Q.A team played 40 games in a season and lost in 16 of them. What percent of games played did the team win?

Percent Calculation

You already understand percent. You just don't know you do.

Think about a test. You get 15 questions right out of 20. How well did you do? You could say "15 out of 20" — that's a fraction, $\frac{15}{20}$. But that number doesn't immediately tell you how good it is compared to, say, 7 out of 10. What you really want is a common scale: "out of 100."

Percent is exactly that. "Per cent" comes from Latin per centum — for each hundred. So 15 out of 20 means: if the test had 100 questions instead of 20, how many would you get right? You scale the fraction:

Solving: $x = \frac{15}{20} \times 100 = 75$. So you scored 75 per hundred — 75%.

That's all percent is: a fraction with denominator 100, written with a % sign.

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The Precise Definition

The $\times 100\%$ is just multiplying by 1 — because $100\% = 1$ — but it converts the decimal into the "per hundred" form.

Example: What percent is 30 of 50?

Example: What is 25% of 200?

Here the percent is given, and you want the part. "25% of 200" means $\frac{25}{100} \times 200 = 50$.

Example: 12 is 30% of what number?

Here the part and percent are given, you want the whole. $12 = \frac{30}{100} \times \text{Whole}$, so $\text{Whole} = 12 \times \frac{100}{30} = 40$.

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The Three Types of Percent Problems

Every percent problem is one of these three:

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Why It Works …