Warm up: Name the sets of numbers to which each number belongs: -2/9 12/2 ⅓π Find the value of 5+9÷3(3)-8

PROPERTIES OF REAL NUMBERS For any real numbers a, b, and c: COMMUTATIVE PROPERTY: 5 + 7 = 7 + 5 Addition: a + b = b + a 1 + 6 = 6 + 1 3.6 + 1.1 = 1.1 + 3.6 9 6 = 6 9 Multiplication: a b = b a 4 20 = 20 4 6.4 5.2 = 5.2 6.4

PROPERTIES OF REAL NUMBERS For any real numbers a, b, and c: ASSOCIATIVE PROPERTY: (3 + 4) +1 = 3 + (4 + 1) Addition: (a + b) + c = a + (b + c) (2 + 5) + 7 = 2 + (5 + 7) (6.2 + 4.1) +3.3 = 6.2 + (4.1 + 3.3) 15 4 7 2 3 5 15 4 7 2 3 5 = Multiplication: a b c= a b c 34 45 6 = 34 45 6 5.7 7.2 2.3 5.7 7.2 2.3 =

PROPERTIES OF REAL NUMBERS For any real numbers a, b, and c: IDENTITY PROPERTY: 5 + 0 = 0 + 5 = 5 Addition: a + 0 = 0 + a=a 1 + 0 = 0 + 1 = 1 3.6 + 0 = 0 + 3.6 = 3.6 9 1 = 1 9 = 9 Multiplication: a 1 = 1 a = a 4 1 = 1 4 = 4 6.4 1 = 1 6.4 = 6.4

PROPERTIES OF REAL NUMBERS For any real numbers a, b, and c: INVERSE PROPERTY: 5 + (-5) = (-5) + 5 = 0 Addition: a + (-a) = (-a) + a=0 3 + (-3) = (-3) + 3 = 0 3.6 + (-3.6) = (-3.6)+ 3.6 = 0 1 2 = 2 1 = 1 If a=0 then 1 5 1 5 = Multiplication: a = a = 1 1 a = 1 3 5 = 5 3 = 1

PROPERTIES OF REAL NUMBERS For any real numbers a, b, and c: DISTRIBUTIVE PROPERTY: Distributive: a(b+c) = ab + ac and (b+c)a = ba + ca 3(5+1) = 3(5) + 3(1) and (5+1)3 = 5(3) + 1(3) 4(2+6) = 4(2) + 4(6) and (2+6)4 = 2(4) + 6(4)

Name the property shown at each equation: 1 45 = 45 a) Identity property (X) 56 + 34 = 34 + 56 b) Commutative property (+) (-3) + 3 = 0 c) Inverse property (+) 5(9 +2) = 45 + 10 d) Distributive property (2 + 1) +b= 2 + (1 + b) e) Associative property (+) -34(23) = 23(-34) f) Commutative property (X)

Simplify 3(4c -7d) + 5(2c + 9c) 3(4c -7d) + 5(2c + 9d) = 3(4c) – 3(7d) +5(2c) +5(9d) Use distributive property =12c – 21d + 10c +45d Multiply Use commutative property to group like terms = 12c + 10c – 21d + 45d = 22c +24d Add like terms Simplify 1 4 (12-4x) 3 5 (15x-10) + 1 4 (12-4x) 3 5 (15x-10) + =( )(12) – ( )(4x) + ( )(15x) – ( )(10) 1 4 3 5 Use distributive property = 3 – x + 9x -6 Multiply = 3 -6 - x + 9x Use commutative property to group like terms = 8x-3 Add like terms and commutative property

Exit Slip- Simplify each expression: 7a+3b-4a-5b 4(0.2m-0.3n)-6(0.7m-0.5n)