Adding & Subtracting Decimals

The one rule that makes decimal addition and subtraction reliable — line up the decimal points — plus filling gaps with zeros and money problems, with worked examples, a worksheet with memo and a quiz.

Adding and subtracting decimals is exactly the same as with whole numbers, with one extra rule that fixes almost every mistake learners make.

1The golden rule: line up the points

Write the numbers under each other so the decimal points line up vertically, then add or subtract as normal.

Worked ExampleCalculate: 12,7 + 3,45

1
Line up the points and fill the gap with a zero: 12,70 + 3,45.
12,7 and 12,70 are the same value — the zero just keeps the columns tidy.
2
Add the hundredths: 0 + 5 = 5. Add the tenths: 7 + 4 = 11, write 1 carry 1.
Work right to left, exactly like whole numbers.
3
Add the units with the carry: 2 + 3 + 1 = 6, then the tens: 1.
4
Answer: 16,15.
The point in the answer sits under the points above it.

Worked ExampleCalculate: 8,3 − 2,75

1
Line up and fill the gap: 8,30 − 2,75.
Writing 8,3 as 8,30 makes the borrowing clear.
2
Hundredths: 0 − 5 needs borrowing → 10 − 5 = 5.
Borrow one hundredth from the tenths column.
3
Tenths: 2 − 7 needs borrowing → 12 − 7 = 5.
4
Units: 7 − 2 = 5. Answer: 5,55.

⚠️

Never line the numbers up on the right-hand edge. Writing 12,7 above 3,45 with the 7 above the 5 gives a badly wrong answer. Line up the points, not the last digits.

2Estimating to check your answer

Before (or after) a decimal calculation, round each number to the nearest whole number and do it in your head. If your exact answer is far from the estimate, you have made a slip.

Worked ExampleEstimate to check: 12,7 + 3,45 = 16,15

1
Round: 12,7 ≈ 13 and 3,45 ≈ 3.
Round to the nearest whole number.
2
13 + 3 = 16.
3
16,15 is very close to 16, so the answer is sensible.
This catches misplaced decimal points instantly.

3Money problems

Worked ExampleSipho buys bread for R18,50 and milk for R24,75. He pays with R50. How much change?

1
Total spent: 18,50 + 24,75 = 43,25.
Line up the points and add.
2
Change: 50,00 − 43,25.
Write R50 as 50,00 so the columns match.
3
= R6,75.
Answer in rands and cents, with the unit.

Practice exercises

Work each one out, then click to reveal the answer.

📄 Worksheet ✅ Memo 📝 Exam paper 🗝️ Marking guide

1
4,6 + 2,35
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4,60 + 2,35 = 6,95
2
13,08 + 7,9
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13,08 + 7,90 = 20,98
3
9,5 − 3,27
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9,50 − 3,27 = 6,23
4
20 − 6,45
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20,00 − 6,45 = 13,55
5
0,75 + 0,8 + 1,2
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2,75
6
Estimate 19,7 + 4,2 by rounding to whole numbers.
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20 + 4 = about 24 (exact: 23,9)
7
A plank is 2,4 m long. 0,85 m is cut off. How much is left?
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2,40 − 0,85 = 1,55 m
8
Ann buys items for R32,40 and R15,85 and pays with R100. What change does she get?
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Total 48,25; 100,00 − 48,25 = R51,75