# 90% of 95.6 is what?

Apr 27, 2017

$= 86.04$

#### Explanation:

$95.6 \times 0.9$

$= 86.04$

Apr 27, 2017

86.04

#### Explanation:

$\textcolor{b l u e}{\text{Preamble about percentages}}$

Basically percentage is just a fraction. It is a special one in that the bottom number (denominator) is fixed at 100.

The symbol % is a sort of unit of measurement but one that is worth $\frac{1}{100}$

So as an example: 20% " "->" "20xx%" "->" "20xx1/100" "->" "20/100
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$\textcolor{b l u e}{\text{Answering your question}}$

In mathematics the word 'of' in 90% of 95.6 is the same as multiply. So we have:

90%" of "95.6" " ->" "90%xx95.6

But 90% is the same as $\frac{90}{100}$ so we have:

$\frac{90}{100} \times 95.6$

" "color(green)(ul(bar(|color(white)(2/2)"Using a calculator I get 86.04 "|))

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$\textcolor{b l u e}{\text{Additional teaching}}$

$\textcolor{b r o w n}{\text{Suppose you do not have a calculator to hand. let me show you a}}$$\textcolor{b r o w n}{\text{sort of cheat method to make the manual calculations easier.}}$

$\textcolor{p u r p \le}{\text{Doing the preparation}}$
Once used to this you would do it in 1 line

Consider the $\frac{90}{100} \equiv \frac{90 \div 10}{100 \div 10} = \frac{9}{10} = 9 \times \frac{1}{10}$

So we can write $\frac{90}{100} \times 95.6 \text{ }$ as $\text{ } \frac{1}{10} \times 9 \times 95.6$

Do not like decimals so lets get rid of them in 95.6

$95.6 \text{ is the same as } 956 \times \frac{1}{10}$

So putting all this together we have:

$\frac{1}{10} \times 9 \times 956 \times \frac{1}{10}$

$\frac{1}{100} \times 9 \times 956$
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$\textcolor{p u r p \le}{\text{Doing the calculation}}$
$956$
$\underline{\textcolor{w h i t e}{95} 9} \leftarrow \text{ Multiply}$
$8604$

Now we deal with the $\frac{1}{100}$

$\frac{1}{100} \times 8604 = 86.04$

" "color(green)(ul(bar(|color(white)(2/2)"Calculating manually I get 86.04 "|))