A percentage is just a special way of talking about a part of a whole. Imagine you have a chocolate bar with 100 small squares. If you eat 20 of them, you've eaten 20 out of 100 squares. As a percentage, we'd say you've eaten 20 percent.

The word percent literally means 'per hundred'. It comes from the Latin phrase per centum. So, whenever you see the % symbol, just think 'out of 100'.

This grid shows what 42% looks like. There are 100 squares in total, and 42 of them are shaded. It's a simple, visual way to understand what a percentage represents.

Percentages, fractions, and decimals are three different ways to talk about the same value. Being able to switch between them is a key skill. Let's start with turning a percentage into a fraction.

Because a percentage is just a number out of 100, you can write it as a fraction by putting it over a denominator of 100. For example, 60% becomes:

But we usually don't leave the fraction like that. We simplify it. This means finding the simplest possible version of the fraction by dividing the top and bottom numbers by the largest number that goes into both.

For $\frac{60}{100}$, both numbers can be divided by 20. So, we get $\frac{3}{5}$. This means 60% is the same as $\frac{3}{5}$.

To go the other way, from a fraction to a percentage, you do the reverse. If you can make the denominator 100, the numerator is your percentage. For a fraction like $\frac{2}{5}$, you can multiply the top and bottom by 20 to get $\frac{40}{100}$, which is 40%.

If the denominator doesn't easily go into 100, just divide the numerator by the denominator and multiply the result by 100. For $\frac{3}{8}$:

Converting between percentages and decimals is even more straightforward. To change a percentage to a decimal, you just divide by 100. For example, 58% becomes 0.58.

A quick way to do this is to move the decimal point two places to the left. For a whole number like 58, the decimal point is hiding at the end (58.0). Move it two spots left, and you get 0.58.

To turn a decimal into a percentage, you do the opposite: multiply by 100. This is the same as moving the decimal point two places to the right.

0.72 becomes 72% 0.05 becomes 5% 1.5 becomes 150%

Some conversions are so common it's worth memorising them. This helps you perform quick calculations in your head and better understand data you see every day.

Knowing that 25% is the same as $\frac{1}{4}$ makes finding 25% of a number much easier. You can just divide the number by 4. This is a handy shortcut we'll explore more later on.

Ready to test your skills? Let's see how well you can switch between these different forms.

Mastering these conversions is the first step. Once you're comfortable moving between percentages, fractions, and decimals, you'll be ready to tackle all kinds of percentage problems.