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Name: ____________________________________________ Date: _______________ Block: ______ Learning Target 7.16: The student will apply the following properties of operations with real numbers: the distributive property; and the multiplicative property of zero. Properties of Real Numbers Associative vs. Commutative Associative Properties Associative Property of Addition Numbers being added may be regrouped without affecting the final sum. Associative Property of Multiplication Numbers being multiplied may be regrouped without affecting the final product. Commutative Properties Commutative Property of Addition Changing the order of the numbers being added will not change the final sum. Commutative Property of Multiplication Changing the order of factors being multiplied will not change the final product. What makes associative and commutative different? __________________________________________________________ Commutative & Associative Properties Match-draw a line to the correct definition. 1. Commutative Property 2. Associative Property a. When adding or multiplying multiple numbers, the order stays the same, but the grouping changes. Your answer will be the same. b. When adding or multiplying multiple numbers the order can change, your answer will be the same. Identify if the equation is an example of the commutative or associative property. Use the following: Commutative of addition Associative of addition 3. 6+5=5+6_____________________ 4. 2(6∙7)=(2∙6)∙7_________________ Commutative of multiplication Associative of multiplication Complete the process for the Commutative Property Ex: 5+6 = 6+5 5. 8∙3=3∙8______________________ 12.12+14=______________________ 6. 14+(22+6)=(14+22)+6__________ 13. ab=_________________________ 7. 7+16=16+7___________________ 14.5∙8=_________________________ 8. ab=ba_______________________ 15.b+a=________________________ 9. a+(b+c)=(a+b)+c______________ Complete the process for the Associative Property 16.2(5∙8)=______________________ 10.m+n=n+m____________________ 11.a (bc)=(ab)∙c__________________ 17.(5+9)+7=_____________________ 18.a+(b+c)=_____________________ 19.(ab)∙c=_______________________ 20.7(8∙9)=______________________ Distributive Property Definition: This property is used to multiply a number by the sum or difference of two numbers in parentheses. The first number is “distributed” across the parentheses by multiplying it with both of the numbers inside the parentheses. Examples: How can you use the Distributive Property to multiply large numbers? 3 • 34 1.) 3.) 5 (4 + 6) 6 • 47 ______________ 8 • 103 2.) 8 (12 – 5) _______________ 4.) –6 (12 + 3) _______________ y (2 – x) __________________ 7.) 9 (13) – 9 (3) = _______________ 8.) 4 (11) + 4 (14) = __________ 22.) 4(12 + 15) 23.) 3(a + 2b) 24.) x (6 + 8) 25.) 6(9 – r) 26.) 15(p – 2q) 27.) 9(f – 3e) 28.) Create your own distributive problem.