Fluent addition and subtraction (age 9+)
Fluently add and subtract whole numbers with more than four digits using the standard columnar algorithm
What a learner can do afterwards
- Calculate 34,567 + 28,945 using columnar addition
- Calculate 500,000 − 234,178 using columnar subtraction with multiple exchanges
- Add three five-digit numbers in a single column layout
1 · Read
You already know how to add and subtract with columns. Now you'll use the exact same steps on numbers with five, six, or more digits. Line up the digits by place value, then work one column at a time from right to left.
Add 47,658 + 35,786. Line up the places and start at the ones. Ones: 8 + 6 = 14, write 4 and carry 1. Tens: 5 + 8 + 1 = 14, write 4 and carry 1. Hundreds: 6 + 7 + 1 = 14, write 4 and carry 1. Thousands: 7 + 5 + 1 = 13, write 3 and carry 1. Ten thousands: 4 + 3 + 1 = 8. The answer is 83,444.
Subtract 300,000 − 152,647. The ones digit is 0, and so is every digit up to the 3. Exchange from the 3: it becomes 2, each 0 it passes becomes 9, and the ones become 10. This exchange is also called borrowing. Now subtract each column: 10 − 7 = 3, 9 − 4 = 5, 9 − 6 = 3, 9 − 2 = 7, 9 − 5 = 4 and 2 − 1 = 1. The answer is 147,353.
You can add three or more numbers in one layout. Line them all up and add each column from the right. A column total from 20 to 29 has 2 tens, so write its ones digit and carry 2 to the next column. For example, 9 + 9 + 8 = 26, so write 6 and carry 2. Estimate first by rounding, so a slip stands out.
The column method works on any size number: line up the place values, then carry or borrow one column at a time.
Practice questions and readings written for the os-taxonomy project.
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.