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Addition: Whole Numbers

Addition , written using the symbol + , is the mathematical operation that represents the total number of objects together in a collection.

For simple addition problems, you can count dots to find the answer.

2 + 7 = 9

There are 2 blue dots and 7 red dots. There are 9 dots altogether.

To add numbers with more than one digit, you can visualize base ten blocks.

115 + 37

115 is equal to 100 + 10 + 5 , so it can be represented by ONE 100 block, ONE ten block, and FIVE unit blocks.

37 is equal to 30 + 7 , so it can be represented by THREE ten blocks and SEVEN unit blocks.

To add, draw all the blocks together.

Altogether we have 12 = 10 + 2 unit blocks, so we can trade them up for ONE ten block and TWO unit blocks.

Now we have 100 + 50 + 2 or 152 .

So 115 + 37 = 152 .

When you add by writing numbers vertically, and adding up the columns, you use "carrying," which is the same as the idea of trading up for the next-largest block.

5625 + 438 _

First add the ones column.   5 + 8 = 13 , so write down the 3 and carry the one.

5 6 2 5 + 4 3 8 _ 3

Next add the tens column.   1 + 2 + 3 = 6 .

1 5 6 2 5 + 4 3 8 _ 6 3

Next add the hundreds column.   6 + 4 = 10 . Write down the 0 and carry the 1 .

1 1 5 6 2 5 + 4 3 8 _ 0 6 3

Next add the thousands column. 1 + 5 = 6 .

1 1 5 6 2 5 + 4 3 8 _ 6 0 6 3

For real numbers , the addition operation is commutative (that is, a + b = b + a ; order does not matter) and associative (that is, ( a + b ) + c = a + ( b + c ) ; grouping does not matter.) See Properties of Addition for more.