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Holt Algebra 1
1-7 Simplifying Expressions1-7 Simplifying Expressions
Holt Algebra 1
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
1-7 Simplifying Expressions
Simplify
1.
2.
Bell Quiz 1-7
5 pts
possible
2 pts
3 pts 42(x + 3) for x = –2
12 – 32 + 10 ÷ 2
Holt Algebra 1
1-7 Simplifying Expressions
Questions on 1-6
Holt Algebra 1
1-7 Simplifying Expressions
Use the Commutative, Associative, and Distributive Properties to simplify expressions.
Combine like terms.
Objectives
Holt Algebra 1
1-7 Simplifying Expressions
term
like terms
coefficient
Vocabulary
Holt 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 Algebra 1
1-7 Simplifying Expressions
Holt Algebra 1
1-7 Simplifying Expressions
Example 1A: Using the Commutative and Associative
Properties
Simplify.
Holt Algebra 1
1-7 Simplifying Expressions
Simplify.
Example 1B: Using the Commutative and Associative
Properties
45 + 16 + 55 + 4
Holt Algebra 1
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 Algebra 1
1-7 Simplifying Expressions
Check It Out! Example 1
Simplify.
1a:
1b:
1c:
410 + 58 + 90 + 2
12
•7 • 8
Holt Algebra 1
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 Algebra 1
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.
4x – 3x + 2
Like terms Constant
Holt 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.
1x2 + 3x
Coefficients
Holt 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
= 3x2
Factor out x2 from both terms.
Perform operations in parenthesis.
Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.
Holt Algebra 1
1-7 Simplifying Expressions
Example 3A: Combining Like Terms
Simplify the expression by combining like terms.
72p – 25p
72p and 25p are like terms.
Subtract the coefficients.
Holt Algebra 1
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.
Write 1 as .
Add the coefficients.
and are like terms.
Holt Algebra 1
1-7 Simplifying Expressions
Example 3C: Combining Like Terms
Simplify the expression by combining like terms.
0.5m + 2.5n
0.5m and 2.5n are not like terms.
Do not combine the terms.
Holt Algebra 1
1-7 Simplifying Expressions
Check It Out! Example 3
Simplify by combining like terms.
3a. 16p + 84p
16p + 84p are like terms.
Add the coefficients.
3b. –20t – 8.5t2
20t and 8.5t2 are not like terms.
Do not combine the terms.
3m2 and m3 are not like terms.
3c. 3m2 + m3
Do not combine the terms.
Holt Algebra 1
1-7 Simplifying Expressions
Example 4: Simplifying Algebraic Expressions
Simplify 14x + 4(2 + x). Justify each step.
14x + 4(2) + 4(x) Distributive Property
Multiply.
Commutative Property
Associative Property
Combine like terms.
14x + 8 + 4x
(14x + 4x) + 8
14x + 4x + 8
18x + 8
14x + 4(2 + x)1.
2.
3.
4.
5.
6.
Procedure Justification
Holt Algebra 1
1-7 Simplifying Expressions
6(x) – 6(4) + 9 Distributive Property
Multiply.
Combine like terms.
6x – 24 + 9
6x – 15
6(x – 4) + 91.
2.
3.
4.
Procedure Justification
Check It Out! Example 4a
Simplify 6(x – 4) + 9. Justify each step.
Holt Algebra 1
1-7 Simplifying Expressions
–12x – 5x + x + 3a Commutative Property
Combine like terms.–16x + 3a
–12x – 5x + 3a + x1.
2.
3.
Procedure Justification
Check It Out! Example 4b
Simplify −12x – 5x + 3a + x. Justify each step.
Holt Algebra 1
1-7 Simplifying Expressions
HOMEWORKSec 1-7 (Pg 49) 1, 2, 5, 14, 17, 20, 21, 26, 27, 34-43, 73-75
Holt Algebra 1
1-7 Simplifying Expressions
HOMEWORK
