Warm Up

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Warm Up
Lesson Presentation
Lesson Quiz
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Warm Up Add. 1.
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Objectives
Use the Commutative, Associative, and
Distributive Properties to simplify
expressions. Combine like terms.
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Vocabulary
term like terms coefficient
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The Commutative and Associative Properties of
Addition and Multiplication allow you to
rearrange an expression to simplify it.
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Example 1A Using the Commutative and
Associative Properties
Simplify.
Use the Commutative Property.
Use the Associative Property to make groups of
compatible numbers.
11(5)
55
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Example 1B Using the Commutative and Associative
Properties
Simplify.
45 16 55 4
45 55 16 4
Use the Commutative Property.
(45 55) (16 4)
Use the Associative Property to make groups of
compatible numbers.
(100) (20)
120
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Check It Out! Example 1a
Simplify.
Use the Commutative Property.
Use the Associative Property to make groups of
compatible numbers.
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Check It Out! Example 1b
Simplify.
410 58 90 2
410 90 58 2
Use the Commutative Property.
Use the Associative Property to make groups of
compatible numbers.
(410 90) (58 2)
(500) (60)
560
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Check It Out! Example 1c
Simplify.
Use the Commutative Property.
Use the Associative Property to make groups of
compatible numbers.
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The Distributive Property is used with Addition
to Simplify Expressions.
The Distributive Property also works with
subtraction because subtraction is the same as
adding the opposite.
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The terms of an expression are the parts to be
added or subtracted. Like terms are terms that
contain the same variables raised to the same
powers. Like terms can also be constants.
Like terms
Constant
4x 3x 2
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A coefficient is a number multiplied by a
variable. Like terms can have different
coefficients. A variable written without a
coefficient has a coefficient of 1. BEWARE
The Invisible 1!
Coefficients
1x2 3x
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Using the Distributive Property can help you
combine like terms. You can factor out the common
factors to simplify the expression.
7x2 4x2
(3)x2
3x2
Notice that you can combine like terms by adding
or subtracting the coefficients and keeping the
variables and exponents the same.
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Example 3A Combining Like Terms
Simplify the expression by combining like terms.
72p 25p
72p 25p
72p and 25p are like terms.
47p
Subtract the coefficients.
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Example 3B Combining Like Terms
Simplify the expression by combining like terms.
A variable without a coefficient has a
coefficient of 1.
Add the coefficients.
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Example 3C Combining Like Terms
Simplify the expression by combining like terms.
0.5b 2.5n
0.5b 2.5n
0.5b and 2.5n are not like terms.
0.5b 2.5n
Do not combine the terms.
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Check It Out! Example 3
Simplify by combining like terms.
3a) 16p 84p
16p 84p
16p 84p are like terms.
100p
Add the coefficients.
3b) 20t 8.5t2
20t 8.5t2
20t and 8.5t2 are not like terms.
20t 8.5t2
Do not combine the terms.
3c) 3m2 m3
3m2 m3
3m2 and m3 are not like terms.
Do not combine the terms.
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Example 4 Simplifying Algebraic Expressions
Simplify 14x 4(2 x). Justify each step.
Procedure
Justification
14x 4(2 x)
1.
14x 4(2) 4(x)
Distributive Property
2.
14x 8 4x
3.
Multiply.
Commutative Property
14x 4x 8
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Associative Property
(14x 4x) 8
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6.
Combine like terms.
18x 8
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Check It Out! Example 4a
Simplify 6(x 4) 9. Justify each step.
Procedure
Justification
6(x 4) 9
1.
6(x) 6(4) 9
Distributive Property
2.
6x 24 9
3.
Multiply.
Combine like terms.
6x 15
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Check It Out! Example 4b
Simplify -12x 5x 3a x. Justify each step.
Procedure
Justification
12x 5x 3a x
1.
12x 5x x 3a
Commutative Property
2.
16x 3a
3.
Combine like terms.
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Lesson Quiz Part II
Simplify each expression by combining like terms.
Justify each step with an operation or property.
1.
14c2 9c
2. 14c2 9c
3. 301x x
300x
4. 24a b2 3a 2b2
27a 3b2