Percent

Calculating with Percent is not difficult.

First you need to understand what Percent is. Percent comes from Latin (pro cent) and means "per hundred".

Percent is the same as hundred parts.

$$ \large 1\% = \frac{1}{100} = 0.01 $$

Other examples:

$$ \large 17\% = \frac{17}{100} = 0.17 $$

$$ \large 81\% = \frac{81}{100} = 0.81 $$

$$ \large 127\% = \frac{127}{100} = 1.27 $$

If Percent is the same as hundred parts, it means that 100% is the whole.

100% of 234 equals 234 – the whole.

50% equals half: 117.

That is quite easy.

But what if it is 27% of 234?

When you need to find a percent share of a number, first find 1% by dividing by 100. Then multiply by 27:

$$ \large \frac{27 \cdot 234}{100}=63.18 $$

You can also choose to multiply by 27 first and then divide by one hundred. It gives the same result. A good rule of thumb is:

First find 1 percent and multiply by the number of percents.

The same method can be used to find any percent share of a number.

Sometimes you need to find how much a number increases if it becomes 10% larger, or how much it decreases if it becomes 15% smaller.

You might be told that you will get 10% more pocket money – but how much is that? Let’s say you already get 25 euros in pocket money.

First find how much 10% of 25 euros is:

$$ \large \frac{10 \cdot 25}{100}=2.5\ euros $$

So you get 2.5 euros more. Now just add the numbers to find the new total:

$$ \large 25 + 2.5 = 27.5\ euros $$

So you take the whole and add a percent share of the whole on top: $25 + 10\% = 25 + 2.5$. There is actually an easy way to do it:

$$ \large 25 \cdot 1.10 = 27.5\ euros $$

When you multiply 25 by 1.00 you get 25 (the whole).

When you multiply 25 by the decimal value of the percent $10\% = 0.10$ you get 2.5.

Therefore you can add the two decimals $1.00 + 0.10 = 1.10$ and multiply by that.

But what if you need to subtract 10%? Then it is the same method, you just subtract the decimal value of the percent instead of adding it.

$$ \large 1.00 - 0.10 = 0.90 $$

The calculation looks like this:

$$ \large 25 \cdot 0.90 = 22.5 $$