Arithmetic/Properties of Operations/Properties of Addition and Subtraction

Sure, you've added 4 + 3 = 7, but have you tried 3 + 4? You get the same answer right? Yes, because of the commutative law of addition.

For any numbers, a and b, a plus b is equal to b plus a. From this we know that addition is commutative, meaning that the operation of addition can be performed in any order with the same result.

What about 5 + 6 = 11? That's right, 6 + 5 = 11 as well.

There is another property of addition, the associative property. Here is an algebraic example:

For any numbers, a , b, and c, a + (b + c) = (a + b) + c

Optional exercises(solve and use the commutative property and associative property to regroup):

8 + 9 = ?

50 + 30 = ?

45 + 9 = ?

36 + 11 = ?

2 + 3 = ?

(5 + 7) + (4 + 3) + (8 + 2) + 5 = ?

Can the same be said about subtraction? Well, let's try it... 7 - 5 = 2, does 5 - 7 = 2? Well, no actually. Because, if you look at a number line you will notice that when you subtract 5 - 7 you go below 0 into the realm of the negative numbers. Specifically, your solution is -2. Even though -2 is same in absolute value as 2, it isn't the same number. Therefore, subtraction is not commutative. Is it associative? No, because the associative law depends on the commutative law in order to work(since it really is just an extension of the commutative law.)

Exercises:

6 - 3 = ?

66-11 = ?

66 - 5 = ?

(80 - 13) - (36 - ５) - 11 + (36-11) = ?