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LESSON 2.6 Number Properties
Goal: Use properties to evaluate expressions.
What is a property? A property is a trait, attribute or characteristic that is “proper” to something.
We all have certain “properties”. One of my properties might be that I have brown hair, brown eyes
or that I can play the piano. Take a few seconds and do the following: Go around your group and
have each person share a property about themselves.
Rational numbers and operations (+, -, * and ÷) have properties too. Today we will review two
properties and look at two new properties to see how we can use them.
Example 1: Identity Properties of Addition and Multiplication
In your own words, define these properties and write an example for each.
Identity Property of Addition:
Example:
Identity Property of Multiplication:
Example:
Example 2: Inverse Property of Addition
In your own words, define this property and write an example for it.
Inverse Property of Addition:
Example:
Example 3: Inverse Property of Multiplication
In your own words, define this property and write an example for it.
Inverse Property of Multiplication:
Finding reciprocals:
1. Put number in fraction form.
2. Switch the numerator and denominator.
Find the reciprocal:
1)
5
4)
0.5
2)
23
5)
2¾
3)
¾
6)
1.2
Examples:
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Example 4: Commutative Property – Go to work…go home….go to work….go home….
Does 3 + 4 + 5 = 5 + 4 + 3. Record your answer here.
This is called the Commutative Property of Addition. When someone “commutes”, it means they
travel the same route to work as they travel to get home.
Commutative Property of Addition:
Number example:
Algebra example:
Is there a commutative property for the other three operations? Do the following problems to
find out:
1) 10 – 2 = 2 – 10??
2) 10(2) = 2(10)??
3) 10 ÷ 2 = 2 ÷ 10??
You should have discovered that there is also a Commutative Property of ___________________.
Commutative Property of ______________________:
Number example:
Algebra example:
Example 5: Using the Commutative Property
a) –5 + 4 + (–6) + 6 + 3
b) -5 + 20 + 5
c) –20(12)(–5)
d) -35(21)(0)
Example 6: Associative Property – Who’s friend’s with who?
Does 3 + (4 + 5) equal (3 + 4) + 5?
What do you notice about this example?
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This is called the Associative Property of Addition. When someone “associates”, it means they have a
connection with another person (the parenthesis). With SOME operations, the association can
change without changing the answer.
Associative Property of Addition:
Number example:
Algebra example:
Is there an associative property for the other three operations? Do the following problems to find
out:
1. (10 – 3) - 2 = 10 – (3 – 2)??
2. (10 * 3) * 2 = 10 * (3 * 2)??
3. (10 ÷ 2) ÷ 2 = 10 ÷ (2 ÷ 2)??
You should have discovered that there is also a Associative Property of ___________________.
Associative Property of ______________________:
Number example:
Algebra example:
Example 7: Using the Associative Property
a. 2.6 + (3.4 + 5)
a.
(20 * 425) * 0
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