Expressions

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Expressions
Lesson 2.1.2
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Lesson 2.1.2
Expressions
California Standard Algebra and Functions
1.2 Write and evaluate an algebraic expression
for a given situation, using up to three
variables.
What it means for you Youll practice how to
make your own expressions, and how to work out
the value of an expression once youre told the
values of the variables.

• Key Words
• variable
• expression
• evaluate

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Lesson 2.1.2
Expressions
Variables are all well and good, but theyre only
useful when you use them to solve math problems.
You can use variables and numbers to describe a
problem in math terms its called an
expression.
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Lesson 2.1.2
Expressions
An Expression Is a Problem Written in Math Terms
Expressions are used to write word problems in
math terms.
Expressions are like instructions that tell you
what you have to do to a number or variable.
x 7
A number, x, is increased by 7
y 7
A number, y, is decreased by 7
a 7
A number, a, is multiplied by 7
A number, k, is divided by 7
k 7
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Lesson 2.1.2
Expressions
An Expression Is a Problem Written in Math Terms
Sometimes you might have to describe a real-life
situation using a mathematical expression.
You need to imagine what would happen to a
quantity, and write that down using variables,
and , , , and .
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Lesson 2.1.2
Expressions
Example 1
Peter has 165 in his savings account. Lottie
has x more dollars than Peter. Write an
expression for the amount of money that Lottie
has.
Solution
Lottie has more money than Peter.
To find how much she has, you need to add x to
the amount that Peter has.
So the expression for the number of dollars that
Lottie has is 165 x.
Solution follows
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Lesson 2.1.2
Expressions
Guided Practice
In Exercises 14, write an expression for each
word problem.
1. A number, x, is decreased by 10. 2. A number,
q, is increased by 27. 3. The variable w is
multiplied by 20. 4. A computer repairman charges
25 per hour to fix computers. How many dollars
should he charge for h hours of work?
x 10
q 27
w 20
25 h
Solution follows
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Lesson 2.1.2
Expressions
Guided Practice
In Exercises 56, write an expression for each
word problem.
5. Aishas jump rope is 2 feet shorter than
Lisas. If y represents the length of Lisas
rope in feet, then write an expression to
represent the length of Aishas rope (also in
feet). 6. Describe the expression 100 (4 z)
in your own words.
y 2
z is multiplied by four, then the result is
subtracted from 100
Solution follows
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Lesson 2.1.2
Expressions
You Can Evaluate if You Know the Value of the
Variable
If youre given a value to use for a variable,
you can work out the value of the expression.
Its called evaluating the expression.
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Lesson 2.1.2
Expressions
Example 2
Evaluate the expression 7 h, if the value of h
is 6.
Solution
Start with 7 h.
But h 6, so replace h with the number 6
7 6
This means evaluating the expression gives 7 6
42
Solution follows
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Lesson 2.1.2
Expressions
Example 3
The expression 120 s is used to find out how
many seats are available in a movie theater
after s people are already seated. How many
seats are available if 73 people are already
seated?
Solution
Start with 120 s.
Youre told that s 73, so replace s with the
number 73
This means that 120 73 47 seats are available.
Solution follows
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Lesson 2.1.2
Expressions
Guided Practice
Evaluate the expressions given in Exercises 712.

• t 28, given that t 19
• y 7, given that y 5
• d 9, given that d 3
• g 5, given that g 25
• x (15), given that x 13
• c (3), given that c 10

t 28 19 28 47
y 7 5 7 2
d 9 3 9 27
g 5 25 5 5
x (15) 13 (15) 13 15 2
c (3) 10 (3) 10 3 13
Solution follows
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Lesson 2.1.2
Expressions
Guided Practice
13. The expression 15 t gives Earls height in
centimeters, where t is his friend Tonys height
in cm. If Tony is 135 cm tall, how tall is
Earl? 14. The amount of money made by a hot dog
stand is 2.5h, where h is the number of hot dogs
sold. How much money does the stand make if it
sells 271 hot dogs in one day?
15 cm t 15 cm 135 cm 150 cm
2.5h 2.5 271 677.50
Solution follows
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Lesson 2.1.2
Expressions
There Are Three ways of Writing Multiplication
In an expression, there are three ways of writing
a multiplication.

The first is to use the sign.
Sometimes a raised period, , is used instead of
.
If youre just multiplying a variable by a
number, then you can leave out the symbol
completely.
They all mean the same thing.
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Lesson 2.1.2
Expressions
Guided Practice
Rewrite Exercises 1518 using as a
multiplication symbol.
15. 5 i 16. 12 t 17. 8r 18.
9k
5 i
12 t
8 r
9 k
Rewrite Exercises 1922 using as a
multiplication symbol.
19. 11 d 20. 4 q 21. 4q 22.
53z
4 q
11 d
4 q
53 z
Solution follows
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Lesson 2.1.2
Expressions
Guided Practice
Rewrite Exercises 2326 without a multiplication
symbol.
23. 7 w 24. 13 t 25. 3 y
26. 4 c
13t
7w
3y
4c
Solution follows
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Lesson 2.1.2
Expressions
Independent Practice
In Exercises 16, evaluate the expression 19 y
for each value of y.
1. y 11 2. y 11 3. y 26
4. y 19 5. y 0 6. y 8
8
30
0
7
27
19
Solution follows
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Lesson 2.1.2
Expressions
Independent Practice
7. A variable, d, is multiplied by 15. Write
this as an expression. Evaluate the expression
for d 4. 8. One palm tree is sixteen feet
taller than another. Write an expression for
the height of the shorter palm tree. 9. Jessica
shares q potato chips between 12 friends.
Write an expression for the number of potato
chips received by each friend. Evaluate the
expression if q 96.
15 d
60
x 16, where x is the height of the taller tree
(in feet)
q 12
8
Solution follows
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Lesson 2.1.2
Expressions
Independent Practice
Exercises 10 and 11 are about Manuel, the manager
at a restaurant.
10. Manuel collected t dollars in tips and wants
to share it equally among his n employees.
Write an expression that can be used to
calculate how much each employee will get in
tips. You can assume that Manuel does not get
any tips. 11. If there are 5 employees and
Manuel collected 90 in tips, use your
expression from Exercise 10 to calculate how
much each employee will get.
t n
18
Solution follows
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Lesson 2.1.2
Expressions
Independent Practice
Rewrite Exercises 1214 to show all three ways of
writing multiplication.
12. 3 w 13. 7 t 14. 9r
3 w, 3w
7 t, 7t
9 r, 9 r
Solution follows
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Lesson 2.1.2
Expressions
Round Up
To evaluate an expression, you just need to
substitute numbers in place of variables.
They take some getting used to, but expressions
are a really good way to write down and then
solve math problems.