The following expression represents Joe's grade in math: Do Now The following expression represents Joe's grade in math: 150 - 100 ÷ 2 Should Joe be happy with his grade? Why or why not?

Learn to use the order of operations to simplify numerical expressions.

A numerical expression is an expression made up of numbers and operations Order of operations are the rules used to simplify a numerical expression

Why do we need the order of operations? Joe’s math grade: 150 - 100 ÷ 2 150 – 100 ÷ 2 150 – 100 ÷ 2 50 ÷ 2 150 - 50 100 25 In mathematics there are often options for what order you can simplify expressions. However, there is a system that ALWAYS works and will give you the correct answer.

P E M D A S arenthesis xponents ultiplication From left to right ivision ddition From left to right ubtraction

*when there is more than one set of parenthesis, complete the inside first *complete multiplication and division from left to right *complete addition and subtraction from left to right Reminders

The term 27 is called a power The term 27 is called a power. If a number is in exponential form, the exponent represents how many times the base is to be used as a factor. Exponent Base 7 2 = 2  2  2  2  2  2  2

Simplify the expression. Example A: Simplify the expression. 23 32 52 2  2  2 3  3 5  5 9 25 8

3 + 15 ÷ 5 Divide. 3 + 3 Add. 6 Example B: Simplify the expression. Use the order of operations to justify your answer. 3 + 15 ÷ 5 3 + 15 ÷ 5 Divide. 3 + 3 Add. 6

Example C: Simplify the expression. Use the order of operations to justify your answer. 44 – 14 ÷ 2 · 4 + 6 44 – 14 ÷ 2 · 4 + 6 Divide and multiply from left to right. 44 – 7 · 4 + 6 44 – 28 + 6 Subtract and add from left to right. 16 + 6 22

Example D: Simplify the expression. Use the order of operations to justify your answer. 3 + 23 · 5 3 + 23 · 5 Evaluate the power. 3 + 8 · 5 Multiply. 3 + 40 Add. 43

Example E: Simplify the expression. 2 (3 · 4) ÷ 6 2 ( 3 * 4 ) ÷ 6 Parenthesis. 2 (12 ) ÷ 6 Multiply and Divide from left to right. 24 ÷ 6 4

Example F: Simplify the expression. [(26 – 4 · 5) + 6]2 The parentheses are inside the brackets, so perform the operations inside the parentheses first. [(26 – 4 · 5) + 6]2 [(26 – 20) + 6]2 [6 + 6]2 122 144

Check your understanding: 1. 43 + 16 ÷ 4 2. 28 - 4 · 3 ÷ 6 + 4 3. 25 – 42 ÷ 8 4. (32 + 11) ÷ 5 5. 26 – 7 * 3 + 2 6. 32 + 6(4 – 22) + 8

(9 – 5)3 · (7 + 1)2 ÷ 4

Lesson Quiz Simplify each expression. 1. 27 + 56 ÷ 7 2. 9 · 7 – 5 3. (28 – 8) ÷ 4 4. 136 – 102 ÷ 5 5. (9 – 5)3 · (7 + 1)2 ÷ 4 35 58 5 116 1,024

Lesson Quiz Evaluate. 6. Denzel paid a basic fee of $35 per month plus $2 for each phone call beyond his basic plan. Simplify the expression 35 + 8(2) to find how much Denzel paid for a month with 8 calls beyond the basic plan. $51

Lesson Quiz 7. Simplify the expression 36 + 63 ÷ 9. A. 11 B. 36 C. 27 D. 43

Lesson Quiz 8. Simplify the expression 3  6 – 12. A. 12 B. 36 C. 24 D. 42

Lesson Quiz 9. Simplify the expression (36 – 6) ÷ 15. A. 15 B. 10 C. 12 D. 2

Lesson Quiz 10. Simplify the expression (8 – 3)3  (9 + 1)2 ÷ 5. A. 1,000 B. 1,500 C. 2,000 D. 2,500

Lesson Quiz 11. Robert paid a $200 basic fee plus $70 a day to get his house painted. Simplify the expression 200 + 90(7) to find how much it cost him if it took 9 days to complete the painting. A. $830 B. $1260 C. $1740 D. $2030