Percentages
A percent is a fraction out of 100.
About this topic
A percentage is a fraction out of 100, written with the % sign. 45% means 45/100 or 0.45. Percentages make it easy to compare amounts of different sizes, such as exam scores, discounts, interest rates and statistics reported in the news.
To find a percentage of a quantity, convert to a decimal and multiply: 20% of 150 is 0.2 × 150 = 30. To find what percent one number is of another, divide and multiply by 100. If you scored 42 out of 60, then 42/60 = 0.7, which is 70%. Percentages can exceed 100% when something has more than doubled. A quick mental trick is that 10% is one tenth, so 10% of 80 is 8 and 5% is half of that, 4.
Picture a jacket priced at 80 dollars with a 25% discount. The discount is 0.25 × 80 = 20 dollars, so you pay 60. Or think of it as paying 75%, and 0.75 × 80 = 60. Sales tax, tips, interest and survey results all work this way.
A common error is adding percentages of different wholes: 50% of a small class and 50% of a large class are not the same number of students. Another is mixing up percentage points with percent: a rise from 10% to 15% is 5 percentage points but a 50% increase.
Key ideas
- Percent means per hundred
- Convert by dividing by 100
- Part = percent × whole
Quick check
Use cases: where Percentages helps
- Homework: review the key idea behind Percentages before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Percentages without notes.
- Visual learning: play with the interactive lab to see how Percentages changes when you adjust its inputs.
- Teaching a friend: explain Percentages in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Percentages?
A percent is a fraction out of 100.
What will I learn in Percentages?
Percent means per hundred. Convert by dividing by 100. Part = percent × whole.
Is Percentages part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Percentages lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Percentages?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.