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Over Lesson 1–2 A.A B.B C.C D.D 5-Minute Check 1 A.15 B.11 C.7 D.6 Evaluate the expression c + 8 – a if a = 4 and c = 3. Evaluate the expression 7a – (2c + b) if a = 4, b = 2, and c = 3. A.36 B.24 C.22 D.20

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Then/Now You have already evaluated numerical and algebraic expressions. (Lessons 1–1 and 1–2) Identify and use properties of addition and multiplication. Use properties of addition and multiplication to simplify algebraic expressions.

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Vocabulary properties counterexample simplify deductive reasoning

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Concept A

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Concept B

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Concept C

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Example 1 Find a Counterexample State whether the following conjecture is true or false. If false, provide a counterexample. Division of whole numbers is commutative. Write two division expressions using the Commutative Property, and then check to see whether they are equal. Answer: The conjecture is false. 12 ÷ 6 = 6 ÷ 12State the conjecture. ? 2 ≠ 0.5Divide. We found a counterexample. That is, 12 ÷ 6 ≠ 6 ÷ 12. So, division is not commutative.

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A.A B.B C.C D.D Example 1 A.true B.false, 7 – 4 = 7 – 4 C.false, 7 – 4 ≠ 4 – 7 D.false, (7 – 4) – 2 ≠ 7 – (4 – 2) State whether the following conjecture is true or false. If false, provide a counterexample. Subtraction of whole numbers is commutative.

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Example 2A Identify Properties A. Name the property shown by the statement. 3 ● 10 ● 2 = 3 ● 2 ● 10 Answer: The order of the numbers changed. This is the Commutative Property of Multiplication.

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Example 2B Identify Properties B. Name the property shown by the statement. (2 + 5) + m = 2 + (5 + m) Answer: The grouping of the numbers and variables changed. This is the Associative Property of Addition.

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A.A B.B C.C D.D Example 2A A.Commutative Property of Multiplication B.Associative Property of Multiplication C.Multiplicative Identity D.Multiplicative Property of Zero A. Name the property shown by the statement. (4 ● 6) ● 2 = 4 ● (6 ● 2)

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A.A B.B C.C D.D Example 2B A.Commutative Property of Addition B.Associative Property of Addition C.Additive Identity D.Distributive Property B. Name the property shown by the statement. 12 + 9 = 9 + 12

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Example 3A Simplify Algebraic Expressions A. Simplify 12 + (x + 18). Label the property for each step Answer: 30 + x Simplify.Associative Property of Addition Commutative Property of Addition

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Example 3B Simplify Algebraic Expressions B. Simplify 5 ● (3 ● r). Label the property for each step Answer: 15r 5 ● (3 ● r) = (5 ● 3)r Associative Property of Multiplication = 15rSimplify.

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A.A B.B C.C D.D Example 3A A.10a B.24 + a C.2a D.24a A. Simplify (6 ● a) ● 4.

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A.A B.B C.C D.D Example 3B A.19 + m B.19m C.5 + m D.12m + 7 B. Simplify 7 + (12 + m).

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End of the Lesson

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