Understanding Percentages and How to Work with Them

Today we dive into an exciting world of numbers you have surely heard a lot about — percentages. So what are percentages? And how do we work with them?

Percentages are simply a way to express a number or ratio as a fraction from 0 to 100. The term comes from the Latin “percentum,” meaning “by the hundred.” That is why the percent symbol (%) looks the way it does — it is a stylized 100!

Percentages are convenient

Why do we use percentages? Because they are very handy. They let us compare quantities easily — whether exam scores, a discount on your favorite book, or the water content of fruit.

How exactly do we work with them? Think of percentages as a loaf of bread. You can divide that loaf into 100 equal parts. Each part is 1% (1 part out of 100) of the whole loaf. So if you ate 25 slices of that loaf, you would have eaten 25% of the bread.

How to get percentages

Converting numbers to percentages is fairly simple. Divide the value you got by the total and multiply by 100. For example, suppose you scored 18 out of 20 on a test. Divide 18 by 20 to get 0.9, then multiply by 100 — you scored 90%.

18 / 20 * 100 = 90%

The same way, we can convert percentages back into numbers. When you see a percentage, it means “out of 100.” So to turn 75% into a number, multiply it by the total and then divide by 100. If we take 75% of 20, we multiply (75 times 20) and divide by 100, which equals 15.

 75 / 100 * 20 = 15

Percentage increase and decrease

Sometimes you need to find a percentage increase or decrease. It is a bit harder, but still straightforward. To find a percentage increase, subtract the original number from the increased number, divide by the original number, then multiply the result by 100. For example, toothpaste originally cost 20 rubles and after a price rise costs 25 rubles. From the increased value (25) subtract the original (20) to get 5, divide by the original (20) to get 0.25, multiply by 100 — the paste rose by 25%.

(Increased price - Original price) / Original price * 100 = (25 - 20) / 20 * 100 = 25%

To find a percentage decrease, do the same process but with the decreased number instead of the increased one. Suppose hand cream originally cost 10 rubles, but on sale it costs 7 rubles. How many percent lower is the price?

 (Decreased price - Original price) / Original price * 100 = (7 - 10) / 7 * 100 = -30%

As you can see, the result is negative — which is natural, because percentages are measured from the original price. In most cases the minus sign is dropped and people simply say “sale price is 30% off.”

Percentages may seem tricky at first, but with regular practice you will master them quickly. Remember, math is not only about learning concepts — it is about understanding them. Next time you see the word “percent,” you will know exactly what it means and how to work with it.