Adding and subtracting decimals

Line up the decimal points

Adding decimals is like adding whole numbers, with one extra job at the start: line up the decimal points. When the points sit in one column, the tenths sit under the tenths, the hundredths under the hundredths, and every digit is added to a digit of the same place value.

Take 3.5 + 1.25. The first number has one decimal place and the second has two, so write 3.5 as 3.50. The value has not changed, and now both numbers have hundredths. The chart below shows the two addends with the points lined up, and the sum underneath.

Add from the right

Add the columns from right to left, exactly as you do with whole numbers. Start with the hundredths, then the tenths, then the ones. If a column reaches ten or more, carry one into the next column on the left. In the example above no column reaches ten, so the sum is simply 4.75.

An example with a carry: 2.7 + 4.68 becomes 2.70 + 4.68. The hundredths add to 8, the tenths add to 13, so write 3 tenths and carry 1 whole. The ones add to 2 + 4 + 1 = 7. The sum is 7.38.

Subtract with padding zeros

Subtraction uses the same setup. Line up the points, pad the shorter number with zeros, and work from the right. The calculation 5.2 - 0.85 becomes 5.20 - 0.85. There are no hundredths to take 5 from, so borrow from the tenths: 20 hundredths take away 5 hundredths leaves 15 hundredths. The tenths column becomes 1, and 1 tenth take away 8 tenths needs another borrow from the ones, leaving 3 tenths. The ones become 4, and 4 take away 0 is 4.

Estimate to check

A quick estimate catches most mistakes. The sum 3.5 + 1.25 is close to 3.5 + 1, which is 4.5, and the exact answer 4.75 is nearby. The difference 5.2 - 0.85 is close to 5 - 1, which is 4, and the exact answer 4.35 is nearby. If your estimate and your answer are far apart, check that the points were lined up.