Decimal Operations Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Decimal Operations.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

Adding, subtracting, multiplying, and dividing numbers that contain decimal points.

Decimal operations follow the same rules as whole numbers, but you must track the decimal point carefully—like keeping track of dollars and cents.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: For addition/subtraction, align decimal points. For multiplication, count total decimal places. For division, shift decimals to make the divisor whole.

Common stuck point: Placing the decimal in multiplication: 0.3 \times 0.4 has two decimal places total, giving 0.12, not 1.2.

Sense of Study hint: Estimate the answer with whole numbers first, then check that your decimal answer is close to that estimate.

Worked Examples

Example 1

easy
Add 12.74 + 5.6 + 0.08.

Solution

  1. 1
    Write each number so decimal points are aligned, padding with zeros as needed: 12.74, 5.60, 0.08.
  2. 2
    Add column by column from right: hundredths 4+0+8=12, write 2 carry 1; tenths 7+6+0+1=14, write 4 carry 1; ones 2+5+0+1=8; tens 1.
  3. 3
    Result: 18.42.

Answer

18.42
Aligning decimal points ensures digits with the same place value are added together. Padding shorter decimals with trailing zeros (e.g., writing 5.6 as 5.60) prevents column-alignment errors.

Example 2

medium
Multiply 0.45 \times 0.8 and explain how to place the decimal point.

Example 3

medium
Calculate 4.25 \times 3.6.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Subtract 14.5 - 6.83.

Example 2

hard
A 3-metre length of rope is cut into pieces, each 0.15 m long. How many complete pieces can be cut, and how much rope is left over?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

decimalsadditionsubtractionmultiplicationdivision