Adding and subtracting decimals
Use place value to align quantities and explain regrouping.
Before you begin
- Whole-number addition and subtraction
- Tenths, hundredths and thousandths
Align equal place values
A decimal point separates whole units from fractional parts. To add or subtract, put tenths under tenths and hundredths under hundredths by aligning the decimal points. You may append zeros to the right without changing a decimal's value: 4.7 = 4.70. Lining up the final digits instead would combine different-sized units, like adding metres directly to centimetres.
Regroup and estimate
When a column has too little to subtract, exchange one unit from the next place for ten units in the current place. The value stays the same. When adding, ten hundredths become one tenth. Estimate first using rounded amounts, then check the exact result against your estimate. For money or measurement, include the unit and round only when the question requires it.
Worked example
Calculate 12.4 − 3.785.
Show the worked solution
- Write 12.400 above 3.785 with the decimal points aligned.
- Regroup across the decimal places and subtract to obtain 8.615.
- Check by addition: 8.615 + 3.785 = 12.400; the result is also close to 12 − 4 = 8.
8.615.
Try it yourself
What is 0.8 + 0.35?
Common mistakes
- Align decimal points, not the last digits.
- Zeros added on the right of a decimal preserve its value.
What can you explain now?
A jug contains 2.05 L. You add 0.875 L, then pour out 1.2 L. What remains?
Compare with the explanation
1.725 L.
First add 2.050 + 0.875 = 2.925. Subtract 1.200 to get 1.725. All amounts are measured in litres.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗