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Understanding Commutative and Associative Properties of Addition and Multiplication

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This resource explains the Commutative and Associative Properties of Addition and Multiplication, foundational concepts in mathematics. The Commutative Property states that the order of numbers does not affect their sum or product, illustrated by a + b = b + a and a * b = b * a. The Associative Property highlights that the way numbers are grouped does not change their sum or product, shown by (a + b) + c = a + (b + c) and (a * b) * c = a * (b * c). It also covers the Distributive Property for multiplying over addition and subtraction.

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Understanding Commutative and Associative Properties of Addition and Multiplication

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  1. Notes 1.8 – Properties

  2. Commutative Properties of Addition and Multiplication The order in which numbers are added does not change the _______. _______ = 6 + 7 For any numbers a and b:  a + b = _______ SUM

  3. Commutative Properties of Addition and Multiplication The order in which numbers are _____________ does not change the product. 4 * 3 = ______ For any numbers a and b:  a * b = ______ MULTIPLIED

  4. ADDENDS Associative Properties of Addition and Multiplication The way in which _____________ are grouped does not change the sum. (1 + 6) +____ = 1 + ( 6 + 8) For any numbers a, band c: (a + b) + c = ____ + ( b + c)

  5. Associative Properties of Addition and Multiplication The way in which factors are grouped does not change the ______________. (5 * 4) *7 = 5 * (____ *____) For any numbers a, band c: (a*___) * c = ____ * ( b* ___) PRODUCT

  6. Distributive Property Multiplication over Addition The product of a sum is equal to the _______ of the products. 2 ( __ + 5) = 2(3) + 2(5) For any numbers a, b, and c a (b + c) = ab + a__ SUM

  7. Distributive Property Multiplication over Subtraction The product of a difference is equal to the _______________ of the products. 5(3 – 2) = __(3) – 5(2) For any numbers a, b, and c a (b - c) = ab – a__ DIFFERENCE

  8. Homework : Section1.8 pages 60-63 #’s 5, 7, 9, 11, 13, 16-21

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