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2-5: Properties of Numbers For every real number a, b, and c PropertyAdditionMultiplicationMeaning Commutativea + b = b + aab = baOrder doesn’t matter Associative(a + b) + c = a + (b + c) (ab)c = a(bc)Grouping doesn’t matter Identitya + 0 = a 0 + a = a a 1 = a 1 a = a + 0 or 1 produces the original number Inversea + (-a) = 0Reciprocals cancel out SymmetricIf a = b, then b = aEach side of an = sign can be swapped

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2-5: Properties of Numbers Example 1: Identifying Properties Name the property that each question illustrates. Explain 9 + 7 = 7 + 9 Commutative Property of Addition, because the order of addition changed (d ● 4) ● 3 = d ● (4 ● 3) Associative Property of Multiplication, because the grouping of multiplication changed t + 0 = t Identity Property of Addition, because the sum of any number and zero is the number

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Y OUR T URN Name the property that each question illustrates. Be prepared to explain 1m = m Identity Property of Multiplication (-3 + 4) + 5 = -3 + (4 + 5) Associative Property of Addition np = pn Commutative Property of Multiplication p + q = q + p Commutative Property of Addition

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You can use the properties of real numbers to reorder sums or products so you can calculate more easily. Example 2 Find the sum of 0.85 + 2.50 + 5.15 0.85 + 2.50 + 5.15 2.50 + 5.15 + 0.85Commutative Property 2.50 + (5.15 + 0.85)Associative Property 2.50 + (6)Calculate Parenthesis 8.50Simplify

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2-5: Properties of Numbers Y OUR T URN At the supermarket, you buy a package of cheese for $2.50, a loaf of bread for $2.15, a cucumber for $0.65, and some tomatoes for $3.50. Find the total cost of the groceries. $8.80

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Deductive Reasoning: Using logic from given facts to make a conclusion. You can use deductive reasoning to justify each step in simplifying an expression. Example 3: Justify each step -4b + 9 + b -4b + 9 + 1bIdentity property of multiplication -4b + 1b + 9Commutative property of addition (-4 + 1)b + 9Distributive property -3b + 9addition

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2-5: Properties of Numbers Y OUR T URN Justify each step 2(3t – 1) + 2 6t – 2 + 2 6t 5a + 6 + a 5a + 6 + 1a 5a + 1a + 6 (5 + 1)a + 6 6a + 6 Distributive Property Inverse property of addition Identity property of multiplication Commutative property of addition Distributive property Addition

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2-5: Properties of Numbers Assignment Worksheet #2-5 Problems 1 – 29, odds

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