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Name_____________________________ Date________________ Period_____ ALGEBRA 1 ASSOCIATIVE/COMMUTATIVE/DISTRIBUTIVE/IDENTITY/INVERSE Properties Worksheet Directions: The following expressions have been simplified. Tell which property was used in each step. As always, SHOW ALL WORK TO RECEIVE ANY CREDIT. ex.) 5 (2 + x) - 8x = (10 + 5x) - 8x = Distributive Property 10 + (5x – 8x) = Associative Property 10 + -3x = -3x + 10 1.) 2.) Commutative Property 3a – 5b + 7a= 3a + 7a - 5b= ________________________ 10a – 5b ________________________ 23 + 5c + 7d – c – d - 27= 23 - 27 + 5c - c+ 7d – d = 3.) Combining Like Terms ________________________ -4 + 4c + 6d ________________________ 4c + 6d - 4 ________________________ 3 (2 + y) - 4y= (6 + 3y) - 4y = ________________________ 6 + (3y - 4y) = ________________________ 6 + -y ________________________ -y + 6 ________________________ Directions: Simplify the expression and tell which property you used for each step. Hint: you should have about as many steps as there are lines. Use #1, 2, and 3 as examples. 4.) 3 (4 + r) = ________________________ ________________________ 5.) 7a – 2 (a + b) = ________________________ ________________________ ________________________ 6.) 8 – x + 4 (3x – 5) ________________________ ________________________ ________________________ ________________________ 7.) -11 (2x + 2) – 16x ________________________ ________________________ ________________________ ________________________ Directions: Identify the properties (distributive, commutative, associative, identity or inverse) that make the below statements true. 8.) (y + 4) – 7 = y + (4 - 7) 9.) 7x + 0 = 7x ____________________ ____________________ 10.) (½) 2x = x ____________________ 12.) 32ab(1) = 32ab 11.) 5x – 7 + 7 = 5x ____________________ ____________________ 13.) 4x – 5 = -5 + 4x ____________________