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Ch. 1 -9 Order of Operations & Distributive Property c 2

Properties of Numbers 1. 2. 3. 4. 5. Commutative of Addition & Multiplication Associative of Addition & Multiplication Identity of Addition & Multiplication Zero of Multiplication Distributive

Here are two families of commuters. Commuter B Commuter A & Commuter B changed lanes. A+B=B+A Ax. B=Bx. A Commuter B Remember… commute means to change. Commuter A

The Associative Property The parentheses identify which two associates talked first. (A + B) + C = A + (B + C) (A x B) x C = A x (B x C) B A B THEN C A C

Identity Property of Addition +0= A+0=A

Identity Property of Multiplication x 1= Ax 1=A

Zero Property of Multiplication x 0=0 Ax 0=0

Properties of Multiplication and Addition 1. 2. 3. 4. 5. Commutative of Addition & Multiplication Associative of Addition & Multiplication Identity of Addition & Multiplication Zero of Multiplication Distributive

Distributive Property and Think of a teacher distributing something to every student in the class.

The Distributive Property PROBLEM: 4(x + 3) Four is multiplying the quantity “x + 3” That means four will multiply both the x and the 3! 4 times 3 Multiply 4 times x 4(x + 3) Answer: Copy the operation sign Multiply 4 times 3 4 x + 12

Distributive Property You take the number on the outside of the parentheses and give it to everything on the inside of parentheses by way of multiplication. 3(a +b) = 3 a + 3 b ac + bc = (a + b)c 14 = 2(7)

(4 - 3)2 = 8 - 6 Distributive Property 4(x + 3) = 4 x + 12 The Distributive Property of Multiplication

3(5) = 15 Distributive Property ac + bc = (a + b)c Distributive Property

Order of Operations: Basically "4" Rules (Do the rules in order): RULE 1 - Do all operations within grouping symbols (parentheses, brackets, vinculum (fraction bar)) RULE 2 - Evaluate the number value for any exponents RULE 3 - Multiply or divide in order from left to right RULE 4 - Add or subtract in order from left to right Example 3: Use the order of operations to simplify each expression below. a. ) (4 + 4) – 5 + 4 * 3 (8) – 5 + 4 * 3 = b. ) 2(2) – 4 + 8/2 4 – 4 + 8/2 = (8) – 5 + 12= 4– 4+4= 3 + 12 = 0+4= 15 4

Example: When there are two or more parenthesis, or grouping symbols, perform the inner most grouping symbol first. 2 + 3[ 5 + (4 - 1)2] 2 + 3[ 5 + (3)2] inner most parentheses are done first 2 + 3[ 5 + 9] then work your way out 2 + 3[ 14] 2 + 42 44 http: //www. learnalberta. ca/content/mejhm/i ndex. html? ID 1=AB. MATH. JR. NUMB&ID 2= AB. MATH. JR. NUMB. INTE&lesson=html/ob ject_interactives/order_of_operations/use_i t. html Order of Operations - click on Explore it & choose levels 3 and higher

Homework Pg 50 #8 -24 even (show your work, underline what you’re doing next and drop problem down) #16 is a word problem – 2 pts for answer Extra credit 26 & 28