Question

How do you find the percent change given the original number is 60 and new number is 45?

Answer 1

`-26%`

Explanation:

Reduction requires subtraction so the percentage is negative as well

`("change")/("original value")-> ("2nd number - 1st number")/("original value") = (-15)/60`

`color(blue)("Shortcut method")`

Most people would show this as: `color(purple)(-15/60xx100% = -25%)`

This can hide from people what is actually happening
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`color(blue)("First principle method with full explanation - so it is long")`

Starting point: you need to end up with: `("some number")/100`

Very important point: the symbol % is like a unit of measurement that is worth `1/100`

So: `("some number")/100 -> "some number "xx1/100`

But `1/100` is the same as % so we have:

`("some number")/100 -> "some number "xx%`

which is the same as: `"some number"%`

`color(brown)("The calculations")`
To change the denominator of 60 into 100 multiply by `100/60`

`color(green)(-15/60color(red)(xx1)" "=" "-15/60color(red)(xx(color(white)(.)100/60color(white)(.))/(100/60))" "=" "-26/100)`

Notice that the numerator of `color(green)(15)color(red)(xx100/60) ->15/60xx100` Which is exactly the same as in the shortcut method.

but `color(green)(-26/100)` is the same as `" "color(green)(-26xx1/100)`

but `1/100 -> %` giving:

`-26%` as in the shortcut method