Chapter 2: Arithmetic 15When you add 3 + 5, you get 8, a single digit. That could be adding 3 ones and 5 ones to get 8
ones, but 3 thousands + 5 thousands make 8 thousands, so the same addition could be done for
larger addends. It’s just about writing the digits in the proper places.
When you add numbers with more than one digit, stack them one under the other, with the deci-
mal points aligned (even if the decimal points are unseen.) To add 43,502 and 12,381, you write
them like this:
This puts the ones under the ones, the tens under the tens, the hundreds under the hundreds,
and so on. You just have to add the digits in each place, starting on the right with the ones place:
2 ones + 1 one equals 3 ones
0 tens + 8 tens equals 8 tens
5 hundreds + 3 hundreds equals 8 hundreds
3 thousands + 2 thousands equals 5 thousands
4 ten-thousands + 1 ten-thousand equals 5 ten-thousands
It’s traditional to start from the right, from the lowest place value, and work up. There are prob-
lems, like this one, which could be done left to right, but in the next example, you’ll see why right
to left is the better choice. The key is that in the previous example, each time you added two
digits, you got a single digit result. That’s not always the case. Let’s change just one digit in that
problem. Change 43,502 to 43,572.
Now when you add the ones digits you get a single digit, 3, which goes in the ones place of the
answer, but when you add the 7 tens to the 8 tens, you get 15 tens, and there’s no way to squeeze
that two-digit 15 into the one space for the tens digit. You have to regroup, or as it’s commonly
called, you have to carry.
43,502
12,381143,502
12,381
55,883
43,572
12,381