Ch 3_Student_Edition.pdf - Algebraic Expressions and...

Algebraic Expressions
and Properties
3.1 Algebraic Expressions
3.2 Writing Expressions 3.2 Writing Expressions
3.3 Properties of Addition and Multiplication 3.3 Properties of Addition and Multiplication
3.4 The Distributive Property 3.4 The Distributive Property
5
6
4
3
2
1
10
12
8
6
4
2
15
18
12
9
6
3
20 24
16
12
8
4
25 30
20
15
10
5
30 36
24
18
12
6
1
2
3
4
5
6
5
6
4
3
2
1
5
6
4
3
2
1
10
12
8
6
4
2
15
18
12
9
6
3
20 24
16
12
8
4
25 30
20
15
10
5
30 36
24
18
12
6
1
2
3
4
5
6
5
6
4
3
2
1
“Did you know that 5
3
6
5
6
3
5,
but 5
4
6
Þ
6
4
5?”
“Only certain operations like addition
and multiplication preserve equality
when you switch the numbers around.”
“Descartes, evaluate this expression
when
x 5
2 to determine the number of
cat treats you are going to eat today.”
“Remember that you evaluate an
algebraic expression by substituting
the value of
x into the expression.”
3.1 Algeb 3.1 Algeb 3 l b 3.1 Algeb
3

Interpreting Numerical
Expressions
Example 1 Write a sentence interpreting the expression 3 × (19,762 + 418). i 3 (19 762 418)
x
0
1
2
4
4 +
x
5
6
“Great! You’re up to
x = 2.
Let’s keep going.”
What You
Learned Before
Example 2 Write a sentence interpreting the expression (316 + 43,449) + 5.
Example 3 Write a sentence interpreting the expression (20,008 − 752) ÷
(20,008 − 752) ÷ 2 is half as large as 20,008 − 752.
Write a sentence interpreting the expression.
2.
+ 4086)
+ 100
+ 564) ÷ 3
3
⋅
4
⋅
4
12
20
÷ 5
⋅
3
7
⋅
3 − 24

110 Chapter 3 Algebraic Expressions and Properties
Algebraic Expressions
3.1
Work with a partner.
a. You babysit for 3 hours. You receive $12. What is your hourly wage?
●
Write the problem. Underline the important numbers and units you
need to solve the problem.
●
Read the problem carefully a second time. Circle the key word for
the question.
●
Write each important number or word, with its units, on a piece of
paper. Write + , − , × , ÷ , and = on five other pieces of paper.
●
Arrange the pieces of paper to answer the key word question, “What is
your hourly wage?”
●
Evaluate the expression that represents the hourly wage.
hourly wage = ÷
Write.
=
Evaluate.
So, your hourly wage is $ per hour.
b. How can you use your hourly wage to find how much you will receive for
any number of hours worked?
ACTIVITY: Reading and Re-Reading
1
How can you write and evaluate an expression
that represents a real-life problem?
You babysit for 3 hours. You receive $12.
What is your hourly wage?
hourly wage ($ per hour)
Algebraic Expressions
In this lesson, you will
●
use order of operations
to evaluate algebraic
expressions.