Lining Up the Columns

Ones under ones

To add 426 + 351 on paper, write one number under the other so that the digits line up by place value: ones under ones, tens under tens and hundreds under hundreds.

Then each column holds only one kind of number. The ones column holds only ones, and the tens column holds only tens, so each column can be added by itself.

The 1 is under the 6, the 5 is under the 2, and the 3 is under the 4.

Start on the right

Start with the ones column, on the right: 6 + 1 = 7. Write the 7 under the line, in the ones column.

The ones: 6 + 1 = 7.

Then the tens and the hundreds

Next, add the tens column: 2 + 5 = 7. These digits are 2 tens and 5 tens, which make 7 tens, so the 7 is written in the tens place.

Last, add the hundreds column: 4 + 3 = 7, and write the 7 in the hundreds place. The answer is 777.

The tens: 2 + 5 = 7.

The hundreds: 4 + 3 = 7. The answer is 777.

4 hundreds and 3 hundreds, 2 tens and 5 tens, 6 ones and 1 one: 7 hundreds, 7 tens and 7 ones make 777.

Line up on the right

Numbers are lined up on the right, where the ones are, not on the left as words are. If 351 is written one place too far to the left, its 1 sits under the tens and counts as 1 ten, and every other digit is worth ten times as much too. The sum becomes 426 + 3510.

This matters most when the numbers have different lengths. For 1204 + 53, the 3 goes under the 4 and the 5 under the 0, so the 53 sits under the last two digits of 1204.

53 is lined up on the right, under the 0 and the 4 of 1204: 1204 + 53 = 1257.

Written from the left, 53 stands in the thousands and hundreds and counts as 5300, so the columns add up to 6504. One place over it counts as 530. Only under the 0 and the 4 is it 53, and the answer 1257.