The word "percentage" might sound complicated, but it's a simple idea we use all the time. It's just a way of talking about a part of a whole, where the whole is always split into 100 pieces. The word itself comes from the Latin phrase per centum, which means "per hundred."

Imagine a large pizza cut into 100 tiny, equal slices. If you eat one slice, you've eaten 1% of the pizza. If you eat 50 slices, you've eaten 50% of the pizza. That's all there is to it. The symbol for percent is %, which you've likely seen on sale signs or your phone battery indicator.

Percentages, fractions, and decimals are like different languages that say the same thing. They're all ways to express parts of a whole. Knowing how to translate between them is a key skill.

Let's start with fractions. To turn a fraction into a percentage, your goal is to make the denominator (the bottom number) equal to 100. For a fraction like $1/2$, you can multiply both the top and bottom by 50. This gives you an equivalent fraction:

Since the new denominator is 100, the numerator (the top number) is your percentage. So, $1/2$ is 50%.

What about converting a decimal to a percentage? This is even easier. You just multiply the decimal by 100. The quickest way to do this is to move the decimal point two places to the right and add a percent sign.

This works in reverse, too. To change a percentage to a decimal, you divide by 100, which means moving the decimal point two places to the left. So, 45% becomes 0.45.

Here are a few common conversions to see the pattern:

Now let's use this knowledge to do a basic calculation: finding a percentage of a number. This is useful for things like figuring out a tip or a discount.

In math, the word "of" almost always means "multiply." The key is to first convert the percentage into a form that's easy to multiply with, like a decimal or a fraction.

Let's say you want to find 20% of $80. First, convert 20% to a decimal by moving the decimal point two places to the left. 20% becomes 0.20.

Now, you just multiply.

So, 20% of $80 is $16.

Here's another one: What is 75% of 200?

You could convert 75% to the decimal 0.75. Or, you might remember from the table above that 75% is the same as the fraction $3/4$, which can be easier for mental math.

Both methods give the same answer. Using the one that feels most comfortable is always the best approach.

Time to test what you've learned.

That's the foundation of percentages. By understanding them as parts of 100, you can easily switch between fractions, decimals, and percents to solve a wide range of problems.