Question

How do you find the percent change given the original number is 48 and new number is 60?

Answer 1

`41color(white)(.) 2/3%`

Explanation:

Goes from `48 -> 60`

So this is an increase of `60-40 = 20`

We express this as a change in relation to the original price. So the change expressed as a fraction of the original price is :

`" "color(green)((+20)/48)`

`color(purple)("Using first principles to explain where the "xx100)`
`color(purple)("in the shortcut method comes from")`

`color(green)(20/48color(red)(xx1)" "=" "20/48color(red)(xx100/100) " "=" "(20color(red)(xx100) )/48color(red)( xx1/100)`

But `1/100` is the same as % giving:

`" "=color(green)((20color(red)(xx100) )/48color(red)( %)`

Writing this as in the shortcut method we have:

`" "=(20/48 xx 100)% = 41.6bar(6)%`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Foot note")`

The bar over the last 6 indicates that the value 6 repeats for ever.

It is really helpful to remember that `0.333bar3" is the same as "1/3`

So `0.666bar6` is the same as `2xx1/3=2/3`

Thus: `41.6bar6 = 41 2/3%`