 100

Or, The fractional change =
`(1)/(3)`× 100

Hence, The fractional change is
`(1)/(3)` % . Answer