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
The lesson
To add or subtract decimals, line up the decimal points first. That puts the ones under the ones, the tenths under the tenths, and the hundredths under the hundredths. If a number is missing a digit, write a zero so every column lines up, like writing 3.4 as 3.40.
Add 3.45 + 2.78. Line up the decimal points, then add from the right. Hundredths: 5 + 8 = 13, so write 3 and carry 1 ten to the tenths. Tenths: 4 + 7 + 1 = 12, so write 2 and carry 1 one. Ones: 3 + 2 + 1 = 6. The sum is 6.23.
Subtracting works the same way, but sometimes you borrow instead of carry. For 5.03 minus 2.67, the tenths place in 5.03 is 0, so you cannot subtract 6 tenths right away. Borrow a one to make 10 tenths, then borrow a tenth to make 13 hundredths. Now you can subtract each column.
Check your work by adding the answer back to the number you subtracted. For 5.03 − 2.67 = 2.36, check that 2.36 + 2.67 = 5.03.
Line up the decimal points, work from the right, and regroup across columns just like you do with whole numbers.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 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.