Howstuffworks "Addition - Encyclopedia Entry"

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Addition

Addition is a way of putting together two or more things to find out how many there are all together. Only like things can be added. This is, you cannot add apples and pencils together.

Suppose you have a set of 5 apples and a set of 3 apples on a table:

Now put the sets together in a new set of 8 apples.

You add when you put together two or more sets to find out how many there are all together.

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Arithmetic