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Number Properties

Explore the essential properties of mathematics that govern addition and multiplication, including the Commutative, Associative, Identity, Inverse, and Distributive Properties. Learn how these rules ensure that numbers can be manipulated in various ways without changing the result. This informative guide breaks down each property with clear examples, illustrating concepts like the order of operations and grouping. Enhance your understanding of everyday math and its foundational rules through this concise overview.

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Number Properties

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  1. Number Properties Rules of the game 2-7-1

  2. Properties • Properties are the rules of the game. • If the rules are changed a different kind of math is played. • These properties are for everyday math.

  3. Commutative Property Order doesn’t matter

  4. Commutative Property • Commutative Property of Addition: • a + b = b + a • 7 + 8 = 8 + 7 • The commutative property says the order doesn’t matter for addition.

  5. Commutative Property • Commutative Property of Multiplication: • a x b = b x a • 7 x 8 = 8 x 7 • The commutative property says the order doesn’t matter for multiplication.

  6. Associative Property Grouping Doesn’t Matter

  7. Associative Property • Associative Property of Addition: • (a+b) + c = a + (b+c) • (7+8) + 2 = 7 + (8+2) • 15 + 2 = 7 + 10 • The associative property says the grouping doesn’t matter for addition.

  8. Associative Property • Associative Property of Multiplication: • (a x b) x c = a x (b x c) • (7 x 8) x 2 = 8 x (7 x 2) • 56 x 2 = 8 x 14 • The associative property says the grouping doesn’t matter for multiplication.

  9. Identity Property No change

  10. Identity Property An identity for a particular operation doesn’t change the identity of the number when the operation is done.

  11. Identity Property • Additive Identity is 0: • a + 0 = a • 7 + 0 = 7 • Zero plus a number is that number.

  12. Identity Property • Multiplicative Identity is 1: • 1 x a = a • 8 x 1 = 8 • One times a number is that number.

  13. Inverse Property Opposite

  14. Inverse Property • Additive inverse – opposite – subtraction • Another number that added to the original number is equal to the Additive Identity: 0 • Multiplicative inverse – opposite – division • Another number that multiplied by the original number is equal to the Multiplicative Identity: 1

  15. Distributive Property Connecting Addition to Multiplication

  16. Distributive Property • Distributive Property • a (b + c) = ab + ac • 6 (3 + 2) = 18 + 12 • 7 (x + 1) = 7x + 7 • Multiplying a sum by some number is the same as multiplying each term by that same number.

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