Question

What percent of 180 is 120?

Answer 1

See the solution process below:

Explanation:

First, let's call the percent we are looking for `p`

"Percent" or "%" means "out of 100" or "per 100", Therefore p% can be written as `p/100`.

When dealing with percents the word "of" means "times" or "to multiply".

Putting this altogether we can write this equation and solve for `p` while keeping the equation balanced:

`p/100 xx 180 = 120`

`color(red)(100)/color(blue)(180) * p/100 xx 180 = color(red)(100)/color(blue)(180) * 120`

`cancel(color(red)(100))/cancel(color(blue)(180)) * p/color(red)(cancel(color(black)(100))) xx color(blue)(cancel(color(black)(180))) = 12000/color(blue)(180)`

`p = 66.bar6`

120 is `66.bar6`% or `66 2/3%` of 180.

Answer 2

`66.bar6%`

Explanation:

You take `120` over `180` and times it by `100%` to get the percentage.

`(120/180)=0.bar6`

`0.bar6 xx 100%=66.bar6%`