1. Warm Up Simplify each expression. 1. 30 – 5 ● 3 2. 8 ÷ 2 ● 4
– 5 ● ÷ 2 ● 4
3. 5(2) + 16 ÷ |-4|
Translate each word phrase into an expression.
The product of 8 and 6
The difference of 10y and 4

2. Lesson Objective: I will be able to …
Page 27
Lesson Objective: I will be able to …
Use the commutative, associative, and
distributive properties to simplify expressions
Combine like terms
Language Objective: I will be able to …
Read, write, and listen about vocabulary, key
concepts, and examples

3. The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it.
Page 27

4. Example 1: Using the Commutative and Associative Properties
Page 28
Simplify. A. B.
Use the Commutative Property.
Use the Associative Property to make groups of compatible numbers.
( ) + (16 + 4)
11(5)
(100) + (20) 55
120

5. ( ) Your Turn 1 1 2 7 • 8 Simplify: 1 2 8 • 7 1 2 8 7 4 7 28 •
Page 28 1 2 •
7 • 8
Simplify: 1 2 •
8 • 7
Use the Commutative Property. ( ) 1 2 • 8 7
Use the Associative Property to make groups of compatible numbers. 4 • 7 28

6. The Distributive Property is used with Addition to Simplify Expressions.
Page 27
The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

7. Example 2: Using the Distributive Property with Mental Math
Page 28
Write the product using the Distributive Property. Then simplify.
5(59)
= 5(50 + 9)
Rewrite 59 as
= 5(50) + 5(9)
Use the Distributive Property. =
Multiply.
= 295
Add.

8. The terms of an expression are the parts to be added or subtracted.
Page 27
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
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

9. Example 3: Combining Like Terms
Page 29
Simplify each expression by combining like terms.
A. 72p – 25p
72p and 25p are like terms.
= 47p
Subtract the coefficients. B.
A variable without a coefficient has a coefficient of and are like terms.
Write 1 as .
Add the coefficients.

10. Simplify by combining like terms.
Your Turn 3
Page 29
Simplify by combining like terms.
A. 16p + 84p
16p + 84p are like terms.
= 100p
Add the coefficients.
B. –20t – 8.5t2
20t and 8.5t2 are not like terms.
= –20t – 8.5t2
Do not combine the terms.

11. Example 4: Simplifying Algebraic Expressions
Page 29
Simplify 14x + 4(2 + x). Justify each step.
Procedure
Justification 1.
14x + 4(2 + x) 2.
14x + 4(2) + 4(x)
Distributive Property 3.
14x x
Multiply. 4.
14x + 4x + 8
Commutative Property 5.
(14x + 4x) + 8
Associative Property 6.
18x + 8
Combine like terms.

12. Cornell Notes Fill in the Essential Question:
“How do I use the Commutative, Associative,
and Distributive Properties to simplify
expressions?”
Write two or three main ideas from this lesson
in the Notes section.
Write a Question for each main idea.
(The answer to the question should be the
main idea.)
Summarize the answers to your questions in
the Summary section.
Page 30

13. Chapter 1 Quest Thursday!
Homework
Assignment #22
1-7 Part 2 Homework Worksheet
Chapter 1 Quest Thursday!