Percentages as parts per hundred
Connect fractions, decimals and percentages to find a part of a whole.
Before you begin
- Equivalent fractions
- Decimal multiplication
Identify the whole before calculating
Percent means per hundred. A percentage describes a relative amount, so 20% can represent different quantities when the wholes differ. Twenty percent of 50 is 10, while twenty percent of 200 is 40. State the whole and its units first. Convert the percentage into a fraction or decimal: 20% = 20/100 = 0.20.
Choose a useful calculation route
Multiply the whole by the decimal form of the percentage, or build the result from convenient parts. Ten percent is one tenth; five percent is half of ten percent; one percent is one hundredth. These mental strategies give an independent check. A percentage above 100% represents more than the original whole and is possible in appropriate contexts.
Worked example
A library has 240 books in a collection. 35% are nonfiction. How many are nonfiction?
Show the worked solution
- The whole is 240 books and 35% = 0.35.
- Calculate 0.35 × 240 = 84.
- Check mentally: 30% is 72 and 5% is 12; their sum is 84.
84 books.
Try it yourself
What percentage is 3/8?
Common mistakes
- The percent sign includes division by 100.
- Always identify which amount represents 100%.
What can you explain now?
Find 125% of 64 kg and explain why the result is larger than 64 kg.
Compare with the explanation
80 kg.
125% = 1.25. The whole 64 kg plus one quarter, 16 kg, is 80 kg. A percentage above 100% exceeds the whole.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗