Addition

Addition is a fundamental mathematical operation where two or more numbers are combined to find their total or sum. We have already seen an example on page 2. Another example of 1-digit addition (which we'll get to in a few minutes) is: 1+3 = 4 or 9 + 3 = 12. Soon you'll realize you can add 1+3 (1,2,3,4) and 3+1 (3,4) to get the same answer. This is because addition is commutative.

The operations addition and multiplication are commutative. Division and subtraction are not commutative, because you cannot switch the minuend and the subtrahend, or the divisor and the dividend.



Because we can take any 2 numbers — say, like 2 and 3 — and do this...

3 - 2 = 1      2 - 3 = (-1)

You see? The differences are different. 1 ≠ -1. Also note that I put parentheses around the -1 so you wouldn't get confused with the = and the -. Sometimes you kittens just get them mixed up and think it's part of the equation. And you may not know about subtraction, multiplication, or division yet, but that's ok! You can always ignore these complicated things we're going to do yet, but all you've got to do is learn, understand, and remember the commutative and associative property, which is what we're doing now.

Now you probably understand already. You can switch the addends and get the same answer, or switch the products and get the same answer.

You bet! Here goes...

2+3=5    3+2=5         3×4=12    4×3=12

That was rather exciting, because we got to prove that it worked for addition and multiplication, and also got to show everybody that subtraction did not work.

Right. Division. Let's show everybody another example of division...

72 ÷ 8 = 9     72 ÷ 9 = 8

See? The quotients are different.

Yes, they are. But not to everybody. You actually might want to move over because...

Yep. All of your friends are here to meet you. All of our EFM Characters!

That's the commutative property. It means the order in which you add or multiply numbers does not change the final result. Let's look at something else...

First let's try adding more than two numbers. 2+2+1. 2,3,4. Add 1. 5. Easy enough.
Now let's try it another way. 2+1+2. Add 1 to 2, 3. Add two more ones- 3, 4, 5- you get the answer. It's also 5.
Now let's do it one more way.
The final way to add it up with the numbers 2, 1, and 2 is: 1+2+2. We can switch around the 2 and the 1 since addition is commutative. The equation becomes 3+ 2. 3, 4, 5 is the answer.

It's cool, isn't it? However you add, as long as the addends match, their sums are equal. This is the associative property. When you are adding or multiplying numbers, the way you group them with parentheses does not change the final result! ISN'T IT?!

Um...were you even listening? I said, when you are adding or multiplying numbers, the way you group them with parentheses does not change the final result.