Transcript Evaluating Expressions and Combining Like Terms


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.
Variable
Expression
Meaning
Operation
5x, 5·x, (5)(x)
(same as x·5)
5 times x
Multiplication
5 divided by Division
x
5 + x (same as x + 5 plus x
Addition
5
,5  x
x
5)
5–x
5 minus x
subtraction
Example 1: Evaluate each expression when n
= 4.
Simplify (means to solve the problem or perform as
a. n + 3
many of the indicated operations as possible.)
n+3=4+3
Solution:
Substitute 4 for n. Simplify
=7
b. n – 3
n–3=4–3
=1

Solution:
Substitute 4 for n. Simplify
Example 2: Evaluate each expression if x
= 8.
a. 5x
Substitute 8 for x. Simplify
5x = 5(8) Using parenthesis is the preferred method to show
Solution:
multiplication. Additional ways to show multiplication are
5 · 8 and 5 x 8.
= 40
b. x ÷ 4
Substitute 8 for x. Simplify
x÷4=8÷4
Solution:
x
8
= 2 Recall that division problems are also

4
4

fractions – this problem could be
written as:
 2;
because
x4 
x
4
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Solution:
Solution:
Example 3: Evaluate each expression if x = 4,
y = 6, and z = 24.
a. 5xy
Substitute 4 for x; 6 for y. simplify
5xy = 5(4)(6)
= 120
b.
z
y
=
4 24
z
y

6
Substitute 24 for z; 6 for y. Simplify.
1.
2.
3.
4.
5.
6.
4ac
a÷c
a+b+c
ba
b–c
c÷b
A
A
A
A
A
A
Evaluate each expression given that a = 6, b =
12, and c = 3.
1.
4ac
4ac = 4(6)(3) Substitute the value for a = 6 and c = 3
into the problem and multiply
= (24)(3)
= 72
Click to return to
“You try it” slide
Evaluate each expression given that a = 6, b =
12, and c = 3.
2. a ÷ c
Substitute the value for a = 6 and c = 3
a÷c=6÷3
into the problem and divide
=2
Click to return to
“You try it” slide
Evaluate each expression given that a = 6, b =
12, and c = 3.
3.
a+b+c
the value for a = 6, b=12,
a + b + c = 6 + 12 +Substitute
3
and c = 3 into the problem, then add.
= 18 + 3
= 21
Click to return to
“You try it” slide
Evaluate each expression given that a = 6, b =
12, and c = 3.
4. ba
ba = (12)(6) Substitute the value for b=12 and a = 6
into the problem, then multiply.
= 72
Click to return to
“You try it” slide
Evaluate each expression given that a = 6, b =
12, and c = 3.
5. b - c
b – c = 12 – 3 Substitute the value for b=12 and a = 3
into the problem, then subtract.
=9
Click to return to
“You try it” slide
Evaluate each expression given that a = 6, b =
12, and c = 3.
6. c ÷ b
Substitute the value for c=3 and b = 12 into
the problem, then Divide
Divide both
numerator and
denominator by
the GCF = (3) to
reduce this
fraction.
c 3
c b  
b 12
3 3 1

12  3 4
Note: It is better to rewrite this division
problem as a fraction.
This fraction can now be reduced to its
simplest form.
It is OK to have a fraction
as an answer.
Click to return to
“You try it” slide
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
Now that we have seen some algebraic
expressions, we need to know how to
simplify them.
Vocabulary
◦ Like terms: In an expression, like terms are the
terms that have the same variables, raised to
the same powers (same exponents).
 i.e. 4x and -3x or 2y2 and –y2
◦ Coefficient: A constant that multiplies a
variable.
 i.e. the 3 in 3a or the -1 in –b
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In algebra we often get very long
expressions, which we need to make simpler.
Simpler expressions are easier to solve!
To simplify an expression we collect like
terms. Like terms include letters that are the
same and numbers.
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Step One: Write the expression.
4x + 5x -2 - 2x + 7
Collect all the terms together which are alike. Remember that each
term comes with an operation (+,-) which goes before it.
4x, 5x, and -2x
-2 and 7
Simplify the variable terms.
4x+5x-2x = 9x-2x = 7x
Simplify the constant (number) terms.
-2+7 = 5
You have a simplified expression by writing all of the results from
simplifying.
7x + 5
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10x – 4y + 3x2 + 2x – 2y
3x2
10x, 2x
-4y – 2y
3x2 + 12x – 6y
Remember you cannot
combine terms with
the same variable but
different exponents.
Simplify the following:

5x + 3y - 6x + 4y + 3z

3b - 3a - 5c + 4b

4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4

5xy – 2yx + 7y + 3x – 4xy + 2x
A
A
A
A
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1.
Simplify the following:
5x + 3y - 6x + 4y + 3z
5x, -6x
3y, 4y
3z
-x + 7y + 3z
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2.
Simplify the following:
3b - 3a - 5c + 4b
3b, 4b
-3a
-5c
-3a + 7b – 5c
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3.
Simplify the following:
4ab – 2a2b + 5 – ab + ab2 + 2a2b + 4
4ab, -ab
-2a2b, 2a2b
5, 4
ab2
3ab + ab2 + 9

4.
Simplify the following:
5xy – 2yx + 7y + 3x – 4xy + 2x
5xy, -2yx, -4xy
7y
3x, 2x
-xy + 7y + 5x


A variable or algebraic expression is an
expression that consists of one or more
________ and _________ along with one or
numbers
variables (Note: No _______
more
________ _________.
arithmetic
operations
sign)
Toequal
evaluate an expression write the
_________, substitute a _______ for each
expression and _________ the number
variable,
result.
simplify


In an expression, __________ are the terms
that have the same ________,
raised to the
like terms
same ________ (same exponents).
A coefficient
is a number that ________ a
variables
variable.
power
multiplies