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
The lesson
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 34,567 and 28,945. Line up the ones, tens, hundreds, and so on, then start at the ones column. 7 + 5 = 12, so write 2 and carry 1. 6 + 4 + 1 = 11, so write 1 and carry 1. 5 + 9 + 1 = 15, so write 5 and carry 1. 4 + 8 + 1 = 13, so write 3 and carry 1. Last, 3 + 2 + 1 = 6. The answer is 63,512.
Subtract 234,178 from 500,000. Every column except the very first is a zero, so you cannot borrow from the column right next door. Instead, the borrow travels all the way to the 5, turning each zero into a 9 along the way, until the very last column gets a 10. Now subtract as usual: 10 − 8 = 2, 9 − 7 = 2, 9 − 1 = 8, 9 − 4 = 5, 9 − 3 = 6, and 4 − 2 = 2. The answer is 265,822.
When you add three or more numbers in one column, the sum can be bigger than 18, so you might carry a 2 instead of a 1. Always check your answer by rounding the numbers and estimating, so a mistake stands out.
The column method works on any size number: line up the place values, then carry or borrow one column at a time.
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.