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1-8 Simplifying Expressions Warm Up Lesson Presentation Lesson Quiz 1-8 Simplifying Expressions Warm Up Add. 1. 427 + 35 462 3. 2. 1.06 + 0.74 1.80 10 Multiply. 4. 25(8) 200 6. 5. 1.3(22) 28.6 1-8 Simplifying Expressions Sunshine State Standards MA.912.A.3.2 Identify and apply the distributive, associative, and commutative properties of real numbers…. 1-8 Simplifying Expressions Objectives Use the Commutative, Associative, and Distributive Properties to simplify expressions. Combine like terms. 1-8 Simplifying Expressions Vocabulary term like terms coefficient 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. Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 11(5) 55 1-8 Simplifying Expressions Additional Example 1B: Using the Commutative and Associative Properties Simplify. 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. Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 21 1-8 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 1-8 Simplifying Expressions Check It Out! Example 1c Simplify. 1 • 7•8 2 1 2 1 (2 • 8 • • 7 8) 7 4•7 28 Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 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 Additional 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 Rewrite 33 as 30 + 3. Use the Distributive Property. Multiply. Add. 1-8 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 Rewrite 52 as 50 + 2. Use the Distributive Property. Multiply. Add. 1-8 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. 1-8 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 Rewrite 34 as 30 + 4. Use the Distributive Property. Multiply. Add. 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. Like terms Constant 4x – 3x + 2 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. Coefficients 1x2 + 3x 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 Factor out x2 from both terms. Perform operations in parentheses. = 11x2 Notice that you can combine like terms by adding the coefficients and keeping the variables and exponents the same. 1-8 Simplifying Expressions Caution! Add only the coefficients. 6.8y2 + (-y2) ≠ 6.8 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. and are like terms. Write 1 as . Add the coefficients. 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 and 2.5n are not like terms. 0.5m + 2.5n 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 3b. –20t – 8.5t –20t – 8.5t –28.5t 16p + 84p are like terms. Add the coefficients. 20t and 8.5t are like terms. Add the coefficients. 3c. 3m2 + m3 3m2 + m3 3m2 + m3 3m2 and m3 are not like terms. Do not combine the terms. 1-8 Simplifying Expressions Additional Example 4: Simplifying Algebraic Expressions Simplify 14x + 4(2 + x). Justify each step. Procedure 1. 2. Justification 14x + 4(2 + x) 14x + 4(2) + 4(x) Distributive Property 3. 14x + 8 + 4x Multiply. 4. 14x + 4x + 8 Commutative Property 5. (14x + 4x) + 8 6. 18x + 8 Associative Property Combine like terms. 1-8 Simplifying Expressions Check It Out! Example 4a Simplify 6(x – 4) + 9. Justify each step. Procedure 1. 6(x – 4) + 9 2. 6(x) – 6(4) + 9 3. 6x – 24 + 9 4. 6x – 15 Justification Distributive Property Multiply. Combine like terms. 1-8 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 Justification Commutative Property Combine like terms. 1-8 Simplifying Expressions Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 1-8 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) 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. 5. 6. 14c2 – 9c 14c2 – 9c 7. 301x – x 300x 8. 24a + b2 + 3a + 2b2 27a + 3b2 1-8 Simplifying Expressions Lesson Quiz for Student Response Systems 1. Which property states that you can add or multiply in any order? A. Associative B. Commutative C. Multiplicative D. Grouping 1-8 Simplifying Expressions Lesson Quiz for Student Response Systems 2. Simplify A. 5 B. 6 C. 10 D. –5 1-8 Simplifying Expressions Lesson Quiz for Student Response Systems 3. Which of the following are like terms? A. 3x and 2y B. 3x and 2x C. 3x and x2 D. 3x and 2x 1-8 Simplifying Expressions Lesson Quiz for Student Response Systems 4. Simplify by combining like terms. 2x2 + x2 A. 2x4 B. 3x4 C. 3x2 D. 4x2