# 77 is what percent of 192?

May 17, 2018

Approximately 40%

#### Explanation:

$\frac{77}{192} \times 100$

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

May 17, 2018

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

May 17, 2018

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: $\frac{77}{192}$

Let the unknown value be $x$

The objective is to end up with $\frac{x}{100}$

Treat $\frac{77}{192}$ 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 $192 \times \frac{100}{192}$

Multiply top and bottom by $\frac{100}{192}$ giving:

$\frac{\textcolor{red}{77 \times \frac{100}{192}}}{192 \times \frac{100}{192}} = \frac{40.104166 \ldots \ldots}{100}$

$\underbrace{\left(40.104166 \ldots \ldots\right)} \textcolor{w h i t e}{\text{d}} \underbrace{\times \frac{1}{100}}$
$\textcolor{w h i t e}{\text{ddddd") darr color(white)("dddddddd}} \downarrow$
color(white)("ddd")40.105color(white)("ddddddd")%

40.105% rounded to 3 decimal places
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{The shortcut}}$

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

As the $\times \frac{1}{100}$ bit is understood to exist they put the % on the end to represent it.