1. 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

2. 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 =
9 6
= 6 9
Multiplication:
a b = b a
4 20 = =

3. 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)
( ) +3.3
= ( ) 15 4 7 2 3 5 15 4 7 2 3 5 =
Multiplication:
a b c= a b c = =

4. 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
9 1
= 1 9
= 9
Multiplication:
a 1 = 1 a = a
4 1
= 1 4
= 4 =
= 6.4

5. 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

6. 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)

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

8. 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
= x + 9x
Use commutative property to group like terms
= 8x-3
Add like terms and commutative property

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