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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. In Number Foundations, the goal is not just to get an answer but to recognize the structure of the problem, choose a reliable strategy, and explain why the result is reasonable. The practice set now includes targeted skill work, transfer questions, and mixed review so students build fluency and retention.

What you'll learn

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.

  1. Convert 15% to 0.15.
  2. Multiply 0.15 by 80.
  3. 0.15 x 80 = 12.
  4. Connect the calculation back to Percents so the method, not just the arithmetic, is clear.

Answer: 12

Practice problems

1. Write 25% as a decimal.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Write 25% as a decimal.
  2. For decimals, keep place value aligned and use estimation to make sure the decimal point is reasonable.
  3. Divide 25 by 100.
  4. 25% = 0.25.
  5. 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
  1. Warm-up: First identify exactly what the question is asking: Write 0.4 as a percent.
  2. For percents, convert the percent to a decimal or fraction and connect it to the base amount in the problem.
  3. Multiply 0.4 by 100.
  4. 0.4 = 40%.
  5. 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
  1. Warm-up: First identify exactly what the question is asking: Which fraction equals 50%?
  2. For fractions, use equivalent forms, common denominators, or reciprocals depending on the operation being used.
  3. 50% means 50 out of 100.
  4. 50/100 simplifies to 1/2.
  5. 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
  1. Core Practice: First identify exactly what the question is asking: Find 10% of 90.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 10% is 0.10.
  4. 0.10 x 90 = 9.
  5. 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
  1. Core Practice: First identify exactly what the question is asking: Find 20% of 45.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 20% is 0.20.
  4. 0.20 x 45 = 9.
  5. 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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