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

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

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

4. Why do we need the order of operations? Joe’s math grade:
÷ 2
150 – 100 ÷ 2
150 – 100 ÷ 2
50 ÷ 2
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.

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

6. *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

7. 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

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

9. 3 + 15 ÷ 5 Divide. 3 + 3 Add. 6 Example B:
Simplify the expression. Use the order of operations to justify your answer.
÷ 5
÷ 5
Divide.
3 + 3
Add. 6

10. 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 –
Subtract and add from
left to right.
16 + 6 22

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

12. 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

13. 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

14. Check your understanding:
÷ · 3 ÷ 6 + 4
3. 25 – 42 ÷ ( ) ÷ 5
5. 26 – 7 * (4 – 22) + 8

15. (9 – 5)3 · (7 + 1)2 ÷ 4

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

17. 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 (2) to find how much Denzel paid for a month with 8 calls beyond the basic plan.
$51

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

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

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

21. 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

22. Lesson Quiz
11. Robert paid a $200 basic fee plus $70 a day to get his house painted. Simplify the expression (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