Order of Operations to Evaluate Expressions

Contributed by:

Diego Mon, Jan 24, 2022 11:17 AM UTC

Order of operations: Parenthesis, Exponents or powers, Multiply and Divide, Add and Subtract. Simplification of mathematical expressions.

1. Objective
The student will be able to:
use the order of operations to
evaluate expressions.
Designed by Skip Tyler, Varina High School

2. Evaluate 7 + 4 • 3.
Is your answer 33 or 19?
You can get 2 different answers
depending on which operation you
did first. We want everyone to get
the same answer so we must follow
the order of operations.

3. Remember the phrase
“Please Excuse My Dear Aunt Sally”
or PEMDAS.
ORDER OF OPERATIONS
1. Parentheses - ( ) or [ ]
2. Exponents or Powers
3. Multiply and Divide (from left to right)
4. Add and Subtract (from left to right)

4. Once again, evaluate 7 + 4  3
and use the order of operations.
= 7 + 12 (Multiply.)
= 19 (Add.)

5. Example #1
14 ÷ 7 • 2 - 3
= 2 • 2 - 3 (Divide l/r.)
= 4 - 3 (Multiply.)
= 1 (Subtract.)

6. Example #2
3(3 + 7) 2 ÷ 5
= 3(10) 2 ÷ 5 (parentheses)
= 3(100) ÷ 5 (exponents)
= 300 ÷ 5 (multiplication)
= 60 (division)

7. Example #3
20 - 3 • 6 + 102 + (6 + 1) • 4
= 20 - 3 • 6 + 102 + (7) • 4 (parentheses)
= 20 - 3 • 6 + 100 + (7) • 4 (exponents)
= 20 - 18 + 100 + (7) • 4 (Multiply l/r.)
= 20 - 18 + 100 + 28 (Multiply l/r.)
= 2 + 100 + 28 (Subtract l/r.)
= 102 + 28 (Add l/r.)
= 130 (Add.)

8. Which of the following represents
112 + 18 - 33 · 5 in simplified form?
1. -3,236
2. 4
3. 107
4. 16,996
Answer Now

9. Simplify
16 - 2(10 - 3)
1. 2
2. -7
3. 12
4. 98
Answer Now

10. Simplify
24 – 6 · 4 ÷ 2
1. 72
2. 36
3. 12
4. 0
Answer Now

11. Evaluating a Variable Expression
To evaluate a variable expression:
1. substitute the given numbers for each
variable.
2. use order of operations to solve.

12. Example # 4
n + (13 - n)  5 for n = 8
= 8 + (13 - 8)  5 (Substitute.)
= 8+55 (parentheses)
= 8+1 (Divide l/r.)
= 9 (Add l/r.)

13. Example # 5
8y - 3x2 + 2n for x = 5, y = 2, n =3
= 8  2 - 3  52 + 2  3 (Substitute.)
= 8  2 - 3  25 + 2  3 (exponents)
= 16 - 3  25 + 2  3 (Multiply l/r.)
= 16 - 75 + 2  3 (Multiply l/r.)
= 16 - 75 + 6 (Multiply l/r.)
= -59 + 6 (Subtract l/r.)
= -53 (Add l/r.)

14. What is the value of
-10 – 4x if x = -13?
1. -62
2. -42
3. 42
4. 52
Answer Now

15. What is the value of
5k3 if k = -4?
1. -8000
2. -320
3. -60
4. 320
Answer Now

16. 2n  m
What is the value of t
if n = -8, m = 4, and t = 2 ?
1. 10
2. -10
3. -6
4. 6
Answer Now

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