Percents
A free Pre-Algebra lesson from the “Number Foundations” unit, with a worked example and practice problems including step-by-step solutions.
Percent means per 100. To convert a percent to a decimal, divide by 100. To find a percent of a number, multiply the decimal form of the percent by the number.
What you'll learn
- Convert between percents, decimals, and fractions
- Find percent of a number
- Solve discount and increase problems
Why it matters: Sales tax, restaurant tips, discount tags, grade percentages, and loan interest all use percents. A percent is a ratio out of 100, which is why a bar or grid model makes the size easy to see.
Worked example
Problem. Find 15% of 80.
- Convert 15% to 0.15.
- Multiply 0.15 by 80.
- 0.15 x 80 = 12.
Answer: 12
Practice problems
1. Write 25% as a decimal.
Show solution
- Warm-up: First identify exactly what the question is asking: Write 25% as a decimal.
- For decimals, keep place value aligned and use estimation to make sure the decimal point is reasonable.
- Divide 25 by 100.
- 25% = 0.25.
- Check the result by substituting or estimating: the response should match 0.25 and make sense in the original problem.
Answer: 0.25
2. Write 0.4 as a percent.
Show solution
- Warm-up: First identify exactly what the question is asking: Write 0.4 as a percent.
- For percents, convert the percent to a decimal or fraction and connect it to the base amount in the problem.
- Multiply 0.4 by 100.
- 0.4 = 40%.
- Check the result by substituting or estimating: the response should match 40 and make sense in the original problem.
Answer: 40
3. Which fraction equals 50%?
Choices: 1/2 · 1/4 · 3/4 · 1/5
Show solution
- Warm-up: First identify exactly what the question is asking: Which fraction equals 50%?
- For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
- 50% means 50 out of 100.
- 50/100 simplifies to 1/2.
- Verify the selected choice by checking that it satisfies the original prompt and that the other choices fail the same test.
Answer: 1/2
4. Find 10% of 90.
Show solution
- Core Practice: First identify exactly what the question is asking: Find 10% of 90.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 10% is 0.10.
- 0.10 x 90 = 9.
- Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.
Answer: 9
5. Find 20% of 45.
Show solution
- Core Practice: First identify exactly what the question is asking: Find 20% of 45.
- Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
- 20% is 0.20.
- 0.20 x 45 = 9.
- Check the result by substituting or estimating: the response should match 9 and make sense in the original problem.
Answer: 9
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