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Decimal Operations

A free Pre-Algebra lesson from the “Decimals, Roots, and the Real Number System” unit, with a worked example and practice problems including step-by-step solutions.

Decimal operations use the same operation rules as whole numbers, but place value matters. For addition and subtraction, line up decimal points. For multiplication, multiply first and then place the decimal based on the total number of decimal places. For division, think about equal groups or convert to whole-number division when helpful.

What you'll learn

Why it matters: Receipts, mileage logs, paycheck calculations, and lab data all add, subtract, multiply, or divide decimals. Aligning the place values is the step that keeps each digit in the correct column.

Worked example

Problem. Compute 3.6 x 0.4.

  1. Multiply 36 x 4 to get 144.
  2. There is one decimal place in 3.6 and one in 0.4, for two decimal places total.
  3. Place the decimal two places from the right: 1.44.

Answer: 1.44

Practice problems

1. Compute 4.7 + 2.1.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute 4.7 + 2.1.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Line up the decimal points.
  4. 4.7 + 2.1 = 6.8.
  5. Check the result by substituting or estimating: the response should match 6.8 and make sense in the original problem.

Answer: 6.8

2. Compute 8.5 - 3.2.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute 8.5 - 3.2.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Line up the decimal points.
  4. 8.5 - 3.2 = 5.3.
  5. Check the result by substituting or estimating: the response should match 5.3 and make sense in the original problem.

Answer: 5.3

3. Compute 0.6 x 5.

Show solution
  1. Warm-up: First identify exactly what the question is asking: Compute 0.6 x 5.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. 6 tenths times 5 is 30 tenths.
  4. 30 tenths is 3.
  5. Check the result by substituting or estimating: the response should match 3 and make sense in the original problem.

Answer: 3

4. Compute 12.4 + 0.86.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute 12.4 + 0.86.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Write 12.4 as 12.40.
  4. 12.40 + 0.86 = 13.26.
  5. Check the result by substituting or estimating: the response should match 13.26 and make sense in the original problem.

Answer: 13.26

5. Compute 9 - 2.75.

Show solution
  1. Core Practice: First identify exactly what the question is asking: Compute 9 - 2.75.
  2. Choose the operation or relationship that matches the wording, then carry it out one clear step at a time.
  3. Write 9 as 9.00.
  4. 9.00 - 2.75 = 6.25.
  5. Check the result by substituting or estimating: the response should match 6.25 and make sense in the original problem.

Answer: 6.25

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