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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. In Decimals, Roots, and the Real Number System, 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: 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.
  4. Connect the calculation back to Decimal Operations so the method, not just the arithmetic, is clear.

Answer: 1.44

Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response). Counts include repeated prompts and variants.

Practice problems

1. Compute 4.7 + 2.1.

Show solution
  1. Line up the decimal points.
  2. 4.7 + 2.1 = 6.8.

Answer: 6.8

2. Compute 8.5 - 3.2.

Show solution
  1. Line up the decimal points.
  2. 8.5 - 3.2 = 5.3.

Answer: 5.3

3. Compute 0.6 x 5.

Show solution
  1. 6 tenths times 5 is 30 tenths.
  2. 30 tenths is 3.

Answer: 3

4. Compute 12.4 + 0.86.

Show solution
  1. Write 12.4 as 12.40.
  2. 12.40 + 0.86 = 13.26.

Answer: 13.26

5. Compute 9 - 2.75.

Show solution
  1. Write 9 as 9.00.
  2. 9.00 - 2.75 = 6.25.

Answer: 6.25

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