1. Holt McDougal Algebra 1 1-7 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

2. Holt McDougal Algebra 1 1-7 Simplifying Expressions Homework: Questions? Answer to 2 nd page was… “When Your Nose Runs And Your Feet Smell”

3. Holt McDougal Algebra 1 1-7 Simplifying Expressions Use the Commutative, Associative, and Distributive Properties to simplify expressions. Combine like terms. Objectives

4. Holt McDougal Algebra 1 1-7 Simplifying Expressions The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it.

5. Holt McDougal Algebra 1 1-7 Simplifying Expressions

6. Holt McDougal Algebra 1 1-7 Simplifying Expressions Example 1: Using the Commutative and Associative Properties Simplify. 11(5) 55 Use the Commutative Property. Use the Associative Property to make groups of compatible numbers.

7. Holt McDougal Algebra 1 1-7 Simplifying Expressions Simplify. Example 3: Using the Commutative and Associative Properties 45 + 16 + 55 + 4 45 + 55 + 16 + 4 (45 + 55) + (16 + 4) 100 + 20

8. Holt McDougal Algebra 1 1-7 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.

9. Holt McDougal Algebra 1 1-7 Simplifying Expressions Example 4 Simplify. 21 Use the Commutative Property. Use the Associative Property to make groups of compatible numbers.

10. Holt McDougal Algebra 1 1-7 Simplifying Expressions Example 5 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

11. Holt McDougal Algebra 1 1-7 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.

12. Holt McDougal Algebra 1 1-7 Simplifying Expressions Example 6 Write the product using the Distributive Property. Then simplify. 5(59) 5(60 – 1) 5(60) – 5(1) 300 – 5 295 Rewrite 59 as 60 - 1. Use the Distributive Property. Multiply. Subtract.

13. Holt McDougal Algebra 1 1-7 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. Example 7 Write the product using the Distributive Property. Then simplify.

14. Holt McDougal Algebra 1 1-7 Simplifying Expressions The terms of an expression are the parts to be added or subtracted. 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

15. Holt McDougal Algebra 1 1-7 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

16. Holt McDougal Algebra 1 1-7 Simplifying Expressions Using the Distributive Property can help you combine like terms. You can factor out the common factors to simplify the expression. 7x 2 – 4x 2 = (7 – 4)x 2 = (3)x 2 = 3x 2 Factor out x 2 from both terms. Perform operations in parenthesis. Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.

17. Holt McDougal Algebra 1 1-7 Simplifying Expressions Example 10 Simplify the expression by combining like terms. 72p – 25p 47p 72p and 25p are like terms. Subtract the coefficients.

18. Holt McDougal Algebra 1 1-7 Simplifying Expressions Example 11 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.

19. Holt McDougal Algebra 1 1-7 Simplifying Expressions Try these on your own… 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 Subtract 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

20. Holt McDougal Algebra 1 1-7 Simplifying Expressions 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

21. Holt McDougal Algebra 1 1-7 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.

22. Holt McDougal Algebra 1 1-7 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.

23. Holt McDougal Algebra 1 1-7 Simplifying Expressions Exit Card 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)

24. Holt McDougal Algebra 1 1-7 Simplifying Expressions Exit Card (Continued) 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. 6. 14c 2 – 9c

25. Holt McDougal Algebra 1 1-7 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

26. Holt McDougal Algebra 1 1-7 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