Adding and subtracting (age 8+)
Add and subtract numbers with up to four digits using formal written methods of columnar addition and subtraction
What a learner can do afterwards
- Set out and solve a columnar addition with up to four-digit numbers
- Set out and solve a columnar subtraction with exchange across multiple columns
- Check the answer using estimation or inverse operations
1 · Read
You already know how to carry and exchange with smaller numbers. Now you will do the same with thousands, hundreds, tens and ones. Line up the digits by place value, ones on the right, and work from right to left. When a column adds up to 10 or more, write the ones digit and carry 1 to the next column on the left.
In subtraction, take the bottom digit away from the top digit in each column. If the top digit is smaller, exchange 1 from the next column on the left for 10. If that column is 0, go one more column left and exchange there first.
Subtract 4,301 − 2,658. Ones: 1 is less than 8, and the tens digit is 0. So exchange 1 hundred for 10 tens, then 1 ten for 10 ones. Ones: 11 − 8 = 3. Tens: 9 − 5 = 4. Hundreds: 2 is less than 6, so exchange 1 thousand for 10 hundreds: 12 − 6 = 6. Thousands: 3 − 2 = 1. The answer is 1,643.
Estimate by rounding each number, then adding or subtracting. The exact answer should be close. Use the opposite operation for an exact check: if 3,842 + 1,765 = 5,607, subtract 1,765 from 5,607 to get 3,842. To check 4,301 - 2,658 = 1,643, add 1,643 + 2,658 to get 4,301.
Line up numbers by place value, carry or exchange when a column doesn't fit, and always check your answer.
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.
18 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.