Adding & Subtracting Decimals: Lining Up the Point
The decimal point is a fixed wall — align it and everything falls into place.
A pocket full of money — and a sneaky trap
You have $2.40 in one pocket and $1.35 in another. Common sense says the total is $3.75 — but what if someone tries to add them by lining up the right edges of the digits instead? The 4 (tenths) ends up next to the 5 (hundredths), like mixing dimes with pennies. The result is wrong every time.
The fix is simple: always line up the decimal points first, then every digit is automatically in its correct place-value column.
When adding or subtracting decimals:
- Write one number above the other with the decimal points in the same column.
- Add trailing zeros so both numbers have the same number of decimal places.
- Add or subtract each column as you would with whole numbers, carrying or borrowing as needed.
- Bring the decimal point straight down into the answer.
Walking through 2.4 + 1.35
Follow each step:
- Add a trailing zero: 2.4 becomes 2.40 (same value, now both numbers have hundredths).
- Align decimal points so they sit in the same column.
- Hundredths column: 0 + 5 = 5.
- Tenths column: 4 + 3 = 7.
- Ones column: 2 + 1 = 3.
- Bring down the decimal point. Answer = 3.75.
That’s exactly $3.75 — what common sense told us from the start!
- Add a trailing zero: 3.2 becomes 3.20.
- Align decimal points so both numbers line up correctly.
- Hundredths: 0 + 8 = 8.
- Tenths: 2 + 4 = 6.
- Ones: 3 + 0 = 3.
- Bring down the decimal point.
Subtraction: line up, then borrow as normal
Subtracting decimals follows the exact same setup: align the decimal points, add trailing zeros, then subtract column by column — borrowing (regrouping) when a top digit is smaller than the bottom digit, exactly as with whole numbers.
The trickiest case is subtracting from a whole number like 5. It has no decimal digits at all, so add two trailing zeros to make 5.00. Now borrow freely across every column including the decimal boundary.
- Add a trailing zero: 5.0 becomes 5.00.
- Align decimal points.
- Hundredths: 0 < 7, so we must borrow. Tenths is also 0, so borrow from ones first: ones becomes 4, tenths becomes 10. Borrow 1 tenth: tenths becomes 9, hundredths becomes 10. Now 10 − 7 = 3.
- Tenths: 9 − 3 = 6.
- Ones: 4 − 2 = 2.
- Bring down the decimal point.
3.2 and 3.20 are the exact same number — the trailing zero does not change the value at all. It simply holds open the hundredths column so columns stay aligned and subtraction is clean.
Think of it like a reserved parking space: the zero saves the spot so the digits line up correctly. You can always add or remove trailing zeros after the decimal point without changing the number.
Check your understanding
- Decimal addition and subtraction are the same as whole-number operations — the key is aligning decimal points first.
- Always line up decimal points, not the right edges of the digits.
- Add trailing zeros to match decimal places; this never changes the value of a number.
- Regroup (borrow) across the decimal point exactly as you do with whole numbers.
- The decimal point drops straight down into the answer line.
- Money problems are a natural everyday application of decimal addition and subtraction.