SKILL IN ARITHMETIC begins with knowing sums that are less than 10. 3 + 4 = 7, 7 + 2 = 9, and so on.
First, though, one of the elementary facts of arithmetic is that the order in which we add does not matter. For if you know that 5 + 3 = 8:
then you would also know that 3 + 5 = 8.
The order in which we add does not matter.
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."
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."
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
for any unit: dollars, apples, chairs, etc.
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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