A topic in the Open Knowledge Graph — a free, open map of 15,290 topics and the order to learn them in.
Adding and subtracting decimals uses the same algorithms as whole numbers, with one critical rule: line up the decimal points (which means lining up the place values). 3.7 + 2.45 becomes 3.70 + 2.45 = 6.15 when you append a trailing zero to align the hundredths. The decimal point in the answer goes directly below the decimal points in the addends. This works because you are adding like units (tenths to tenths, hundredths to hundredths), just as with whole-number addition. Regrouping and borrowing work identically.
Start with money: $3.70 + $2.45 is natural and intuitive. Then generalize to non-money contexts. Use base-ten blocks or hundredths grids to model the addition physically. Emphasize lining up decimal points (not right-justifying the numbers as with whole numbers). Practice with addends of different lengths (some with more decimal places than others) to reinforce trailing-zero thinking.
You already know how to add and subtract multi-digit whole numbers by stacking them and working column by column. Adding decimals uses exactly the same process — the only change is how you line up the columns. For whole numbers, right-aligning puts ones under ones automatically. For decimals, the rule is: align the decimal points, not the right edges.
The reason comes down to place value. The decimal point marks the boundary between whole-number places (to its left) and fractional places (to its right). Aligning the decimal points ensures that tenths line up with tenths, hundredths with hundredths, and so on. If you right-align 3.7 and 2.45 like whole numbers, the 7 (tenths) lands above the 5 (hundredths), and you would be adding them as if they were the same unit — like adding dimes to pennies without converting first.
The practical fix is to append trailing zeros so both numbers have the same number of decimal places, then stack. Write 3.7 as 3.70 (its value is unchanged — 3.70 and 3.7 are identical), then stack with 2.45. Now the hundredths column has 0 and 5, the tenths column has 7 and 4, and the ones column has 3 and 2. Add exactly as with whole numbers: 3.70 + 2.45 = 6.15. The decimal point in the answer drops straight down from the decimal points in the addends.
Subtraction works identically. To compute 5.3 − 1.84, rewrite 5.3 as 5.30 and then borrow and subtract column by column: 5.30 − 1.84 = 3.46. The trailing zero just makes the hundredths column explicit so you can see there is a 0 to borrow against.
Money is the most natural context for this skill: you already know intuitively that $3.70 + $2.45 = $6.15. Recognizing that all decimal arithmetic is dollar-and-cents arithmetic in disguise gives you a built-in check — if a computation produces a wildly off answer, misaligned columns are usually the culprit.