1. Order of Operations Arizona State 8 th Grade Math Standard – Strand 1, Concept 2, PO5 Simplify numerical expressions using the order of operations that include grouping symbols, square roots, cube roots, absolute values, and positive exponents.

2. Objective I will be able to apply the order of operations to simplify expressions.

3. Simplify To simplify an expression when there are more than two operations in the expression, you must use a set of rules called the order of operations.

4. ORDER OF OPERATIONS 1. Simplify the terms within parentheses. 2. Simplify the terms with exponents. 3. Multiply and divide from left to right. 4. Add and subtract from left to right. PEMDAS

5. Example Find 8 + (4 x 24) ÷ 32 Step 1: Simplify within the parentheses. 8 + (4 x 24) ÷ 32 8 + (96) ÷ 32 Step 2: Divide 96 ÷ 32 8 + 3 Step 3: Add 8 +3 11 Solution: 8 + (4 x 24) ÷ 32 = 11 24 X 4 32 96 8 + 3

6. What happens if we don’t follow the order of operations? If we just work the problem from left to right, we won’t get the correct answer! 8 + (4 x 24) ÷ 32 8+4 = 12 12 x24 = 288 288 ÷ 32 9 9 does not equal 11!

7. Another Example Simplify: (20 – 2) ÷ 3 Step 1: Simplify within parentheses (20 -2) ÷ 3 Step 2: Divide (18) ÷ 3 Solution: (20 – 2) ÷ 3 = 6

8. Look at the two students and decide which one correctly followed the order of operations! Janet 14 – (5+2) X 2 14 – 7 x 2 7 x 2 14 John 14 – (5+2) X 2 14 – 7 x 2 14 – 14 0

9. Another example (12 ÷ 4) x (4 x 5) – (8 - 4) + 5 (3) x (20) – (4) + 5 60 – 4 + 5 56 + 5 61

10. Give it a try! 1.5 + (8 – 6) 2. (14 ÷ 2) x 5

11. Examples 3. 25 – (4 2 ÷ 32) x 4 4. 257 + (5 x 2) 3 – 15 5. 159 – (2 8 – 40) x 7

12. Review I am able to apply the order of operations to simplify expressions The order of operations can be remember by PEMDAS First you must – Simplify within parentheses Second you must – Simplify exponents Third you must – Multiply and divide from left to right Fourth you must – Add and subtract from left to right

13. On your own Practice – Page 18 # 5 - 26