Basic Number Properties Unit Two
Properties of Addition
Addition is counting. Numbers have certain properties when they are being added.
Remember in algebra we never really subtract. We always add the numbers opposite.
Therefore 13 - 7 is really 13 + (-7)
In the last unit we remembered that all numbers have certain consistent properties. Therefore we can conclude that we can solve for any unknown number by applying these properties. In this unit we will explore the number properties of addition.
These properties do not typically have numbers assigned to them. This page refers to each property by number only for organizational purposes.
Addition Property 1
The following is a slide show of our first Basic Number Property of Addition
Click on the show to begin.
Addition Property 2
What comes to mind when you think of identity?
Let's explore the identity property of addition.
What happens when you add 0 to any number.
Notice that every answer is itself.
The Identity property says when 0 is added to any number the result will be that same number.
Makes sense doesn't it?
Addition Property 3
How do you get to school each day?
If you walk or ride a bus or drive a car, it means you commute.
In English the word commute means to move from one location to another.
So what does it mean in math in terms of addition?
Both examples have a total of 5 dogs therefore
3 + 2 is the same as 2 + 3. They both = 5
3 + 2 = 2 + 3
So the commutative (see commute in the word?) property says even if we move stuff around it will still be equal
a + b = b + a and even a + b + c = a + c + b = c + b + a
Addition Property 4
Who do you associate with?
In English the word association deals with a group.
For example your group of friends would be considered your associates.
In Math its the same thing. We associate groups of numbers by using parenthesis.
(2 + 3) is an association that says these numbers should be added together first.
However in addition the Associative Property says that regardless of Association the result will be the same.
Consider 2 + (3 + 5) = 2 + 8 = 10 is the same as
- (2 + 3) + 5 = 5 + 5 = 10
notice that even though we grouped the numbers differently both examples added up to 10
Therefore the Associative property of addition is a + (b + c) = (a + b) + c
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