Math Basics: Percentages

Percentages show up in test scores, shopping discounts, and statistics. Here is how they work.

What Is a Percentage?

The word "percent" comes from the Latin phrase meaning "per hundred." A percentage is simply a fraction with 100 as the denominator.

So 40% means 40 out of 100. It is the same as the fraction 40/100, which simplifies to 2/5.

  Percent means "out of 100"

  40% = 40/100 = 0.40

  [ 0% |---------40%----------| 100% ]
        |-------- 2/5 ---------|

Converting Between Percents, Fractions, and Decimals

Fraction Decimal Percent
1/20.550%
1/40.2525%
3/40.7575%
1/50.220%
1/100.110%
1/30.333...33.3%

Fraction to Percent

Divide the numerator by the denominator, then multiply by 100.

Example: Convert 3/8 to a percent

3 / 8 = 0.375

0.375 x 100 = 37.5%

Percent to Decimal

Divide by 100 (or move the decimal point two places left).

Example: 65% as a decimal

65 / 100 = 0.65

Finding a Percentage of a Number

This is the most common percentage calculation. The formula is:

  Percent x Whole = Part

  (Percent / 100) x Whole = Part

Example: What is 30% of 200?

(30 / 100) x 200 = 0.30 x 200 = 60

So 30% of 200 is 60.

Example: What is 15% of 80?

0.15 x 80 = 12

15% of 80 is 12.

Quick Shortcut To find 10% of any number, just move the decimal one place left. 10% of 350 = 35. Then you can build from there: 20% = double it = 70. 5% = half of 10% = 17.5.

Finding What Percent One Number Is of Another

Use this when you know the part and the whole, and want to find the percentage.

  Percent = (Part / Whole) x 100

Example: You scored 18 out of 25 on a quiz. What percent is that?

(18 / 25) x 100 = 0.72 x 100 = 72%

Your score is 72%.

Percent Increase and Decrease

This tells you how much something grew or shrank, expressed as a percentage of the original value.

  Percent Change = ((New - Old) / Old) x 100

  Positive result = increase
  Negative result = decrease

Example: A jacket costs $80 and goes up to $100. What is the percent increase?

((100 - 80) / 80) x 100 = (20 / 80) x 100 = 25%

The price increased by 25%.

Example: A store drops a price from $50 to $35. What is the percent decrease?

((35 - 50) / 50) x 100 = (-15 / 50) x 100 = -30%

The price decreased by 30%.

Calculating Discounts

A discount is a percentage removed from the original price.

  Discount Amount = (Discount % / 100) x Original Price
  Sale Price = Original Price - Discount Amount

Example: 25% off a $60 item

Discount: 0.25 x 60 = $15

Sale price: $60 - $15 = $45

Or faster: $60 x 0.75 = $45 (you pay 75%, not 100%)

Percentages in Real Life

Summary

Frequently Asked Questions

What does percent actually mean?
Percent means "per hundred." So 45% is just another way of saying 45 out of every 100. Think of it as a standardized way to compare parts to a whole, always using 100 as the reference point.
How do I quickly find 10% of a number in my head?
Move the decimal point one place to the left. So 10% of 340 is 34. 10% of 85 is 8.5. Once you have 10%, you can easily find 20% (double it), 5% (halve it), or 15% (add 10% and 5% together).
What is the difference between percent increase and percent of a number?
Finding a percent of a number tells you a piece of a whole - like finding 30% of 200. Percent increase or decrease compares two different values and tells you how much one changed relative to the other.
Can a percentage be over 100?
Yes. 150% means one and a half times something. If you earn 120% of your original salary, you earn more than you did before. Percentages above 100% just mean more than the original whole amount.

Quick Quiz

Check your understanding. Click an answer to see if you got it right.

← FractionsDecimals →