Name: _______________________________________________
Date: _________________
Algebra 1
1.1 Evaluate Expressions
Question: How do you evaluate algebraic expressions and powers?
Answer: By substituting numbers in for the variable and performing the indicated operation(s)
Vocabulary:
1. Variable—a letter used to represent one or more numbers (ex: n)
2. Expressions-numbers, variable, and operations (ex: mn)
3. Algebraic Expression—an expression that includes at least one variable (ex: 4n)
Algebraic
Expression
Meaning
Operation
5(n) or 5 *n or 5n
5 times n
Multiplication
14/y
14 divided by y
Division
6+c
6 plus c
Addition
8-x
8 minus x
Subtraction
To evaluate an algebraic expression, substitute a number for the variable,
perform the operation(s), and simplify the result, if necessary. The resulting number is the value of the expression.
Evaluate algebraic expressions
Evaluate the expression when n = 3.
a. 13 •n =13 •3
Substitute 3 for n.
=39
Multiply.
b. 9/n =9/3
c. n -1 = 3 - 1
d. n + 8 = 3 + 8
=2
Substitute 3 for n.
Subtract.
=3
= 11
Substitute 3 for n
Divide.
Substitute 3 for n.
Add.
GUIDED PRACTICE:
Let y = 2
8
1. 6y
(A = 12)
2.
y (A = 4)
3. y + 4 (A = 6)
4. 11 – y (A = 9)
WORD PROBLEM:
You’re saving money to buy an iPhone… If you know how much it costs and how much you earn each week, you can
determine how many weeks it will take you to save enough money. The phone is $360 and you earn about $64/week,
how many weeks will it take you to buy your iPhone?
You can do this by EVALUATING AN EXPRESSION THAT INVOLVES A VARIABLE: 64w
Evaluate the expression 64w when w = 2, w = 3, w = 4… until you get an answer.
64w = ?
64(2) = 128
64(3) = 192
64(4) = 256
64(5) = 320
64(6) = 384
Therefore, after 6 weeks you will have enough money to buy the iPhone.
WORD PROBLEM:
The total cost of seeing a movie at a theater can be represented by the expression a + r where a is the cost (in dollars) of
admission and r is the cost (in dollars) of refreshments. Suppose you pay $7.50 for admission and $7.25 for refreshments.
Find the total cost.
Total cost = a + r
= 7.50 + 7.25
= 14.75
The total cost is $14.75.
Write expression.
Substitute 7.50 for a and 7.25 for r.
Add.
GUIDED PRACTICE:
In Example 2, suppose you go back to the theater with a friend to see an afternoon movie. You pay for both admissions.
Your total cost (in dollars) can be represented by the expression 2a. If each admission costs $4.75, what is your total
cost?
2a
2 (4.75)
9
Therefore, the total cost is $9.50.
Vocabulary:
1. Power—an expression that represents repeated multiplication of the same factor
For example, 81 is a power of 3 because 81 = 3 • 3 • 3 • 3
2. Exponent—the number of times the base gets repeated
3. Base—the number that is multiplied as many times as the exponent (ex: 2 4 – 2 is base, 4 is exponent, whole thing is
power)
Ex: 24 = two to the fourth power = 2 • 2 • 2 • 2 = 16
Power
Words
Product
71
Seven to the first power
7
52
5•5
(1/2)3
Five to the second power
One half to the third power -ORone half cubed
½•½•½
Z5
Z to the fifth power
z•z•z•z•z
GUIDED PRACTICE:
Write in words and numbers
1. 95
2. 28
3. n4
Answers:
1. nine to the fifth power, 9*9*9*9*9
2. two to the eighth power, 2*2*2*2*2*2*2*2
3. n to the fourth power, n*n*n*n
4. 83 = 8 * 8 * 8 = 512
5. 2.52 = 2.5 * 2.5 = 6.25
4. x3 when x = 8
5. k2 when k = 2.5
WORD PROBLEM:
Each edge or side of a medium sized pop-up storage cube is 14 inches long. The storage cube is made so that it can be
folded flat when not in use. Find the volume of the storage cube.
V = s3
= 143
= 2,744
The volume of the storage cube is 2,744 cubic inches.