The word "percent" comes from the Latin phrase per centum, which means "per hundred." A percentage is just a special kind of fraction where the denominator is always 100. It's a way to talk about parts of a whole in a standardized way.

Because percents, fractions, and decimals are all ways of representing parts of a whole, we can easily switch between them. This is useful because sometimes it's easier to calculate with a decimal, and other times a fraction is more intuitive.

Let's look at how to move between these three formats.

Converting between percents and fractions is also straightforward.

Percent to Fraction: Write the percent value over 100, then simplify the fraction if possible. For example, $60\%$ becomes $\frac{60}{100}$. We can divide both the top and bottom by their greatest common divisor, which is 20. This simplifies to $\frac{3}{5}$.

Fraction to Percent: The goal here is to get a denominator of 100. You can do this by first converting the fraction to a decimal. Simply divide the numerator by the denominator. Then, convert that decimal to a percent. For example, to convert $\frac{1}{4}$, you first calculate $1 \div 4 = 0.25$. Then you convert $0.25$ to a percent, which is $25\%$.

A common task is finding a certain percentage of a number. In math, the word "of" almost always means "multiply." To find the percent of a number, you first convert the percentage into a decimal or a fraction, and then multiply it by the number.

Let's find 40% of 200.

Both methods give the same answer, so you can use whichever one you find easier. The general rule can be written like this:

Now, let's test your understanding.

Mastering these basics is the key. Once you're comfortable converting between these forms and finding a percent of a number, you're ready to use percentages in more complex situations.