Question

Express $2.00 as a percentage of $8.00 ?

Answer 1

25%

Explanation:

First let's think about a normal percentage as a ratio.

If I wanted to think about `4%` as a ratio I would say well... That's 4 parts of `100%` or `4/100` and from there I could simplify the fraction into `1/25` and now I have a mathematical representation of `4%`. Anything that I multiply by `1/25` will give me `4%` of that thing.

"How does this help me?" you say
I'm very glad you asked

Let's think about `8` as our `100%` and we want to find 2 parts of 8, so using what we just learned we say that "2 parts of 8 is the same as `2/8`." To turn `2/8` into a percentage we just need the denominator to equal 100 since earlier we said that 8 is our `100%`

We could use an equation for this, so let's use an equation for this :D

We know that `8*("some number") = 100` so;
`8x = 100`

`1/8*8x = 100*1/8 = 100/8 = 25/2 = 12.5`

Now we know that if we multiply the denominator by 12.5 we will get 100 and if we multiply the numerator by 12.5 we will get a ratio with 100 as the denominator, so our percentage must be the numerator!

`2/8*12.5/12.5 = 25/100 = 25%`

Answer 2

`25%`

Explanation:

Given: `($2)/($8)`

We have:

`(color(red)cancelcolor(black)$2)/(color(red)cancelcolor(black)$8)=1/4`

Now, we convert `1/4` to a percent.

We got:

`1/4*100%=25%`

`:.($2)/($8)=25%`