1. 1-8 Simplifying Expressions Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation

2. 1-8 Simplifying Expressions Warm Up Add. 1. 427 + 35 2. 1.06 + 0.74 3. Multiply. 4. 25(8) 6. 5. 1.3(22)28.6 200 10 462 1.80

3. 1-8 Simplifying Expressions MA.912.A.3.2 Identify and apply the distributive, associative, and commutative properties of real numbers…. Sunshine State Standards

4. 1-8 Simplifying Expressions Use the Commutative, Associative, and Distributive Properties to simplify expressions. Combine like terms. Objectives

5. 1-8 Simplifying Expressions term like terms coefficient Vocabulary

6. 1-8 Simplifying Expressions The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it.

7. 1-8 Simplifying Expressions

8. 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.

9. 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.

10. 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.

11. 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.

12. 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.

13. 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. 1212 7 8 1212 8 7 ( ) 1212 87 4 7

14. 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.

15. 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.

16. 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.

17. 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.

18. 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.

19. 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.

20. 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

21. 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. 1x 2 + 3x Coefficients

22. 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. 7x 2 + 4x 2 = (7 + 4)x 2 = (11)x 2 = 11x 2 Factor out x 2 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.

23. 1-8 Simplifying Expressions Add only the coefficients. 6.8y 2 + (-y 2 ) ≠ 6.8 Caution!

24. 1-8 Simplifying Expressions Additional Example 3A: Combining Like Terms Simplify the expression by combining like terms. 72p – 25p 47p 72p and 25p are like terms. Subtract the coefficients.

25. 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.

26. 1-8 Simplifying Expressions Additional 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.

27. 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. 3m 2 + m 3 3m 2 and m 3 are not like terms. 3c. 3m 2 + m 3 Do not combine the terms. 3m 2 + m 3

28. 1-8 Simplifying Expressions Additional 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

29. 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.

30. 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.

31. 1-8 Simplifying Expressions Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

32. 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

33. 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 + b 2 + 3a + 2b 2 5. 300x 27a + 3b 2 6. 14c 2 – 9c 14c 2 – 9c

34. 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

35. 1-8 Simplifying Expressions 2. Simplify A. 5 B. 6 C. 10 D. – 5 Lesson Quiz for Student Response Systems

36. 1-8 Simplifying Expressions 3. Which of the following are like terms? A. 3x and 2y B. 3x and 2x C. 3x and x 2 D. 3x and 2x Lesson Quiz for Student Response Systems

37. 1-8 Simplifying Expressions 4. Simplify by combining like terms. 2x 2 + x 2 A. 2x 4 B. 3x 4 C. 3x 2 D. 4x 2 Lesson Quiz for Student Response Systems