Real Numbers Types and properties

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

Homework Answers P. 13 # 41-63 odd and 64 57)9 41) 15 55)a)1=1 59)135 43) 111 b)4=2 63) 308 45) 51 c) varies 64) 135 47) 242 d) no, because 49) 71.6 its not true for all 51) 5/6 a’s and b’s 53)

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.

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. -12 2) 5/12 3) -4.67 4) 6/3 5) 0 6) Π Rational, Integer Rational Rational, Integer, whole, Natural Rational Irrational Rational, Integer, whole

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

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.

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-15 ___________________ 2) -4b+9+b=-4b+9+1b ____________________ =-4b+1b+9 ____________________ = (-4+1)b+9 ____________________ = -3b+9 ___________________ 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

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, 3x3y2 d) 4x2y, 3yx2 Combine like terms yes no no yes a) 3x+2x d) 4x2y+3x2y (3+2)x 5x (4+3) x2y 7x2y

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

Simplifying Expressions 6(m+5) 2) 2(3-7T) 3) –(7-5b) 4) 7Y+6Y 5) 3T-T 6) -9w3-3w3 7) 7+4t+6+t 8)3(2x+6)+2 9) 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

Simplifying Expressions 10) 7b[8+6(b-1)] 11) –[-5(y+2z)-3z] 7b[8+6b-6] -[-5y-10z-3z] 7b[2+6b] -[-5y-13z] 14b+42b2 5y+13z 42b2 + 14b

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