Skill: decimals-add-subtract

Add & Subtract Decimals

Add and subtract decimals by lining up the decimal points, estimate first, and always sanity-check the answer against the estimate.

1 Line up the points

The one rule of decimal arithmetic: line up the decimal points. Everything else works like whole numbers.

Why lining up matters

2.45 + 1.2: the points line up, so tenths add to tenths and hundredths to hundredths. If the points drift, you are adding tenths to hundredths — nonsense.

2.45
+ 1.20
3.65

Pad with zeros

Write 1.2 as 1.20 so every column has a digit. Trailing zeros change nothing about the value.

Estimate first

4.87 + 2.95 ≈ 5 + 3 = 8. The real answer 7.82 is close to 8 — but 78.2 or 0.782 would scream “point in the wrong place.”

Subtraction needs the same lineup

5.2 − 1.35: write 5.20 − 1.35, line up the points, borrow like whole numbers → 3.85.

2 See it: 2.45 + 1.20 in columns

The gold rings mark the lined-up decimal points.

Pad 1.2 as 1.20, line up the points, add each column.

3 Worked examples

Line up, pad, compute, estimate-check.

Example 1 Add: 2.45 + 1.2

Thinking: estimate first: 2.45 + 1.2 ≈ 2.5 + 1 = 3.5.
Line up the points; pad 1.2 as 1.20.
Add columns: 5 + 0 = 5 hundredths; 4 + 2 = 6 tenths; 2 + 1 = 3 ones.
Answer 3.65 — close to the estimate. Correct.

2.45 + 1.2 = 3.65

Example 2 Subtract: 5.2 − 1.35

Thinking: estimate: 5.2 − 1.35 ≈ 5 − 1.5 = 3.5.
Line up the points; pad 5.2 as 5.20.
Subtract columns with borrowing: 20 − 35 needs a borrow → 120 − 35 = 85 hundredths…
Carefully: 5.20 − 1.35 = 3.85. Close to the estimate. Correct.

5.2 − 1.35 = 3.85

Example 3 Tenths that make a whole: 0.3 + 0.7

Thinking: 3 tenths + 7 tenths = 10 tenths.
10 tenths = 1 whole.
Answer 1.

0.3 + 0.7 = 1

Example 4 Estimate: 4.87 + 2.95

Thinking: round each to the nearest whole: 4.87 → 5, 2.95 → 3.
5 + 3 = 8.
(The exact answer is 7.82 — the estimate 8 is close.)

Estimate: 8

4 Common mistakes

Two traps catch almost everyone.

Mistake 1: lining up the right edge instead of the points

Wrong

2.45 + 1.2 lined up at the right:
2.45 + 12.0 = 14.45 — the 2 tenths became 2 tens.

Right

Line up the decimal points: 2.45 + 1.20 = 3.65.

Fix: the points must form a vertical line before you add a single digit.

Mistake 2: skipping the estimate

Wrong

Computing 48.7 + 29.5 = 7.82 and moving on, never noticing the point slipped.

Right

Estimate first: 49 + 30 ≈ 79. 7.82 is nowhere near 79 — recheck the point.

Fix: an estimate takes five seconds and catches every slipped point.

5 Key vocabulary

Line up: Aligning the decimal points vertically before adding or subtracting.
Pad: Adding trailing zeros (1.2 → 1.20) so columns match.
Estimate: A quick rounded answer used to check reasonableness.
Borrow/regroup: Trading 1 tenth for 10 hundredths (and so on) during subtraction.