1.1 Evaluate Expressions
Goal • Evaluate algebraic expressions and use exponents; review area and perimeter formula
Warm-up: Perform the indicated operation. Do this without a calculator.
1) 12 ÷ 1.5
2) 3.3 • 7
3) 11.6 – 5.92
4) Julia ran 10 2/3 miles last week and 8 5/6 miles this week. How many more miles did she run
last week?
5) Do the following puzzle.
Write down your current age:______
Step 1: Add 5 to the age
Step 2: Multiply the result of Step 1 by 2
Step 3: Subtract twice the age that you started with from the result of Step 2.
Step 4: Subtract 10 from the result of step 3.
Compare your result to the rest of your tribe. What do you notice?
6) Repeat the steps in problem five for another age. Compare your result to the results of the rest
of your tribe. Even though they picked different ages, what do you notice?
What conclusion can you make about this puzzle? Explain why you think the puzzle works this way.
______________________________________________________________________________
VOCABULARY
Variable
Algebraic expression (a.k.a. variable expression)
Evaluating an expression
Simplifying an expression
Exponent
Page
Base
1
Power
ALGEBRAIC EXPRESSIONS
Algebraic
Meaning
Expression
Operation
7t
7 times t
________________
x
20
__________________
Division
y−8
__________________
________________
12 + a
__________________
________________
Example 1 - Evaluate algebraic expressions
Evaluate the expression when n = 4.
a) 11n = 11 • ______
b)
12
=
n
Substitute ______ for n.
12
Substitute ______ for n.
c) n – 3 = _____ − 3
To evaluate an
expression,
substitute a
number for the
variable, perform
the operation(s),
and simplify.
Substitute ______ for n.
Now You Try It! Evaluate the expression when y = 8.
1) 7y
2) y ÷ 2
3) 10 − y
4) y + 6
Product of Factors
a) 121
twelve to the ____________ power
________________
b) 23
two to the ______________ power,
or two _______________
________________
d) a
4
2
one fourth to the _____________ power,
or one fourth _____________
________________
a to the ____________ power
________________
2
⎛1⎞
c) ⎜ ⎟
⎝4⎠
Page
Example 2 - Read and write powers
Write the power in words and as a product of factors.
Power
Words
Now You Try It! Write the power in words and as a product of factors.
5) 75
⎛1⎞
6) ⎜ ⎟
⎝ 3⎠
2
7) (1.4)3
Example 3 - Evaluate powers
Evaluate the expression.
a) y 3 when y = 3
y 3 = _____3
Substitute _____ for y.
b) a 5 when a = 1.2
a 5 = _____5
Now You Try It!
Substitute _____ for a.
Evaluate the expression.
8) t 2 when t = 3
9) m 5 when m =
1
2
10) x 3 when x = 4
Example 4 - Review Area and Perimeter of a Rectangle and Square
12 in.
a)
18 in.
Area of rectangle= length • width or base • height
A = lw or A = bh
Find the area of the rectangle above.
Find the perimeter of the rectangle above.
P = 2l + 2w
3
Perimeter of rectangle = 2 • length + 2 • width
Page
b)
6 cm
c)
Area of square = side • side
A = s²
Find the area of the square above.
d)
Perimeter of square = side + side + side + side
P = 4s
Page
4
Find the perimeter of the square above.