Adding and subtracting decimals

The golden rule: line up the decimal points

When adding or subtracting decimals, line up the decimal points so that each place value is in its own column: tenths under tenths, hundredths under hundredths.

Adding decimals

Example: 12.4 + 3.75

  12.40
+  3.75
-------
  16.15

1. Line up the decimal points.
2. Add a placeholder zero so both have two decimal places (12.40).
3. Add from right to left, regrouping as usual: 0 + 5 = 5; 4 + 7 = 11 (write 1, carry 1); 2 + 3 + 1 = 6; 1 + 0 = 1.
4. Bring the decimal point straight down.

Sum: 16.15.

Subtracting decimals

Example: 8 − 2.65

  8.00
− 2.65
------
  5.35

Write 8 as 8.00, then subtract, borrowing as needed.

Whole numbers have a hidden decimal point

7 = 7.0 = 7.00. The decimal point is just after the ones digit.

Estimate first

If your exact answer is far from the estimate, check whether the decimal points lined up.

Money

Money calculations are decimal calculations:

• $25.00 − $13.47 = $11.53
• $4.99 + $3.50 + $0.75 = $9.24

Mental strategies

• Compensation: 6.8 + 2.9 → 6.8 + 3 − 0.1 = 9.7
• Make a whole: 0.75 + 0.25 = 1, so 3.75 + 2.25 = 6
• Count up for change: from $13.47 to $25.00: + 0.53 → $14.00, + 11 → $25.00. Change = $11.53.

Worked examples

Example 1: 5.6 + 2.48

5.60 + 2.48 = 8.08.

Example 2: 10.3 − 4.75

10.30 − 4.75 = 5.55.

Example 3: A runner’s times are 12.85 s and 13.1 s. What’s the difference?

13.10 − 12.85 = 0.25 s.

Common mistakes

• Lining up the last digits instead of the decimal points: adding 12.4 + 3.75 as if it were 124 + 375.
• Forgetting placeholder zeros in subtraction, so you can’t borrow properly.
• Leaving out the decimal point in the answer.

Try it yourself

1. 4.3 + 2.56
2. 15 − 6.42
3. 0.8 + 0.27 + 1.5
4. 20.05 − 9.8
5. You have $50. You spend $18.65 and $12.40. How much is left?

Answers: 1) 6.86 2) 8.58 3) 2.57 4) 10.25 5) $18.95

Quick recap

• Line up the decimal points.
• Add placeholder zeros so the decimal places match.
• Estimate first and check.