ELEMENTARY ADDITION

THE COUNTING NUMBERS, also called the natural numbers, are the numbers 1, 2, 3, 4, and so on. The problem of "adding" any two of them, is the problem of naming the number that results when, starting with the first, we continue counting as many times as there are 1's in the other.

6 + 3 = ?

Since 3 is three 1's -- 3 = 1 + 1 + 1 -- then, starting at 6, we continue counting three times.

"Six -- seven, eight, nine."

6 + 3 = 9.

The addition sign is this:  + , which we read "plus."  The solution to the problem -- the result of adding -- we call the sum; the numbers that we are adding we call the terms of the sum.  And so when we add 6 + 3, the terms are 6 and 3; their sum is 9.  We also call '6 + 3' a sum -- even if we do not name the answer

Now practice these sums that are less than 10.

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Do the problem yourself first!

Composing 10 itself

Next, it is useful to know all the ways of composing, that is, adding to get, 10.

Sums between 10 and 20

Finally, the student must know sums such as  9 + 6 = 15 ,  8 + 5 = 13, and so on.  To become familiar with them, you can first compose 10 by regrouping.  But eventually, you must know them.

Example 1.   9 + 6.

On splitting 6 into 1 + 5,

9 + 6 = 9 + 1 + 5 = 10 + 5 = 15.

Say, "9 + 1 is 10, plus 5 is 15."

That is, regroup 1 with 9 to compose 10.

Example 2.   5 + 7.

"5 + 5 is 10, plus 2 is 12."

Example 3.     3 + 8.

"8 + 2 is 10, plus 1 is 11."

Doubling

It will help to know the sum of a number added to itself.

5 + 5 = 10

6 + 6 = 12

7 + 7 = 14

8 + 8 = 16

9 + 9 = 18

Now, once you know that

6 + 6 = 12,

then you could know that

6 + 7 = 13,

and

6 + 5 = 11.

7 + 7 = 14

7 + 8 = 15

7 + 6 = 13

8 + 8 = 16

8 + 9 = 17

8 + 7 = 15

9 + 9 = 18

9 + 8 = 17

Zero

0 is a number. It can answer the question How much? or How many?
0 is best introduced by subtraction.

Say, for example, that you have 2 dollars.  If you spend those 2 dollars, you now have 0 dollars.

2 dollars − 2 dollars = 0 dollars.

That is,

2 − 2 = 0.

Whenever you subtract a number from itself, you get 0.

Here is a basic fact about 0:  If you add it to any number, that number does not change.

5 + 0 = 5.

0 + 6 = 6.

0 means no units.

There is a subtle difference between 0 units and nothing. Say that you have an account at the First National Bank and that your balance is $10.  If you now withdraw $10, your balance is 0 dollars. But say that you have no account at that bank. Then you do not have a balance of 0 dollars there -- you have nothing!

That is the difference between 0 and nothing.

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Practice the following until you remember each one.