4 Properties of Addition

Hi boys and girls, I hope that you are having a great day!

Today we will be discussing the different properties of addition that will be useful in your future math classes, perhaps even in college, yes I said college!) as these are properties that will never go away.  There are five properties of addition.  They include: commutative, associative, identity, distributive, and inverse.  I will give the general form of each property in a list below.

1.) Commutative property of addition: a + b = b + a (or) a + (b + c) = (b + c) + a
2.) Associative property of addition: (a + b) + c  = a + (b + c)
3.) Identity property of addition: a + 0 = a = 0 + a
4.) Additive inverse property: a + (-a) = 0
5.) Distributive property of addition: a (b + c) = ab + ac 

Now, these may seem confusing or foreign to you, but all you need to do is memorize them, and examples will help you.  If you look at the commutative and associative properties, they look similar.  However, for the commutative property, what is inside the parentheses will NOT change.  For the associative property, what is inside the parentheses WILL change.  And for the first two properties, you are basically adding two or three numbers, but in a different order.  Properties three and four are pretty self-explanatory; for property three, you are simply interested in adding some number to "x" (x being any number) to always get "x."  In this case, we want zero because any number added to zero gives us zero.  For property four, it is called the inverse property of addition because you are adding the 'inverse' of a number to get zero.  Property five is pretty easy.  You must 'distribute' the 'a' to the 'b' and 'c.'  So you are essentially multiplying 'a' to both 'b' and 'c' and then adding them together.

Examples:  Which property of addition holds for the following?

1.) 5 (4 + 9) = 20 + 45.

2.) 8 + (-8) = 0.

3.) 6 + 1 = 1 + 6.

4.) 7 + (1 + 2) = (7 + 1) + 2.

5.) 6 + (-6) = 0.

6.) 3 + 0 = 0 + 3.

7.) 5 + 6 = 6 + 5.

8.) 0 + 4 = 4 + 0.

9.) (1 + 1) + 5 = 1 + (1 + 5).

10.) 9 (4 + 8) = 36 + 72.

Answers: =)

1.) Distributive
2.) Inverse
3.) Commutative
4.) Associative
5.) Inverse
6.) Identity
7.) Commutative
8.) Identity
9.) Associative
10.) Distributive

Do you understand them?

For more help, go to help with associative, commutative, and distributive properties, properties of addition put into different words, YouTube video with properties of addition

Thanks!