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Simplifying Expressions Using Properties

Learn to simplify expressions with properties like commutative, associative, and distributive. Combine like terms efficiently for math success. Discover the importance of coefficients and variables in simplifying algebraic expressions. Practice and enhance your math skills with the provided examples.

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Simplifying Expressions Using Properties

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

  2. 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. B. 45 + 16 + 55 + 4 Example 1: Using the Commutative and Associative Properties Page 28 Simplify. A. Use the Commutative Property. 45 + 55 + 16 + 4 Use the Associative Property to make groups of compatible numbers. (45 + 55) + (16 + 4) 11(5) (100) + (20) 55 120

  5. ( ) 7 1 2 1 2 8•7 7 • 8 • • 1 2 8 • 4 7 • Your Turn 1 Page 28 Simplify: Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 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) Rewrite 59 as 50 + 9. = 5(50 + 9) Use the Distributive Property. = 5(50) + 5(9) = 250 + 45 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 coefficientis 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. B. A variable without a coefficient has a coefficient of 1. and are like terms. Write 1 as . 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. Add the coefficients.

  10. 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. Multiply. 14x + 8 + 4x Commutative Property 4. 14x + 4x + 8 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. Homework • Assignment #22 • 1-7 Part 2 Homework Worksheet • Chapter 1 Quest Thursday!

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