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1-8 Simplifying Expressions
Warm UpWarm Up
Lesson QuizLesson Quiz
Lesson PresentationLesson Presentation
1-8 Simplifying Expressions
Warm UpAdd.
1. 427 + 35 2. 1.06 + 0.74
3.
Multiply.
4. 25(8)
6.
5. 1.3(22) 28.6200
10
462 1.80
1-8 Simplifying Expressions
MA.912.A.3.2 Identify and apply the distributive, associative, and commutative properties of real numbers….
Sunshine State Standards
1-8 Simplifying Expressions
Use the Commutative, Associative, and Distributive Properties to simplify expressions.
Combine like terms.
Objectives
1-8 Simplifying Expressions
termlike termscoefficient
Vocabulary
1-8 Simplifying Expressions
The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it.
1-8 Simplifying Expressions
1-8 Simplifying Expressions
Additional Example 1A: Using the Commutative and Associative Properties
Simplify.
11(5)
55
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers.
1-8 Simplifying Expressions
Simplify.
Additional Example 1B: Using the Commutative and Associative Properties
45 + 16 + 55 + 4
45 + 55 + 16 + 4
(45 + 55) + (16 + 4)
(100) + (20)
120
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers.
1-8 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.
1-8 Simplifying Expressions
Check It Out! Example 1a
Simplify.
21
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers.
1-8 Simplifying Expressions
Check It Out! Example 1b
Simplify.
410 + 58 + 90 + 2
410 + 90 + 58 + 2
(410 + 90) + (58 + 2)
(500) + (60)
560
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers.
1-8 Simplifying Expressions
Check It Out! Example 1c
Simplify.
28
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers.
12
• 7 • 8
12
• 8 • 7
( )12
• 8 7
4 • 7
1-8 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.
1-8 Simplifying Expressions
Additional Example 2A: Using the Distributive Property with Mental Math
Write the product using the Distributive Property. Then simplify.
5(59)
5(50 + 9)
5(50) + 5(9)
250 + 45
295
Rewrite 59 as 50 + 9.
Use the Distributive Property.
Multiply.
Add.
1-8 Simplifying Expressions
8(33)
8(30 + 3)
8(30) + 8(3)
240 + 24
264
Rewrite 33 as 30 + 3.
Use the Distributive Property.
Multiply.
Add.
Additional Example 2B: Using the Distributive Property with Mental Math
Write the product using the Distributive Property. Then simplify.
1-8 Simplifying Expressions
Check It Out! Example 2a
9(52)
9(50) + 9(2)
9(50 + 2)
450 + 18
468
Rewrite 52 as 50 + 2.
Use the Distributive Property.
Multiply.
Add.
Write the product using the Distributive Property. Then simplify.
1-8 Simplifying Expressions
Check It Out! Example 2b
12(98)
1176
Rewrite 98 as 100 – 2.
Use the Distributive Property.
Multiply.
Subtract.
12(100 – 2)
1200 – 24
12(100) – 12(2)
Write the product using the Distributive Property. Then simplify.
1-8 Simplifying Expressions
Check It Out! Example 2c
7(34)
7(30 + 4)
7(30) + 7(4)
210 + 28
238
Rewrite 34 as 30 + 4.
Use the Distributive Property.
Multiply.
Add.
Write the product using the Distributive Property. Then simplify.
1-8 Simplifying Expressions
The terms of an expression are the parts that are added together. 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
1-8 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
1-8 Simplifying Expressions
Using the Distributive Property can help you combine like terms. You can factor out the common factor to simplify the expression.
7x2 + 4x2 = (7 + 4)x2
= (11)x2
= 11x2
Factor out x2 from both terms.
Perform operations in parentheses.
Notice that you can combine like terms by adding the coefficients and keeping the variables and exponents the same.
1-8 Simplifying Expressions
Add only the coefficients.6.8y2 + (-y2) ≠ 6.8
Caution!
1-8 Simplifying Expressions
Additional Example 3A: Combining Like Terms
Simplify the expression by combining like terms.
72p – 25p
72p – 25p
47p
72p and 25p are like terms.
Subtract the coefficients.
1-8 Simplifying Expressions
Additional 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.
1-8 Simplifying Expressions
Additional Example 3C: Combining Like Terms
Simplify the expression by combining like terms.
0.5m + 2.5n
0.5m + 2.5n
0.5m + 2.5n
0.5m and 2.5n are not like terms.
Do not combine the terms.
1-8 Simplifying Expressions
Check It Out! Example 3
Simplify by combining like terms.
3a. 16p + 84p
16p + 84p
100p
16p + 84p are like terms.
Add the coefficients.
3b. –20t – 8.5t
–20t – 8.5t 20t and 8.5t are like terms.
–28.5t Add the coefficients.
3m2 + m3 3m2 and m3 are not like terms.
3c. 3m2 + m3
Do not combine the terms.3m2 + m3
1-8 Simplifying ExpressionsAdditional 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
1-8 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.
1-8 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.
1-8 Simplifying Expressions
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
1-8 Simplifying Expressions
Lesson Quiz: Part I
Simplify each expression.
1. 165 +27 + 3 + 5
2.
Write each product using the Distributive Property. Then simplify.
3. 5($1.99)
4. 6(13)
200
8
5($2) – 5($0.01) = $9.95
6(10) + 6(3) = 78
1-8 Simplifying Expressions
Lesson Quiz: Part II
Simplify each expression by combining like terms. Justify each step with an operation or property.
7. 301x – x
8. 24a + b2 + 3a + 2b2
5.
300x
27a + 3b2
6. 14c2 – 9c 14c2 – 9c
1-8 Simplifying Expressions
1. Which property states that you can add or
multiply in any order?
Lesson Quiz for Student Response Systems
A. Associative
B. Commutative
C. Multiplicative
D. Grouping
1-8 Simplifying Expressions
2. Simplify
A. 5
B. 6
C. 10
D. –5
Lesson Quiz for Student Response Systems
1-8 Simplifying Expressions
3. Which of the following are like terms?
A. 3x and 2y
B. 3x and 2x
C. 3x and x2
D. 3x and 2x
Lesson Quiz for Student Response Systems
1-8 Simplifying Expressions
4. Simplify by combining like terms.
2x2 + x2
A. 2x4
B. 3x4
C. 3x2
D. 4x2
Lesson Quiz for Student Response Systems