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1-7 Expressions 1-7 Simplifying Simplifying Expressions Warm Up Lesson Presentation Lesson Quiz Holt HoltAlgebra Algebra11 1-7 Simplifying Expressions Learning Target Students will be able to: Use the Commutative, Associative, and Distributive Properties to simplify expressions and Combine like terms. Holt Algebra 1 1-7 Simplifying Expressions Vocabulary term like terms coefficient 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. Holt Algebra 1 1-7 Simplifying Expressions Holt Algebra 1 1-7 Simplifying Expressions 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 Holt Algebra 1 1-7 Simplifying Expressions Example 1B: Using the Commutative and Associative Properties Simplify. 45 + 16 + 55 + 4 45 + 55 + 16 + 4 (45 + 55) + (16 + 4) (100) + (20) 120 Holt Algebra 1 Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 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. Holt Algebra 1 1-7 Simplifying Expressions Check It Out! Example 1a Simplify. Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 21 Holt Algebra 1 1-7 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 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. Holt Algebra 1 1-7 Simplifying Expressions 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 Holt Algebra 1 Rewrite 59 as 50 + 9. Use the Distributive Property. Multiply. Add. 1-7 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) Holt Algebra 1 Rewrite 98 as 100 – 2. Use the Distributive Property. 1200 – 24 Multiply. 1176 Subtract. 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. Like terms Constant 4x – 3x + 2 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. Coefficients 1x2 + 3x 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. 7x2 – 4x2 = (7 – 4)x2 = (3)x2 Factor out x2 from both terms. Perform operations in parenthesis. = 3x2 Notice that you can combine like terms by adding or subtracting the coefficients and keeping the variables and exponents the same. Holt Algebra 1 1-7 Simplifying Expressions Example 3A: Combining Like Terms Simplify the expression by combining like terms. 72p – 25p 72p – 25p 47p Holt Algebra 1 72p and 25p are like terms. Subtract the coefficients. 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. and are like terms. Write 1 as . Add the coefficients. Holt Algebra 1 1-7 Simplifying Expressions Check It Out! Example 3 Simplify by combining like terms. 3a. 16p + 84p 16p + 84p 100p 3b. –20t – 8.5t2 –20t – 8.5t2 –20t – 8.5t2 16p + 84p are like terms. Add the coefficients. 20t and 8.5t2 are not like terms. Do not combine the terms. 3c. 3m2 + m3 3m2 + m3 3m2 + m3 Holt Algebra 1 3m2 and m3 are not like terms. Do not combine the terms. 1-7 Simplifying Expressions 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) 3. 14x + 8 + 4x 4. 14x + 4x + 8 5. (14x + 4x) + 8 6. Holt Algebra 1 18x + 8 Distributive Property Multiply. Commutative Property Associative Property Combine like terms. 1-7 Simplifying Expressions Check It Out! Example 4a Simplify 6(x – 4) + 9. Justify each step. Procedure Justification 1. 6(x – 4) + 9 2. 6(x) – 6(4) + 9 Distributive Property 3. 6x – 24 + 9 4. 6x – 15 Multiply. Combine like terms. Holt Algebra 1 1-7 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. Holt Algebra 1 –16x + 3a Justification Commutative Property Combine like terms. 1-7 Simplifying Expressions Warm Up Add. 1. 427 + 35 462 3. 2. 1.06 + 0.74 1.80 10 Multiply. 4. 25(8) 200 6. Holt Algebra 1 5. 1.3(22) 28.6 1-7 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) Holt Algebra 1 5($2) – 5($0.01) = $9.95 6(10) + 6(3) = 78