If 45% of a number is 36, what is the number?

As `45%` of a number is `36`,

`45%xx"Number"=36`

or `45/100xx"Number"=36`

or `45/100xx100/45xx"Number"=36xx100/45`

or `cancel45^1/cancel100^1xxcancel100^1/cancel45^1xx"Number"=cancel36^4xx100/cancel45^5`

or `"Number"=(4xxcancel100^20)/(cancel5^1)`

or `"Number"=80`

Let the number be `x`

`45%` of `x=36`

`45%` of `x` can also be written as `45% xx x`

`45/100 xx x=36`

`0.45x=36`

`x=36/0.45.`

`x=80`

check:

`:.45% xx 80`

`:.cancel45^9/cancel100^20 xx 80`

`:.9/cancel20^1 xx cancel80^4/1`

`:.9 xx 4=36`

Percentage questions can always be done by a direct proportion method, which is the same as using equivalent fractions.

In this case we are told that 36 is `45%` of a certain number. The number itself would represent `100%`

If we use `x` for the number, we have:

`36/45 = x/100" "larr` "If 36 is 45%, how much is `100%?`"

`45x = 36xx100" "larr` cross multiply

`x = (36xx100)/45`

`x = 80`

This method is particularly useful with reverse percentages.

Whenever I come across these kind of questions, I use a formula. `x` will represent the number because we don't know the number yet. For this case, the formula would be,
`x``\cdot``45/100``=``36`.

The value of `x` will be the answer. So let's start!

`x``\cdot``45/100``=``36`

`x``=``36``\cdot``100/45` (Leave `x` on one side)

`x``=``cancel36^4/1``\cdot``100/cancel45^5` (Multiply)

`x``=``400/5` (Simplify)

`x``=``80`

Did you know that in mathematics, of means `times` and/or `*`! So `45%` of `80` is,

`45/100``times``80`!

Let's check if the answer is correct!

`45/100``times``80/1`

`=``45/cancel100^5``times``cancel80^4/1`

`=``180/5`

`=``36`

I learned how to type the multiplication sign (dot) here! That's one source, and my other source is my brain!
Now since we checked the answer, we know that `80` is correct!
I hope that helps and that you understood it!

All the best,
Moksha :D