Algebra 1 Notes SOL A.1 Expressions and Order of Operations
Mr. Hannam
Name: ______________________________________ Date: _____________ Block: _______
Evaluate Expressions
Vocabulary
variable
A letter used to represent one or more numbers...the "unknown."
numeric expression
A mathematical phrase involving numbers and one or more
operations.
Also called a variable expression; a mathematical phrase that includes
at least one variable.
algebraic expression
power
An expression that represents repeated multiplication of the same
factor.
base
The number or expression that is used as a factor in a repeated
multiplication.
exponent
The number or expression that represents the number of times the
base of a power is used as a factor.
Be careful with powers.

Do NOT multiply the base by the exponent! Use the base as a factor exponent
number of times: 35 = 3∙3∙3∙3∙3, NOT 3∙5.

For example, 24 = _____________ NOT __________!
Evaluting Expressions: Substitute the numeric value for the variable.
 5x when x = 3  ___________

r – 3 when r = 7  ___________

k4 when k = 2  ___________

24
when f = 8  ___________
f

3x – 2 when x = 4  ___________
 3 + 4x3 – 6 ÷ 6 when x = 2  ___________
You try:
Write the power in words and as a product; then find the numeric value if possible:
a)
83
b)
48
1
c)  
3
4
d) x2
Evaluate:
d) 15x when x = 4
e) 0.4t when t = 6
f) 2.5m when m = 4
g) x3, when x = 3
Algebra 1 Notes SOL A.1 Expressions and Order of Operations
Mr. Hannam Page 2
Order of Operations

Follow the same convention of order when we evaluate an expression.

For example, how many different ways can we evaluate 3 + 4x3 – 6 ÷ 6 when x = 2?
By convention, we order operations in the following way:
P
Parentheses
Evaluate terms in parentheses first
E
Exponents
Next evaluate exponents
M/D
Multiply / Divide
Multiply or Divide terms next (left to right)
A/S
Addition / Subtraction
Finally, add or subtract terms (left to right)
Note: There are various ways to remember this order convention:
1. Just remember it!
2. PEMDAS
3. Please Excuse My Dear Aunt Sally
4. Your acronym:
What is the correct evaluation of 3 + 4x3 – 6 ÷ 6 when x = 2?
Example:

What is the correct evaluation of 2 × 3 + 42 ÷ 2?

How would the evaluation change if we added parentheses: 2 × (3 + 4)2 ÷ 2?
You try:
a) 42 ∙ 5 - 62
b) 20 – 32 + 7
c) 5 ∙ 23 ÷ 6
d) 6[23 + (13 – 8)]
Evaluate the expressions below when w = 9.
e) 17 – 3w
f) 2w2 – 15
g)
5w
w 6
h) 5w -
1
w
3