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Number Properties

Number Properties. Rules of the game 2-7-1. 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. Commutative Property. Order doesn’t matter. Commutative Property.

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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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