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Transcript of Algebra unit 1.7

• UNIT 1.7 COMMUTATIVE, ASSOCIATIVE AND DISTRIBUTIVE PROPERTIES

1. 427 + 35 2. 1.06 + 0.743. Multiply.4. 25(8)6. 5. 1.3(22)28.6200104621.80

• Use the Commutative, Associative, and Distributive Properties to simplify expressions.

Combine like terms.Objectives

• termlike termscoefficient

Vocabulary

• The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it.

• Example 1A: Using the Commutative and Associative PropertiesSimplify.11(5)55Use the Commutative Property.Use the Associative Property to make groups of compatible numbers.

• Simplify.Example 1B: Using the Commutative and Associative Properties45 + 16 + 55 + 445 + 55 + 16 + 4(45 + 55) + (16 + 4)(100) + (20)120Use the Commutative Property.Use the Associative Property to make groups of compatible numbers.

• Check It Out! Example 1aSimplify. 21Use the Commutative Property.Use the Associative Property to make groups of compatible numbers.

• Check It Out! Example 1bSimplify. 410 + 58 + 90 + 2410 + 90 + 58 + 2(410 + 90) + (58 + 2)(500) + (60)560Use the Commutative Property.Use the Associative Property to make groups of compatible numbers.

• Check It Out! Example 1cSimplify. 28Use the Commutative Property.Use the Associative Property to make groups of compatible numbers.

• 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.

• 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 + 45295Rewrite 59 as 50 + 9.Use the Distributive Property.Multiply.Add.

• 8(33)8(30 + 3)8(30) + 8(3)240 + 24264Rewrite 33 as 30 + 3.Use the Distributive Property.Multiply.Add.Example 2B: Using the Distributive Property with Mental Math Write the product using the Distributive Property. Then simplify.

• Check It Out! Example 2a9(52)9(50) + 9(2)9(50 + 2)450 + 18468Rewrite 52 as 50 + 2.Use the Distributive Property.Multiply.Add.Write the product using the Distributive Property. Then simplify.

• Check It Out! Example 2b12(98)1176Rewrite 98 as 100 2.Use the Distributive Property.Multiply.Subtract.12(100 2)1200 2412(100) 12(2)Write the product using the Distributive Property. Then simplify.

• Check It Out! Example 2c7(34)7(30 + 4)7(30) + 7(4)210 + 28238Rewrite 34 as 30 + 4.Use the Distributive Property.Multiply.Add.Write the product using the Distributive Property. Then simplify.

• 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 + 2Like termsConstant

• 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 1.1x2 + 3xCoefficients

• 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= 3x2Factor out x2 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.

• Example 3A: Combining Like TermsSimplify the expression by combining like terms.72p 25p 72p 25p 47p72p and 25p are like terms.Subtract the coefficients.

• Example 3B: Combining Like TermsSimplify the expression by combining like terms.A variable without a coefficient has a coefficient of 1.Add the coefficients.

• Example 3C: Combining Like TermsSimplify the expression by combining like terms.0.5m + 2.5n0.5m + 2.5n0.5m + 2.5n0.5m and 2.5n are not like terms.Do not combine the terms.

• Check It Out! Example 3Simplify by combining like terms.3a. 16p + 84p16p + 84p100p16p + 84p are like terms. Add the coefficients.3b. 20t 8.5t220t 8.5t220t and 8.5t2 are not like terms.20t 8.5t2Do not combine the terms.3m2 + m33m2 and m3 are not like terms.3c. 3m2 + m3Do not combine the terms.

• Example 4: Simplifying Algebraic ExpressionsSimplify 14x + 4(2 + x). Justify each step.14x + 4(2) + 4(x)Distributive PropertyMultiply.Commutative PropertyAssociative PropertyCombine like terms.14x + 8 + 4x(14x + 4x) + 8 14x + 4x + 818x + 814x + 4(2 + x)1. 2. 3. 4. 5. 6. ProcedureJustification

• 6(x) 6(4) + 9Distributive PropertyMultiply.Combine like terms.6x 24 + 96x 156(x 4) + 91. 2. 3. 4. ProcedureJustificationCheck It Out! Example 4aSimplify 6(x 4) + 9. Justify each step.

• 12x 5x + x + 3aCommutative PropertyCombine like terms.16x + 3a12x 5x + 3a + x1. 2. 3. ProcedureJustificationCheck It Out! Example 4bSimplify 12x 5x + 3a + x. Justify each step.

• Lesson Quiz: Part ISimplify each expression.1. 165 +27 + 3 + 5Write each product using the Distributive Property. Then simplify. 3. 5(\$1.99)4. 6(13)20085(\$2) 5(\$0.01) = \$9.956(10) + 6(3) = 78

• Lesson Quiz: Part IISimplify each expression by combining like terms. Justify each step with an operation or property.7. 301x x 8. 24a + b2 + 3a + 2b2 5.300x27a + 3b26. 14c2 9c 14c2 9c

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