1. Real Numbers
Types and properties

2. Warm-up Simplify …don’t forget the order of operations
2[(1+5)2 – (18÷3)]
2p2+3s when p=3 and s=11

3. Homework Answers P. 13 # 41-63 odd and 64 57)9 41) 15 55)a)1=1 59)135
43) b)4= ) 308
45) c) varies ) 135
47) d) no, because
49) its not true for all
51) 5/ a’s and b’s
53)

4. Types of Real Numbers Think – Pair – Share
1) Make a list of all the types of numbers that you know.
2) When time is called pair with a classmate and compare answers.
3) Then when time is called you will share your answers with the class.

5. Rational, Integer, whole
Rational Numbers
Real Numbers
Irrational Numbers
Integers
Whole Numbers
Natural Numbers
Rational Numbers: Numbers that can be written as a fraction using integers, a terminating decimal or a repeating decimal.
Identify which sets and following numbers belong to.
) 5/12
3) ) 6/3
5) ) Π
Rational, Integer
Rational
Rational, Integer,
whole, Natural
Rational
Irrational
Rational, Integer, whole

6. Real Number Properties
Of Addition
Of Multiplication
Commutative Property
Associative Property
Identity Property
Inverse Property
a + b=b + a; 1+2=2+1
a · b=b · a; 1·2=2·1
(a + b)+c=a+(b+c); (1+2)+3=1+(2+3)
(a · b) · c=a ·(b · c); (1 · 2) · 3=1 ·(2 · 3)
a + 0= a; 1+0=1
a · 1= a; 2 · 1=2
a + -a = 0; 1+(-1) =0
a · 0=a; 1·0=0
Multiplication Property of zero
Multiplication Property of -1
Distributive Property
a · (-1)=-a; 2·(-1)=-2
a(b + c)= ab + ac; 2(3+4)=2·3+2·4

7. Properties Scavenger Hunt
Around the room there are different examples of these properties .
With a partner find an example of each property.
Write the examples on your sheet.
When finished turn your sheet into the tray and take a seat.

8. Identify the Properties Used
1) 7z-5(3+Z)=7Z-15-5Z ___________________
= 7Z+(-15)+(-5Z) ___________________
=7Z +(-5Z) +(-15) ___________________
=(7+-5)z+(-15) ___________________
=2Z+(-15) ___________________
=2Z ___________________
2) -4b+9+b=-4b+9+1b ____________________
=-4b+1b ____________________
= (-4+1)b ____________________
= -3b ___________________
Distributive Property
Definition of subtraction
Commutative Property of Addition
Distributive Property
Definition of addition
Definition of subtraction
Identity property of multiplication
Commutative Property of Addition
Distributive Property
Definition of addition

9. Use the Properties to Simplify
Identify like terms
They have exactly the same variable factors
Are the following like terms?
a) 3x,2x b) 4x,8y c) 2x2y3, 3x3y d) 4x2y, 3yx2
Combine like terms
yes no no
yes
a) 3x+2x d) 4x2y+3x2y
(3+2)x 5x
(4+3) x2y
7x2y

10. More with Real Numbers 14 -15 4 Combining irrational numbers
Absolute value (like a parenthesis that makes everything positive) 14
-15 4

11. Simplifying Expressions
6(m+5) ) 2(3-7T) ) –(7-5b)
4) 7Y+6Y ) 3T-T ) -9w3-3w3
7) 7+4t+6+t )3(2x+6) ) 2(4x+3)+3(x+2)
6m+30
-7+35b
6-14t 2T
13y
-12w3
4t+t+7+6
6x+18+2
8x+6+3x+6
5t+13
6x+20
11x+12

12. Simplifying Expressions
10) 7b[8+6(b-1)] ) –[-5(y+2z)-3z]
7b[8+6b-6]
-[-5y-10z-3z]
7b[2+6b]
-[-5y-13z]
14b+42b2
5y+13z
42b2 + 14b

13. Journal What is does it mean to simplify an expression?
How do you know when an expression is simplified? For example is 2x+3y+3x simplified ? How do you know?
Homework: See agenda