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Variables and Expressions
Goal: Evaluate and write variable expressions.
Vocabulary
Variable:
A symbol, usually a letter, that is used to represent
numbers.
An expression that consists of numbers,
variables, and operations.
Variable expression:
EXAMPLE
1
Using a Variable Expression
Biking You are taking a bike trip. After riding 8 miles, you change your speed
to 12 miles per hour. What is the total distance you travel if you stay at this
speed for 2 hours? for 3 hours?
Solution
Let t represent the time, in hours that you ride at 12 miles per hour. So,
the total distance you travel is original distance speed time, which
is 8 12t.
1. Write hours
traveled, t.
2. Substitute for t in the
expression 8 + 12t.
3. Evaluate to find
the total distance.
2
8 12( 2 )
32
3
8 12( 3 )
44
ANSWER If you ride at 12 miles per hour for 2 hours, you travel a total of
32 miles . After 3 hours, you travel a total of 44 miles .
Guided Practice
Use the information in Example 1.
1. If you travel for 4 hours, what is the total distance?
56 miles
1
2
2. If you travel for 1 hours, what is the total distance?
26 miles
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Chapter 1
Notetaking Guide
EXAMPLE
2
Evaluating Variable Expressions
Evaluate the expression when x 6 and y 3.
a. 9x 14 9( 6 ) 14
Substitute 6 for x.
54 14
Multiply.
40
Subtract.
b. 4x 7y 4( 6 ) 7( 3 )
Substitute 6 for x and 3 for y.
24 21
Multiply.
45
Add.
Writing Expressions
The following common words and phrases indicate addition, subtraction,
multiplcation and division.
Addition
Subtraction
Multiplication
Division
plus
the sum of
increased by
total
more than
added to
minus
the difference of
decreased by
fewer than
less than
subtracted from
times
the product of
multiplied by
of
divided by
the quotient of
per
EXAMPLE
3
Translating Verbal Phrases
Verbal Phrase
Order is important
when translating verbal
expressions that suggest
subtraction and division.
The difference of a
number and 10 means
n 10, not 10 n.
The quotient of a
number and 9 means
n 9, not 9 n.
Variable Expression
The sum of 8 and a number
8
The difference of 24 and a number
24 n
The product of 5 and a number
+n
5n
35
The quotient of 35 and a number
Two thirds
of a number
n
2
n
3
Lesson 1.3
Variables and Expressions
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7
Guided Practice
Evaluate the expression when a 14 and b 4.
3. 7a
4. ba
98
56
5a
ab
5. b(a 6)
6. 80
7
Write the phrase as a variable expression using x.
7. A number decreased by 16
72
x
x 16
EXAMPLE
4
8. 72 divided by a number
Writing and Evaluating Expressions
Fundraising Your school’s fundraising committee is making team banners.
The committee can make n banners in 15 minutes. Multiply by 4 to find the
number of banners the committee can make per hour.
a. Use n to write an expression for the number of banners the committee
can make per hour.
b. The committee makes 9 banners in 15 minutes. Find the number of
banners the committee can make per hour.
Solution
a. The phrase multiply by suggests multiplication. So, the variable expression
for the number of banners the committee can make per hour is 4n.
b. Substitute 9 for n in the expression 4n to find the number of banners the
committee can make per hour.
4n 4( 9 )
36
ANSWER The committee can make 36 banners per hour.
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Chapter 1
Notetaking Guide