Addition and subtraction strategies (age 10+)
Add and subtract decimals to hundredths using strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate strategies to written methods and explain reasoning
What a learner can do afterwards
- Correctly compute 3.45 + 2.78 and explain regrouping across decimal places
- Use a number line or base-ten blocks to model 5.03 − 2.67
- Explain why the standard algorithm works for decimal addition by connecting to place-value understanding
1 · Read
You already line up whole numbers by ones, tens and hundreds. Decimals keep going past the point: first tenths, then hundredths, each ten times smaller. In 4.67, the 6 is 6 tenths and the 7 is 7 hundredths. To add or subtract decimals, line up the decimal points first. That puts ones under ones, tenths under tenths and hundredths under hundredths. If a digit is missing, write a zero, like writing 3.4 as 3.40.
Add 4.67 + 2.85. Line up the decimal points, then add from the right. Hundredths: 7 + 5 = 12, so write 2 and carry 1 tenth. Tenths: 6 + 8 + 1 = 15, so write 5 and carry 1 one. Ones: 4 + 2 + 1 = 7. The sum is 7.52.
Subtracting works the same way, but sometimes you borrow instead of carry. For 6.04 minus 3.58, the tenths place in 6.04 is 0, so you cannot borrow a tenth for the hundredths. Borrow a one to make 10 tenths, then borrow a tenth to make 14 hundredths. Now subtract each column. The answer is 2.46.
Check your work by adding the answer back to the number you subtracted. For 6.04 − 3.58 = 2.46, check that 2.46 + 3.58 = 6.04.
Why does lining up the points work? Each column holds pieces of one size: ones, tenths or hundredths. Ten hundredths make one tenth, and ten tenths make one one. A carry trades 10 small pieces for 1 bigger piece in the next column on the left. So you start at the right, with the smallest pieces.
Line up the decimal points, work from the right, and regroup across columns just like you do with whole numbers.
Practice and reading text written for the os-taxonomy project. Videos by Khan Academy, embedded from YouTube.
2 · Watch
Take it off screen
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
17 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.