Adding Multi-Digit Numbers

Line the numbers up so like units sit in the same column.

Regroup wherever a column fills

Ten ones become a ten. Ten tens become a hundred. Ten hundreds become a thousand.

It is still one ten

The digit you write above the next column is one of that unit, not one of anything else.

Estimate first

Round both numbers before you start, so a wrong answer stands out.

Why the standard algorithm is allowed

Column addition works because each column holds a different unit and like units can be combined. Adding the ones, then the tens, then the hundreds is just adding the expanded forms in pieces. The algorithm is a compact record of that, not a separate magic procedure.

What the little carried digit is

When a column totals ten or more, ten of that unit bundle into one of the next unit up. The small 1 you write above the next column is that bundle. It is not a mark to remember — it is a real quantity that has moved to the column where it belongs.

Alignment is not neatness, it is correctness

A digit written one column out is added to the wrong unit and changes the answer by a factor of ten. With five- and six-digit numbers, use squared paper or draw the columns. This is the most common error in multi-digit addition and it is entirely avoidable.

Estimate before, check after

Round both numbers to the leading place and add: 4,382 + 2,715 is roughly 4,000 + 3,000 = 7,000. The exact answer, 7,097, sits close. An estimate cannot confirm a small slip, but it catches every misalignment, which is the error that matters.