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1-7
Expressions
1-7 Simplifying
Simplifying
Expressions
Warm Up
Lesson Presentation
Lesson Quiz
Holt
1 Algebra 1
HoltAlgebra
McDougal
1-7 Simplifying Expressions
Warm Up
Add.
1. 427 + 35 462
3.
2. 1.06 + 0.74 1.80
10
Multiply.
4. 25(8) 200
6.
Holt McDougal Algebra 1
5. 1.3(22) 28.6
1-7 Simplifying Expressions
Objectives
Use the Commutative, Associative, and
Distributive Properties to simplify expressions.
Combine like terms.
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Vocabulary
term
like terms
coefficient
Holt McDougal Algebra 1
1-7 Simplifying Expressions
The Commutative and Associative Properties
of Addition and Multiplication allow you to
rearrange an expression to simplify it.
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Holt McDougal Algebra 1
1-7 Simplifying Expressions
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
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Example 1B: Using the Commutative and Associative
Properties
Simplify.
45 + 16 + 55 + 4
45 + 55 + 16 + 4
(45 + 55) + (16 + 4)
(100) + (20)
120
Holt McDougal Algebra 1
Use the Commutative Property.
Use the Associative Property
to make groups of compatible
numbers.
1-7 Simplifying Expressions
Helpful Hint
Compatible numbers help you do math
mentally. Try to make multiples of 5
or 10. They are simpler to use when
multiplying.
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Check It Out! Example 1a
Simplify.
Use the Commutative Property.
Use the Associative Property
to make groups of compatible
numbers.
21
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Check It Out! Example 1b
Simplify.
410 + 58 + 90 + 2
410 + 90 + 58 + 2
Use the Commutative Property.
Use the Associative Property
(410 + 90) + (58 + 2) to make groups of compatible
numbers.
(500) + (60)
560
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Check It Out! Example 1c
Simplify.
1 •
7•8
2
1
2
1
(2
•
8
•
•
7
8) 7
4•7
28
Holt McDougal Algebra 1
Use the Commutative Property.
Use the Associative Property
to make groups of compatible
numbers.
1-7 Simplifying Expressions
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.
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Example 2A: Using the Distributive Property with
Mental Math
Write the product using the Distributive
Property. Then simplify.
5(59)
5(60 – 1)
5(60) – 5(1)
300 – 5
295
Holt McDougal Algebra 1
Rewrite 59 as 60 - 1.
Use the Distributive Property.
Multiply.
Subtract.
1-7 Simplifying Expressions
Example 2B: Using the Distributive Property with
Mental Math
Write the product using the Distributive
Property. Then simplify.
8(33)
8(30 + 3)
8(30) + 8(3)
240 + 24
264
Holt McDougal Algebra 1
Rewrite 33 as 30 + 3.
Use the Distributive Property.
Multiply.
Add.
1-7 Simplifying Expressions
Check It Out! Example 2a
Write the product using the Distributive
Property. Then simplify.
9(52)
9(50 + 2)
9(50) + 9(2)
450 + 18
468
Holt McDougal Algebra 1
Rewrite 52 as 50 + 2.
Use the Distributive Property.
Multiply.
Add.
1-7 Simplifying Expressions
Check It Out! Example 2b
Write the product using the Distributive
Property. Then simplify.
12(98)
12(100 – 2)
12(100) – 12(2)
Rewrite 98 as 100 – 2.
Use the Distributive Property.
1200 – 24
Multiply.
1176
Subtract.
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Check It Out! Example 2c
Write the product using the Distributive
Property. Then simplify.
7(34)
7(30 + 4)
7(30) + 7(4)
210 + 28
238
Holt McDougal Algebra 1
Rewrite 34 as 30 + 4.
Use the Distributive Property.
Multiply.
Add.
1-7 Simplifying Expressions
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. Constants are also like terms.
Like terms
Constant
4x – 3x + 2
Holt McDougal Algebra 1
1-7 Simplifying Expressions
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.
Coefficients
1x2 + 3x
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Using the Distributive Property can help you
combine like terms. You can factor out the
common factors to simplify the expression.
7x2 – 4x2 = (7 – 4)x2
= (3)x2
Factor out x2 from both terms.
Perform operations in
parenthesis.
= 3x2
Notice that you can combine like terms by
adding or subtracting the coefficients and
keeping the variables and exponents the same.
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Example 3A: Combining Like Terms
Simplify the expression by combining like
terms.
72p – 25p
72p – 25p
47p
Holt McDougal Algebra 1
72p and 25p are like terms.
Subtract the coefficients.
1-7 Simplifying Expressions
Example 3B: Combining Like Terms
Simplify the expression by combining like
terms.
A variable without a coefficient
has a coefficient of 1.
and
are like terms.
Write 1 as .
Add the coefficients.
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Example 3C: Combining Like Terms
Simplify the expression by combining like
terms.
0.5m + 2.5n
0.5m + 2.5n
0.5m and 2.5n are not like terms.
0.5m + 2.5n
Do not combine the terms.
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Check It Out! Example 3
Simplify by combining like terms.
3a. 16p + 84p
16p + 84p
100p
3b. –20t – 8.5t
–20t – 8.5t
–28.5t
16p + 84p are like terms.
Add the coefficients.
−20t and 8.5t are like terms.
Subtract the coefficients.
3c. 3m2 + m3
3m2 + m3
3m2 + m3
Holt McDougal Algebra 1
3m2 and m3 are not like terms.
Do not combine the terms.
1-7 Simplifying Expressions
Example 4: Simplifying Algebraic Expressions
Simplify 14x + 4(2 + x). Justify each step.
Procedure
1.
2.
14x + 4(2 + x)
14x + 4(2) + 4(x)
3.
14x + 8 + 4x
4.
14x + 4x + 8
5.
(14x + 4x) + 8
6.
Justification
18x + 8
Holt McDougal Algebra 1
Distributive Property
Multiply.
Commutative Property
Associative Property
Combine like terms.
1-7 Simplifying Expressions
Check It Out! Example 4a
Simplify 6(x – 4) + 9. Justify each step.
Procedure
Justification
1.
6(x – 4) + 9
2.
6(x) – 6(4) + 9
Distributive Property
3.
6x – 24 + 9
4.
6x – 15
Multiply.
Combine like terms.
Holt McDougal Algebra 1
1-7 Simplifying Expressions
Check It Out! Example 4b
Simplify −12x – 5x + 3a + x. Justify each step.
Procedure
1.
–12x – 5x + 3a + x
2.
–12x – 5x + x + 3a
3.
–16x + 3a
Holt McDougal Algebra 1
Justification
Commutative Property
Combine like terms.
1-7 Simplifying Expressions
Lesson Quiz: Part I
Simplify each expression.
1. 165 +27 + 3 + 5 200
2.
8
Write each product using the Distributive
Property. Then simplify.
3. 5($1.99)
4. 6(13)
Holt McDougal Algebra 1
5($2) – 5($0.01) = $9.95
6(10) + 6(3) = 78
1-7 Simplifying Expressions
Lesson Quiz: Part II
Simplify each expression by combining like
terms. Justify each step with an operation or
property.
5.
6. 14c2 – 9c
14c2 – 9c
7. 301x – x
300x
8. 24a + b2 + 3a + 2b2
Holt McDougal Algebra 1
27a + 3b2