variables_expressions

Vocabulary
Variable – A symbol, usually a letter of the alphabet, such as the
letter n, that is used to represent a number.
Variable expression (A.K.A. - Algebraic Expression) – An
expression, such as n – 5, that consists of one or more numbers
and variables along with one or more arithmetic operations.
(Note: No equal sign)
 Evaluate a Variable Expression – write the expression,
substitute a number for each variable, and simplify the result.

How Do You Describe a
Variable Expression?
Variable
Expression
Meaning Operation
5x, 5 x, (5) (x)• 5 times x
x
x
5
5, ÷ x divided by 5
Multiplication
Division
x + 5 Addition
x − 5 x minus 5
x plus 5
Subtraction

State the meaning of the
variable expression and name
the operation
A
A
A
x−81.
w22.
n
7
3.
p64. + A
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Answer:
State the meaning of the variable expression
and name the operation
1. 8 minus x; Subtraction
2. 2 times w; Multiplication
3. 7 divided by n; Division
4. 6 plus p; Addition
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Examples:
7.1 −
b
a
kr 4.2 ×
zxy 35.3 ÷
Algebraic Expressions
**Verbal expression
a divided by b; minus 7
(note: fractions are division problems)
r times the product of 4 and k
(note: multiplication is implied when two or more
letters xy or numbers 4k are together and there
is no operation symbol).
The product of 5xy divided by 3z
mn ÷+ )4(.4 The sum of 4 and n; divided by m
**Verbal
expressions are
usually more
detailed than
stating the
meaning. Verbal
expressions are
used to translate
words or
language into
variable or
algebraic
equations. They
consist of key
words that help
identify the type
of equation that
will need to be
simplified. These
key words are
usually
introduced when
writing variable
expressions and
writing equations
for problem
solving.
**Verbal
expressions are
usually more
detailed than
stating the
meaning. Verbal
expressions are
used to translate
words or
language into
variable or
algebraic
equations. They
consist of key
words that help
identify the type
of equation that
will need to be
simplified. These
key words are
usually
introduced when
writing variable
expressions and
writing equations
for problem
solving.


Evaluate a Variable Expression – write
the expression, substitute a number for
each variable, and simplify the result.
 Value of a Variable – A number that
may be substituted or assigned to a
particular variable; such as n = 3; or x
= 5.

Example 1: Evaluate each expression when n = 4
Substitute 4 for n. Simplify
Simplify (means to solve the problem or perform as many
of the indicated operations as possible.)
7
343
=
+=+nSolution:Solution:
3b. −n Substitute 4 for n. Simplify
1
343
=
−=−nSolution:Solution:
3a. +n

Example 2: Evaluate each expression when x = 8
Substitute 7 for x. Simplify
Solution:Solution:
4b. ÷x
2
484
=
÷=÷xSolution:Solution:
x5a.
40
)8(55
=
=x
Note: No operation sign
between a variable and
number– indicates
multiplication problem.
Note: No operation sign
between a variable and
number– indicates
Using parenthesis is the preferred method to
show multiplication. Additional ways to show
multiplication are:
Using parenthesis is the preferred method to
show multiplication. Additional ways to show
multiplication are:
85;85;85);8)(5( ∗×•
Substitute 7 for x. Simplify
Recall that division problems are also
fractions – this problem could be
written as:
Recall that division problems are also
fractions – this problem could be
written as:
4
4
2;
4
8
4
x
x
because
x
=÷
=
=

Example 3: Evaluate each expression when x = 4, y = 6,
z = 24.
xy5a. Substitute 4 for x; 6 for y. simplify
solutionsolutionRecall: No
operation sign
between
variable(s) and a
number–
indicates
multiplication
problem.
Xy means 4(6);
5xy means 5(4)
(6)
Recall: No
operation sign
between
variable(s) and a
number–
indicates
multiplication
problem.
Xy means 4(6);
5xy means 5(4)
(6)
)6()4)(5(5 =xy
)6()20(=
120=
yz ÷b.
Solution:Solution: 624 ÷=÷ yz
4=
Recall that:Recall that:
4
6
24
624
so,
==÷
=÷
y
z
yz

Evaluate each expression when a = 6, b = 12, and c = 3
ac41.
ca ÷2.
cba3. ++
ba4.
cb −5.
bc ÷6.
A
A
A
A
A
A

ac41.
)3()6)(4(4 =ac
Notice that all the numbers and letters are
together and that there are no operation
symbols which indicates that this is a
Notice that all the numbers and letters are
together and that there are no operation
symbols which indicates that this is a
Substitute the value for a = 6 and c = 3
into the problem and multiply
into the problem and multiply
)3()24(=
72=
multiplymultiply
SimplifiedSimplified
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ca ÷2.
36 ÷=÷ca
Division ProblemDivision Problem
into the problem and divide
into the problem and divide
2= SimplifiedSimplified
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Another way to
solve division
problems is to
write them as
fractions and
simplify.
Another way to
solve division
problems is to
write them as
fractions and
simplify. 2
3
6
===÷
c
a
ca
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cba ++3.
3126 ++=++ cba
Addition problemAddition problem
Substitute the value for a = 6, b=12,
and c = 3 into the problem, then add
Substitute the value for a = 6, b=12,
and c = 3 into the problem, then add
318+=
21=
AddAdd
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ba4.
)6)(12(=ba
multiplication problemmultiplication problem
Substitute the value for b=12 and a = 6
into the problem, then multiply
into the problem, then multiply
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cb −5.
312 −=− cb
Subtraction problemSubtraction problem
into the problem, then Subtract
into the problem, then Subtract
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bc ÷6.
123÷=÷bc
Division problemDivision problem
Substitute the value for c=3 and b = 12 into
the problem, then Divide
Note: It is better to rewrite this division
problem as a fraction.
This fraction can now be reduced to its
simplest form.
Substitute the value for c=3 and b = 12 into
the problem, then Divide
Note: It is better to rewrite this division
problem as a fraction.
This fraction can now be reduced to its
simplest form.
12
3
=
3
3
÷
÷
12
3
=
4
1
=
Divide both
numerator and
denominator by
the GCF = (3) to
reduce this
fraction.
Divide both
numerator and
denominator by
the GCF = (3) to
reduce this
fraction.
It is OK to have a fraction
as an answer.
It is OK to have a fraction
as an answer.
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variables_expressions

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