Question

32 is 16% of what number?

Answer 1

32 is 16% of 200

Explanation:

32 is 16% of What Number

"is" means equal
"of" means multiply

`32 = 16% (n)`

`32 = .16n`

`(32)/(.16) = (cancel(.16)n)/cancel(.16)`

`200 = n`

Answer 2

16% of 200 is 32

Explanation:

Let the unknown value be `x`

Then 16% of `x=32`
`color(white)(.)`

Write as
`color(brown)(" "16/100 x=32)`
`color(white)(.)`

Multiply both sides by `color(blue)(100/16)` turning `16/100` into 1:

`color(brown)(" "color(blue)(100/16xx)16/100xx x= 32color(blue)(xx100/16))`

`color(white)(.)`

But `100/16xx16/100" is the same as "100/100xx16/16 = 1xx1 = 1`

`color(white)(.)`

`color(brown)(" "1xx x=32xx100/16)`

`color(brown)(" "x=cancel(32)^2xx100/(cancel(16)^1))`

`color(green)(" "x=200)`