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1 PROPERTIES Pre-Algebra

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2 Vocabulary Equivalent expressions — expressions that have the same value Property — Statement that is true for any # or variable

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3 Vocabulary Distributive Property—To multiply a sum by a number, multiply each addend of the sum by the number outside the parentheses. Ex: 3(4 + 6) = 3(4) + 3(6)

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4 Vocabulary Commutative Property—The order in which two numbers are added or multiplied does not change their sum or product. Ex:5 + 4 = 4 + 5 9 x 7 = 7 x 9

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5 Vocabulary Associative Property—The way in which three numbers are grouped when they are added or multiplied does not change their sum or product. Ex:(2 x 3) x 7 = 2 x (3 x 7) (6 + 4) +8 = 6 + (4 + 8)

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6 Vocabulary Identity Property—The sum of an addend and zero is the addend. The product of a factor and one is the factor. Additive Identity—Identity is zero. Multiplicative Identity—Identity is one. Ex:5 x 1 = 59 + 0 = 9

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7 Name the property shown by each statement. a. 6 + (2 + 7) = (6 + 2) +7 b.15 x 10 = 10 x 15 c.4 x 1 = 4 d.4(6 + 8) = 4(6) + 4(8) e.1 x (3 x 4) = (1 x 3) x 4

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8 Name the property shown by each statement. a. 4(a + 5) = 4(a) + 4(5) b. 7 = 1 x 7 c. 24 + 5 = 5 + 24 d. 7 + 0 = 7 e.(11 x 4) x 8 = 11 x (4 x 8)

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9 Name the property shown by each statement. m + n = n + m 123456789101112131415161718192021222324252627282930 1. associative 2. commutative 3. identity 4. distributive

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10 Name the property shown by each statement. 3 + 0 = 3 123456789101112131415161718192021222324252627282930 1. associative 2. commutative 3. identity 4. distributive

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11 How to use the Distributive Property to write an expression as an equivalent expression… Example: 3(7 + 4) Example: 3(7 + 4) Step 1: Multiply the number outside the parenthesis to each number inside the parenthesis. 3 ∙ 7 + 3 ∙ 4 ----- This is your equivalent expression, now evaluate. Step 2: Add the two products. 21 + 12 = 33

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12 Use the distribute property to write an equivalent expression then evaluate. (3 + 8)4 (3 + 8)4 (11 + 3)8 (11 + 3)8 7(8-6) 7(8-6)

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13 Use the distributive property to write 2(5 + 3) as an equivalent expression then evaluate. 123456789101112131415161718192021222324252627282930 1. 2(8); 16 2. 2(5) + 2(3); 16 3. 2(5) + 3; 13 4. (5 + 3)2; 16

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14 Class Work

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