# Math: How Do I Work Out Percentages?

## Simple Sums

There all sorts of great math self-help books out there- some people just have a knack for explaining numbers in a way that's easy to understand. When it comes to calculating percentages, though, it really couldn't be easier to get your head around.

The key to understanding percentages is to remind yourself that percentages are just a shorthand way of describing a number as a fraction, as a one-hundredth of another number. If you want to know how to calculate percentages, think to yourself "I want to know how many hundredths of this number over there my number right here is equal to." Put algebraically, when calculating percentages, you want to know how many one hundredths of X fit into Y, or Y / (X/100).

Does that sound simple? It really is. Calculating percentages is really easy. Let's try an example. Say you want to know what percentage of a bag of marbles are red. There are 75 marbles, and 33 of them are red. So... you want to know how many one-hundredths of 75 fit into 33. First of all, divide 75 by 100. To do this, move the decimal point two places to the left. This gives you 0.75. Next, see how many lots of 0.75 fit into 33, so 33/0.75 =44. Therefore, 44% of the marbles are red. See? That's how to calculate percentages.

## Calculating Percentage Change

This is where it gets a little bit more complicated. At least it seems to, but really calculating percentage change is very similar to calculating percentages. You might struggle to understand which number to divide by 100 and which needs to be divided by the number of hundredths. But if you think it through slowly, it's not so hard. To understand percentages you want to know a number that portrays the change as a proportion of the original value. Looking algebraically again, you want to know Y-X / (X/100). In this example, X is the original value, and Y is the new value, so Y-X gives you the difference. To calculate the percentage change, you just divide the difference by one hundredth of the original value (X).

To give an example, imagine you want to calculate the percentage change in a magazine's circulation over the last six months. The circulation today is 54,000. Six months ago, it was 29,000. So to calculate the percentage change, first work out the difference: 54,000 - 29,000 = 25,000. Next you want to know what 25,000 is as a proportion of the initial value, so 25,000 / (29,000/100). Move the decimal two places to the left on the 29,000, so now you want to know how many times 290 fits into 25,000. 25,000 / 290 = 86.2. Therefore, the magazine grew its circulation by 86.2% over six months.

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