How this instrument works
Long addition breaks a bigger sum into pieces you can handle one at a time: start at the ones place, add those two digits, then move left to the tens place. Each position is added on its own, and when a column's total climbs to ten or more, the extra amount cannot stay where it is — a single spot only holds one figure — so it gets sent into the next column to the left.
That carried amount is not a trick; it is place value doing its job. Ten units in one column are worth exactly one unit in the position beside it, so when the ones place produces a two-figure total, the leftmost of those two belongs one step over. Write down the remainder for that spot, then add the carried one in alongside whatever is already waiting next door.
This page exists to make that step visible on its own, separate from mental shortcuts that hide it. A sibling sheet on this site, long subtraction, walks through the mirror-image mechanic of borrowing — what happens when a column's top figure is smaller than the one being taken away from it. Between the two, you get the full bookkeeping behind adding and taking away multi-digit numbers by hand.
- Enter the first number's digits into Number 1: tens digit and Number 1: ones digit.
- Enter the second number's digits into Number 2: tens digit and Number 2: ones digit.
- Read Ones digit of the sum for the result of adding the two ones digits, wrapped below ten.
- Check Carry into the tens column — it reads 1 whenever the ones column reached ten or more, otherwise 0.
- Read Tens digit(s) of the sum for the tens total plus that carry, the final tens portion of the answer.
Worked example — 37 plus 48, then two more sums
Take 37 plus 48. The ones place adds 7 and 8 to make 15 — too large for a single spot, so the sheet writes down 5 as the ones digit of the sum and sends a carry of 1 into the tens column. That position then adds 3, 4, and the carried 1 together: 3+4+1=8. Put the pieces back together and the full sum reads 85, matching 37+48 worked out any other way.
Two more sums show the range of behavior this method covers. Adding 10 and 20 needs no carry at all — 0+0=0 in the ones place, 1+2=3 in the tens column, giving 30. Adding 55 and 35 lands right on the carry threshold: 5+5=10 exactly, so the ones digit becomes 0 with a carry of 1, and the tens position turns 5+3+1 into 9, for a final answer of 90.
Questions
Why does long addition carry a 1 into the next column?
Because ten units in one column are worth exactly one unit in the position to its left. Once a place's total reaches ten or more, that surplus has to move over — a single spot can only display one figure, so the extra portion of a total like 15 gets carried while the 5 stays put.
What happens when both ones digits add up to exactly ten?
The ones digit of the sum becomes 0 and a carry of 1 moves into the tens column, exactly as if the total had climbed higher still. Fifty-five plus thirty-five shows this: 5+5=10 gives an ones digit of 0 and a carry of 1, so the tens position becomes 5+3+1=9 for a final 90.
Can the tens result be larger than 9?
Yes, when both original tens digits are large enough that adding them plus a carry pushes past nine. This calculator does not wrap that figure the way it wraps the ones column; tens₁+tens₂+carry is reported exactly, which is why the label reads 'tens digit(s)' rather than a single digit.
Is long addition different from long subtraction?
They are opposite operations built from the same place-by-place habit. Addition sends a surplus forward whenever a column's total tops ten; subtraction, covered on its own sheet, borrows from the position to the left whenever the top figure is smaller than the one being removed.
Does this method work for numbers with more than two digits?
Yes — the same place-by-place habit, carrying whenever a spot reaches ten, extends to numbers of any length. This calculator sticks to two two-digit numbers to keep every carry visible; longer sums just repeat the same rule one more place to the left each time.
Why teach carrying separately instead of just giving the total?
Because the carry step is where most arithmetic mistakes creep in. Seeing 7+8=15 split into a written 5 and a carried 1, rather than a single jump to 85, shows which piece of the answer came from where and makes the whole calculation checkable by hand.