Subtracting Decimals – Align, Borrow, and Subtract
Subtracting decimals follows the same column-by-column approach as subtracting whole numbers. Line up the decimal points, borrow when needed, and keep the decimal point in the answer directly below those in the question.
The Method
1. Line up the decimal points.
2. Pad with trailing zeros if the numbers have different lengths.
3. Subtract right to left, borrowing from the next column when the top digit is smaller than the bottom digit.
4. Place the decimal point in the answer directly below.
Simple Subtraction
Tenths: 7-4=3. Ones: 8-3=5. Answer: 5.3.
Pad 1.8 as 1.80. Hundredths: 2-0=2. Tenths: 5-8 — need to borrow. Borrow from ones: 15-8=7, ones become 5. Ones: 5-1=4. Wait, we need to recalculate: 6.52 - 1.80. Tenths: 5-8 requires borrowing. Borrow 1 from ones (6 becomes 5): 15-8=7. Ones: 5-1=4. Answer: 4.72.
Subtraction with Borrowing
Pad 12.3 as 12.30. Hundredths: 0-5, borrow: 10-5=5, tenths become 2. Tenths: 2-7, borrow: 12-7=5, ones become 1. Ones: 1-4, borrow: 11-4=7, tens become 0. Tens: 0. But tens of 12 is 1: 1-0=1. Answer: 7.55.
Write 5 as 5.00. Hundredths: 0-7, borrow: 10-7=3, tenths become 9. Tenths: 9-3=6. Wait — tenths: after borrowing, we have 9. But 9-3 = 6. Ones: 5-1=4. But we borrowed from ones for tenths: 4-1=3. Answer: 3.63.
Checking by Addition
You can always check a subtraction by adding your answer back to the number you subtracted. 3.63 + 1.37 should equal 5. Let us verify: 3.63 + 1.37 = 5.00. Correct.
Real-Life Examples
- Change from £10.00 after spending £6.49: 10.00 - 6.49 = £3.51.
- Rainfall difference: 34.7 mm last month vs 29.85 mm this month. Difference = 4.85 mm.
- Temperature drop from 15.2°C to 8.75°C = 6.45°C decrease.
Key Takeaways
- Align decimal points before subtracting.
- Add trailing zeros so columns match.
- Borrow from the next column when needed, exactly as with whole numbers.
- Check your answer by adding result to the subtracted value.
Practice Questions
- 9.6 - 4.3
- 7.4 - 2.85
- 20 - 6.37
- A bag of flour weighed 2.5 kg. After baking, 0.875 kg was used. How much is left?
- A journey is 14.5 km. After travelling 8.75 km, how far remains?