1. Order of Operations
Objective: Evaluate numerical and algebraic expressions by using the order of operations.

2. Evaluate Numerical Expressions
To evaluate an expression means to find its value.

3. Example 1
Evaluate 26.
26 = 2 • 2 • 2 • 2 • 2 • 2
= 64

4. Check Your Progress Choose the best answer for the following.
Evaluate 44. 64
128
192
256

5.   Order of Operations P Parenthesis E Exponents M
Multiply and\or Divide, in order from left to right.
Exponents
Add and/or Subtract, in order from left to right.  

6. Example 2
Evaluate 48 ÷ 23 •
48 ÷ 8 • 3 + 5
6 • 3 + 5
18 + 5 23

7. Check Your Progress Choose the best answer for the following.
Evaluate [(92 – 9) ÷ 12]5. 6 15 30 45
When one or more grouping symbols are used, evaluate within the innermost grouping symbols first.
= [(81 – 9) ÷ 12]5
= [72 ÷ 12]5
= [6]5

8. Example 3 Evaluate each expression. (8 – 3) • 3(3 + 2)
4[12 ÷ (6 – 2)]2
= 5 • 3(5)
= 4[12 ÷ 4]2
= 5 • 15
= 4[3]2
= 75
= 4[9]
= 36
When dealing with fractions, the numerator and denominator are both groups. Simplify each separately before dividing.
= 2

9. Check Your Progress Choose the best answer for the following.
Evaluate the expression 2(4 + 7) • (9 – 5).
-60 66 88 68
= 2(11) • 4
= 22 • 4

10. Check Your Progress Choose the best answer for the following.
Evaluate the expression 3[5 – 2 • 2]2. 9 18
108 3
= 3[5 – 4]2
= 3[1]2
= 3[1]

11. Check Your Progress Choose the best answer for the following. Evaluate1
69/15 4
5/9

12. Evaluate Algebraic Expressions
To evaluate an algebraic expression, replace the variables with their values.
Then find the value of the numerical expression using the order of operations.

13. Example 4 Evaluate 2(x2 – y) + z2 if x = 4, y = 3, and z = 2.
2(42 – 3) + 22
= 2(16 – 3) + 4
= 2(13) + 4 =
= 30

14. Check Your Progress Choose the best answer for the following.
Evaluate x3 – y2 + z, if x = 3, y = 2, and z = 5. 6 28 36 10
= 33 –
= 27 – 4 + 5 =

15. Example 5
Each side of the Great Pyramid of Giza, Egypt, is a triangle. The base of each triangle once measured 230 meters. The height of each triangle once measured 187 meters. The area of a triangle is one-half the product of the base b and its height h.
Write an expression that represents the area of one side of the Great Pyramid.
½ bh
Find the area of one side of the Great Pyramid.
½ (230)(187)
115(187)
21,505 m2

16. Check Your Progress Choose the best answer for the following.
Find the area of a triangle with a base of 123 feet and a height of 62 feet.
3813 ft2
7626 ft2
15,252 ft2
32 ft2
= ½ (123)(62)
= 61.5(62)