Question

77 is what percent of 192?

Answer 1

Approximately 40%

Explanation:

`77/192 xx 100`

77 multiplied by 192 (total number) and then multiplied by 100 to get a percentage!

Answer 2

40.104% to 3 decimal place

Explanation:

From the formula of percentage:
`"Part"/"Whole"xx100=%`

just substitute

`77/192xx100 = 40.104%`

77 is 40.104% of 192

Answer 3

A slightly different approach and teaching where things come from.

`40.105%` rounded to 3 decimal places

Explanation:

Using ratio

This where the shortcut of divide by the denominator and multiply by 100 comes from.

As a fraction of the whole we have: `77/192`

Let the unknown value be `x`

The objective is to end up with `x/100`

Treat `77/192` as a ratio. To maintain the proportionality, for multiply and divide, what we do to the bottom we also do to the top.

To change denominator of 192 into 100 we use `192xx100/192`

Multiply top and bottom by `100/192` giving:

`(color(red)(77xx100/192))/(192xx100/192) = (40.104166......)/100`

`ubrace((40.104166......)) color(white)("d") ubrace(xx1/100)`
`color(white)("ddddd") darr color(white)("dddddddd")darr`
`color(white)("ddd")40.105color(white)("ddddddd")%`

`40.105%` rounded to 3 decimal places
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("The shortcut")`

`color(red)(77xx100/192 color(white)("dd")->color(white)("dd") 77/192xx100)larr" This is the "x" from "x/100`

As the `xx1/100` bit is understood to exist they put the % on the end to represent it.