September 27, 2013
Lesson 2.5 Properties of Real Numbers
Student Goals:
1. Use the properties of real numbers to simplify
algebraic expressions.
2. Justify steps in simplifying expressions with
properties of real numbers.
3. Classify equations using the property of real
numbers.
September 27, 2013
2.5 Properties of Numbers
The numbers can commute without changing the value.
*** ORDER does not matter ***
*** Does not change the VALUE ***
*** GROUPING does not matter ***
The parenthesis associate themselves with different numbers.
*** how to get an answer of zero ***
*** It is the equal on both sides ***
September 27, 2013
September 27, 2013
September 27, 2013
Properties of Numbers - What we have seen already
How you undo adding or multiplying by a number.
Numbers don't want to lose their identity!!
*** Does not change the VALUE ***
*** how to get an answer of zero ***
Multiplicative Property of -1
· For every real number n, n -1 = -n
*** It is the equal on both sides ***
· For example, 35 -1 = -35 and -1 35 = -35
September 27, 2013
Simplify each expression below.
-4b + 9 + 6(8-2b)
7(3 + 4z + 8z)
September 27, 2013
Justify each step with a property:
What do you look for?
5(2 - j) + (2j - 3) = 10 - 5j + 2j - 3
= 10 + (-5j) + 2j + (-3)
= 10 + (-3) + (-5j) + 2j
= 10 + (-3) + j(-5 + 2)
= 7 + j(-5 + 2)
= 7 + j(-3)
= 7 + (-3)j
= 7 - 3j
2(1 - d) - (2d + 1) = 2 - 2d - (2d + 1)
= 2 - 2d + (-2d - 1)
= 2 + (-2d) + (-2d) + (-1)
= 2 + (-1) + (-2d) + (-2d)
= 2 + (-1) + 2(-2d)
= 1 + 2(-2d)
= 1 + (-4d)
= 1 - 4d
September 27, 2013
Classify each equation.
Associative
Distributive
Identity Property of Addition
Commutative Property of Multiplication
Inverse Property of Multiplication
Inverse Property of Addition
Commutative Property of Multiplication
Distributive Property
Inverse Property of Multiplication
Identity Property of Multiplication
Identity Property of Multiplication
Associative
Distributive Property
Commutative Property of Addition
Substitution
Symmetric Property
Distributive Property of Addition
Identity Property of Addition
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Identity Property of Multiplication
Inverse Property of Addition
Inverse Property of Multiplication
Distributive Property of Multiplication
Multiplication Property of Zero
Multiplication Property of -1
September 27, 2013
Classify each equation.
Identity Property of Addition
Associative Property
Distributive Property
Associative Property
Substitution
Multiplication Property of -1
Substitution
Symmetric Property
Distributive Property of Addition
Identity Property of Addition
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
Identity Property of Multiplication
Commutative Property of Multiplication
Inverse Property of Addition
Symmetric Property
Inverse Property of Multiplication
Commutative Property of Multiplication
Distributive Property
Distributive Property of Multiplication
Multiplication Property of Zero
Commutative Property of Multiplication
Identity Property of Multiplication Multiplication Property of -1
Multiplication Property of Zero
September 27, 2013
Book Assignment
Chapter 2.5 assignment (pg. 88 1-9, 18, 22, 26, 44)