1. Holt Algebra 1 1-7 Simplifying Expressions 1-7 Simplifying Expressions Holt Algebra 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

2. Holt Algebra 1 1-7 Simplifying Expressions Warm Up Add. 1. 2. 3. 4. 6.5.

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

4. Holt Algebra 1 1-7 Simplifying Expressions term like terms coefficient Vocabulary

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

6. Holt Algebra 1 1-7 Simplifying Expressions

7. Holt Algebra 1 1-7 Simplifying Expressions 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.

8. Holt Algebra 1 1-7 Simplifying Expressions Simplify. 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.

9. Holt 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.

10. Holt Algebra 1 1-7 Simplifying Expressions Check It Out! Example 1a Simplify. 21 Use the Commutative Property. Use the Associative Property to make groups of compatible numbers.

11. Holt Algebra 1 1-7 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.

12. Holt Algebra 1 1-7 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

13. Holt 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.

14. Holt 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. Like terms can also be constants. 4x – 3x + 2 Like terms Constant

15. Holt 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. BEWARE: The “Invisible 1”! 1x 2 + 3x Coefficients

16. Holt 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 = = (3)x 2 = 3x 2 Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same.

17. Holt Algebra 1 1-7 Simplifying Expressions Example 3A: Combining Like Terms Simplify the expression by combining like terms. 72p – 25p 47p 72p and 25p are like terms. Subtract the coefficients.

18. Holt Algebra 1 1-7 Simplifying Expressions 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.

19. Holt Algebra 1 1-7 Simplifying Expressions Example 3C: Combining Like Terms Simplify the expression by combining like terms. 0.5b + 2.5n 0.5b and 2.5n are not like terms. Do not combine the terms.

20. Holt Algebra 1 1-7 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 2 –20t – 8.5t 2 20t and 8.5t 2 are not like terms. –20t – 8.5t 2 Do not combine the terms. 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

21. Holt 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

22. Holt 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.

23. Holt 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.

24. Holt 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. 3. 301x – x 4. 24a + b 2 + 3a + 2b 2 1. 300x 27a + 3b 2 2. 14c 2 – 9c 14c 2 – 9c