Adding and Subtracting Decimals

🧱 See It

Every digit has to stay in its own place-value house — ones under ones, tenths under tenths, hundredths under hundredths. If the points don't line up in a column, the digits end up in the wrong houses and the answer comes out wrong, even though the arithmetic itself is simple.

✏️ Draw It

To add 3.45 + 2.7, stack them so the decimal points line up in one column. Pad the shorter number with a trailing zero so both have the same number of decimal places:

Ones	.	Tenths	Hundredths
3	.	4	5
2	.	7	0

The grey 0 isn't extra value — it just fills the hundredths house so both numbers line up column by column.

🔢 Write It

Once the columns line up, add (or subtract) exactly like whole numbers, then drop the decimal point straight down into the answer:

3.45 + 2.70 = 6.15

Line up the points FIRST. Calculate SECOND. Never the other way around.

💡 Worked Examples

Example 1 — Addition: 5.6 + 3.25

Pad to match decimal places: 5.60 + 3.25
Add column by column: ones 5+3=8, tenths 6+2=8, hundredths 0+5=5
Answer: 8.85

Example 2 — Subtraction: 7.2 − 4.85

Pad to match decimal places: 7.20 − 4.85
Hundredths: 0 − 5 needs borrowing from the tenths column — borrow, making it 10 − 5 = 5
Tenths (after lending 1): 1 − 8 needs borrowing from the ones column — borrow, making it 11 − 8 = 3
Ones (after lending 1): 6 − 4 = 2
Answer: 2.35

🧠 Quick Reference

1. Line up the decimal points in a column. 2. Pad with trailing zeros so both numbers have the same number of decimal places. 3. Add or subtract like whole numbers. 4. Drop the decimal point straight down into the answer.