1 PROPERTIES Pre-Algebra

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

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)

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

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)

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 = = 9

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

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

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

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

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 ∙ ∙ This is your equivalent expression, now evaluate. Step 2: Add the two products = 33

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)

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

14 Class Work