1. Commutative Property: + =+ EXAMPLES: a + b = b + a OR 5 + 3 = 3 + 5 a b = b a 5 3 = 3 5 EXAMPLES: a + b = b + a OR 5 + 3 = 3 + 5 a b = b a 5 3 = 3 5 ORDER CHANGES! Your Turn: Apply the Commutative Property by finishing the below examples: 1.6 + 7 = __________ 2. 4 + 3 + 2 = ___________ 3. -5 + x = __________ 4.6 8 = __________ 5. 3x y = __________ 6. -2(4x) = __________ Associative Property: EXAMPLES: a + (b + c) = (a + b) + c OR 3 + (5 + 4) = (3 + 5) + 4 a (b c) = (a b) c 3 (5 4) = (3 5) 4 EXAMPLES: a + (b + c) = (a + b) + c OR 3 + (5 + 4) = (3 + 5) + 4 a (b c) = (a b) c 3 (5 4) = (3 5) 4 + + + + = GROUPING CHANGES! Works for both Addition and Multiplication Your Turn: Apply the Associative Property by finishing the below examples: 1. 4 + (7 + 3) = __________ 2. 2x + (3 + y) = __________ 3. (-3x + 1) + 2 = __________ 4. 3(-2 5) = __________ 5. (xy)z = __________6. 6 (8 4) = __________ Math-7 NOTES DATE: ______/_______/_______ What: properties Why: To identify and apply the commutative, associative, distributive, identity, inverse, and zero properties. What: properties Why: To identify and apply the commutative, associative, distributive, identity, inverse, and zero properties. NAME:

2. Distributive Property: + + = EXAMPLES: a (b + c) = a(b) + a(c) OR 3(5 + 4) = 3(5) + 3(4) EXAMPLES: a (b + c) = a(b) + a(c) OR 3(5 + 4) = 3(5) + 3(4) Your Turn: Apply the Distributive Property by finishing the below examples: 1. 4 (2 + 3) = __________ 2. 2(x + y) = __________ 3.(-5x + 1) 8 = __________ 4. x(9 + 3) = __________ Just remember you can secure your identity if you: Add 0 OR Multiply by 1 EXAMPLES: a + 0 = a OR 5 + 0 = 5 a 1 = a OR 5 1 = 5 EXAMPLES: a + 0 = a OR 5 + 0 = 5 a 1 = a OR 5 1 = 5 Identity Property: Nobody wants to lose their identity! Your Turn: Apply the Identity Property by finishing the below examples: 1. 4 + 0 = _____ 2. x + ____ = _____ 3.8 1 = _____4. -5x _____ = _____

3. Inverse Property: Your Turn: Apply the Inverse Property by finishing the below examples: 1. -8 + 8 = _____ 2. 2y + _____ = _____ 3. = _____ 4. = _____ Zero Property of Multiplication: Your Turn: Apply the Zero Property by finishing the below examples: 1. 12 0 = _____ 2. -5x _____ = _____ 3. x(0) = _____ ALL ABOUT THE OPPOSITE! ALL ABOUT THE OPPOSITE! EXAMPLES: -a + a = 0 OR -5 + 5 = 0 a b 3 4 b a 4 3 EXAMPLES: -a + a = 0 OR -5 + 5 = 0 a b 3 4 b a 4 3 = 1 This is like a zero pair! = 1 ANSWER IS ALWAYS ZERO! ANSWER IS ALWAYS ZERO! If you have 5 empty plates, how much food do you have? Answer: Zero! 5 0 = 0 If you have 5 empty plates, how much food do you have? Answer: Zero! 5 0 = 0

4. RULES FOR PICTURES: 1.Be Creative !!!! 2.Can not use same picture from Notes 3.Name of Property is the Title/Heading (BIG LETTERS) 4.Name must appear in bottom corner (on front) 5.Must turn in by end of block (classwork grade)

5. Math-7 PRACTICE DATE: ______/_______/_______ NAME:__________________________ “Properties” Apply the Commutative Property by re-ordering the following expressions in order to make them easier to evaluate MENTALLY (left to right). Give final answers as well. 1.12 + 11 + 8 = _________________________________________________________________________ 2.(4)(4)(5)= ____________________________________________________________________________ 3.(12)(5)(2)= ___________________________________________________________________________ 4.35 + 13 + 5= ___________________________________________________________________________ Apply the Associative Property by re-grouping the following expressions in order to make them easier to evaluate MENTALLY. Give final answers as well. 5. 9 + (1 + 17) =__________________________________________________________________________ 6. (3 + 19) + 11= ________________________________________________________________________ 7.5(2 ● 9) = ______________________________________________________________________________ Apply BOTH the Commutative and Associative Properties to re-order/ re-group the following expressions in such a way that it is easier to evaluate MENTALLY. Give final answers as well. 8. 4 + 22 + 6 + 8 = ______________________________________________________________________ 9.33 + 5 + 7 + 25 = _____________________________________________________________________ 10.(3)(2)(5)(3) = _________________________________________________________________________ Apply the Distributive Property in order to make it easier to evaluate the following expressions MENTALLY. Give final answers as well. 11.2(5 + 12) =____________________________________________________________________________ 12.4(5 + 9) = _____________________________________________________________________________ 13.4(11 + 6) = ____________________________________________________________________________ 12 + 8 + 11 = 31 Apply the Commutative Property by re-ordering the following expressions in order to make them easier to evaluate MENTALLY (left to right). Give final answers as well. 1.12 + 11 + 8 = _________________________________________________________________________ 2.(4)(4)(5)= ____________________________________________________________________________ 3.(12)(5)(2)= ___________________________________________________________________________ 4.35 + 13 + 5= ___________________________________________________________________________ Apply the Associative Property by re-grouping the following expressions in order to make them easier to evaluate MENTALLY. Give final answers as well. 5. 9 + (1 + 17) =__________________________________________________________________________ 6. (3 + 19) + 11= ________________________________________________________________________ 7.5(2 ● 9) = ______________________________________________________________________________ Apply BOTH the Commutative and Associative Properties to re-order/ re-group the following expressions in such a way that it is easier to evaluate MENTALLY. Give final answers as well. 8. 4 + 22 + 6 + 8 = ______________________________________________________________________ 9.33 + 5 + 7 + 25 = _____________________________________________________________________ 10.(3)(2)(5)(3) = _________________________________________________________________________

6. Apply the Inverse Property in order to make it easier to evaluate the following expressions MENTALLY. Give final answers as well. 14.28 + (4 + -4) = _____________________________________________________________________ 15.(-50 + 50) + -100 = ________________________________________________________________ 16.( 2 / 5 )( 5 / 2 )(-50) = _________________________________________________________________ Identify the properties used for EACH STEP in order to simplify the following expressions: 17. 8 + 5 + (-8) Step 1 = 8 + (-8) + 5_____________________________ Property of Addition Step 2 = [ 8 + (-8) ] + 5_____________________________ Property of Addition Step 3 = 0 + 5_____________________________ Property of Addition Step 4 = 5 _____________________________ Property of Addition 18. 7 + [3(3 + 11)] + 1 Step 1 = 7 + [9 + 33] + 1 _____________________________ Property Step 2 = 1 + [9 + 33] + 7 _____________________________ Property of Addition Step 3 = [ 1 + 9] + [ 33 + 7] _____________________________ Property of Addition Step 4 = 10 + 40 Step 5 = 50 19. [ ( 3 / 4 )(25)( 4 / 3 ) ] + (-25) Step 1 = [ ( 3 / 4 )( 4 / 3 )(25) ] + (-25) _____________________________ Property of Mult. Step 2 = [ 1(25)] + (-25) _____________________________ Property of Mult. Step 3 = [ 25] + (-25) _____________________________ Property of Mult. Step 4 = 0 _____________________________ Property of Add. 20. 3(7 + 8) + ( -5 + 5) Step 1 = 21 + 24 + (-5 + 5) _____________________________ Property Step 2 = 21 + 24 + 0 _____________________________ Property of Addition Step 3 = (21 + 24) + 0 _____________________________ Property of Addition Step 4 = 45 + 0 Step 5 = 45 ______________________________ Property of Addition