### The Percentage of A Number

To find the percentage of any number;

$$\frac{30}{100}.40$$

Let us simply, above and below.

- Divide the number into 100 equal parts, (this way you can find out its 1%)
- Multiply with the percentage you need (this way whatever % you need, you can calculate this)

What is 40% of 30?

into 100 equal parts. What I am looking for is the value of the yellow part, so the 40 piece

value.

Let us divide 30 into 100 equal parts then multiply with 40, to find 40 percent.

You can carry out this equation step by step or at once.

$$\frac{30}{100}.40$$

Let us simply, above and below.

$$\frac{3\not0}{1\not0\not0}.4\not0=12$$

So the result is 12 .
What is 75% of 120 ?

$$\frac{120}{100}.75=90$$

$$\frac{120}{100}.75=90$$

The result is 90.

If you have trouble with simplifying please look at the topic of simplifying.

You can do the same calculations on a calculator (first

dividing by 100 then by the percentage you want), but

this is not the point; I am going to show you how to find

the percentage with one calculation.

$$\frac{80}{100}.0,5$$

What confuses us here is that if 0.5 was 5, or 2 or 3 – a whole number, it would be a lot simpler to calculate. Can we not find another solution to 0.5?

Let’s remember expanding;

If you expand the number of a division, the result won’t be different.

$$\frac{12}{3}.\frac{10}{10}=\frac{120}{30}=4$$

Let us calculate the same problem through a different method.

Remember our goal is to write the decimal as a whole number.

"We can write the decimal as a fraction."

Instead of \( \displaystyle \frac{80}{100}.0,5 \) we can write , \( \displaystyle \frac{80}{100}.\frac{5}{10} \)

Now we simply above and below…

$$ \frac{80}{100}.\frac{5}{10}=0,4$$

dividing by 100 then by the percentage you want), but

this is not the point; I am going to show you how to find

the percentage with one calculation.

**“You can convert the wanted percentage into a decimal number and then multiply”**

**What is 25% of 180?**

$$\frac{180}{100}.25=180.\frac{25}{100}=180.0,25=45$$

I moved the 100 further on a little . We have written 25% as a decimal number.
I hope you have understood with the above examples why we have converted the percentage into decimals.

## Some decimal numbers of percentages :

$$1\%=\frac{1}{100}=0,01$$

$$120\%=\frac{120}{100}=1,20$$

$$200\%=\frac{200}{100}=2$$

$$466\%=\frac{466}{100}=4,66$$

$$118\%=\frac{118}{100}=1,18$$

$$3\%=\frac{3}{100}=0,03$$

$$30\%=\frac{30}{100}=0,30$$

$$120\%=\frac{120}{100}=1,20$$

$$200\%=\frac{200}{100}=2$$

$$466\%=\frac{466}{100}=4,66$$

$$118\%=\frac{118}{100}=1,18$$

$$3\%=\frac{3}{100}=0,03$$

$$30\%=\frac{30}{100}=0,30$$

## The explanation of percentages in written form

Practically, knowing some of the meaning of some percentages will help you in your daily life.

\( \displaystyle 1\% \) 1 percent of a number, divide the number into 100 equal parts .

\( \displaystyle 10\% \) 10 percent of a number , divide the number into 10 parts . \( \displaystyle \frac{10}{100}=\frac{1}{10} \)

\( \displaystyle 20\% \) 20 percent of a number ,divide the number into 5 parts . \( \displaystyle \frac{20}{100}=\frac{1}{5}\)

\( \displaystyle 25\% \) 25 percent of a number , divide the number into 4 parts . \( \displaystyle \frac{25}{100}=\frac{1}{4} \)

\( \displaystyle 50\% \) half of a number . \( \displaystyle \frac{50}{100}=\frac{1}{2} \)

\( \displaystyle 75\% \) 75 percent of a number , divide by 4 and multiply by 3 . \( \displaystyle \frac{75}{100}=\frac{3}{4} \)

\( \displaystyle 100\% \) The complete number as a whole . \( \displaystyle \frac{100}{100}=\frac{1}{1}=1\)

\( \displaystyle 200\% \) Twice the number . \( \displaystyle \frac{200}{100}=\frac{2}{1}=2 \)

\( \displaystyle 300\% \) Three times the number . \( \displaystyle \frac{300}{100}=\frac{3}{1}=3 \)

\( \displaystyle 400\% \) Four times the number . \( \displaystyle \frac{400}{100}=\frac{4}{1}=4 \)

\( \displaystyle 500\% \) Five times the number . \( \displaystyle \frac{500}{100}=\frac{5}{1}=5 \)

exct..

## How to calculate the percentage of a number through guessing

Through using the percentages you know about, we can try and calculate percentages

we don’t know or harder percentages by using the help of simple percentages.

Let’s calculate 30% of 640

- If 50% of a number is wanted, this means the half of a number. 30% of a number must be a smaller number than half of the number; so it must be smaller than 320.
- 30% is roughly \( \displaystyle \frac{1}{3} \) of a number . if we round 640 to 600 , \( \displaystyle \frac{1}{3} \) of 600 is 200 . So the number is roughly 200 – it could be slightly larger or slightly less.

Let us find the result;

Let us first find 10%, first finding 10% is a lot easier than finding 30% because 10% of a number is \( \displaystyle \frac{1}{10} \) so if we divide a number by 10, we find \( \displaystyle \frac{1}{10} \) of it .

\( \displaystyle 10\% \) of 640 \( \displaystyle >> \) 64

$$10\%+10\%+10\%=30\%$$

$$64+64+64=192$$

## Calculating Decimal Percentages

There is no logical difference between calculating a whole number percentage and a

decimal percentage. For example, you calculate 0.2% or 0.5% in the same way as 20%.

Let us calculate 0.5% of 80.decimal percentage. For example, you calculate 0.2% or 0.5% in the same way as 20%.

**1. Method; through calculating percentages .**$$\frac{80}{100}.0,5$$

What confuses us here is that if 0.5 was 5, or 2 or 3 – a whole number, it would be a lot simpler to calculate. Can we not find another solution to 0.5?

Let’s remember expanding;

If you expand the number of a division, the result won’t be different.

Let’s expand the number that is being divided and being used for division

too. For this equation I have chosen 10, you can use whatever number you

would like.

$$\frac{12}{3}=4$$$$\frac{12}{3}.\frac{10}{10}=\frac{120}{30}=4$$

As you can see both results of the division are the same.

Turn back to our problem ;

$$\frac{80}{100}.0,5.\frac{2}{2}=\frac{80}{100}.\frac{1}{2}=0,4$$

(Fraction expanded by 2 , numerator multiplied by 2 , 2.0,5=1)

Remember our goal is to write the decimal as a whole number.

"We can write the decimal as a fraction."

Instead of \( \displaystyle \frac{80}{100}.0,5 \) we can write , \( \displaystyle \frac{80}{100}.\frac{5}{10} \)

Now we simply above and below…

$$ \frac{80}{100}.\frac{5}{10}=0,4$$

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