You add and subtract whole numbers with the standard algorithm: ones under ones, tens under tens. Decimals work the same way once the places line up, and you can read them to thousandths.
Key idea
Line up the decimal points, so tenths are under tenths and hundredths under hundredths. Fill empty places with zeros. Then add or subtract as with whole numbers, and keep the point in line.
Why it works
You can only add like things: tenths to tenths, hundredths to hundredths, just as you add ones to ones. Lining up the points lines up the places. Writing $3.5$ as $3.50$ changes nothing about its value, but it shows that $3.5$ has 0 hundredths.
| ones | tenths | hundredths | |
|---|---|---|---|
| 3 | 5 | 0 | |
| + | 1 | 2 | 5 |
| = | 4 | 7 | 5 |
Worked examples
Worked example: Different numbers of places
Find $3.5 + 1.25$.
- Write $3.5$ as $3.50$.
- Hundredths: $0 + 5 = 5$. Tenths: $5 + 2 = 7$. Ones: $3 + 1 = 4$.
- Estimate: $3.5 + 1 = 4.5$. Close.
Answer: $4.75$
Worked example: Subtract from a whole number
Find $6 - 2.37$.
- Write $6$ as $6.00$.
- Regroup: $6.00$ is 5 ones, 9 tenths, 10 hundredths.
- $10 - 7 = 3$ hundredths, $9 - 3 = 6$ tenths, $5 - 2 = 3$ ones.
- Check by adding: $3.63 + 2.37 = 6.00$.
Answer: $3.63$
Common mistake
Lining up the last digits, as with whole numbers, so $3.5 + 1.25$ becomes $1.60$. That adds 5 tenths to 5 hundredths. Check with an estimate: $3.5 + 1.25$ is more than $3.5$, so $1.60$ cannot be right.