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Properties of Real Numbers

Properties of Real Numbers. Commutative Associative Distributive Identity + × Inverse + ×. Commutative Properties. Changing the order of the numbers in addition or multiplication will not change the result. Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a.

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Properties of Real Numbers

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  1. Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×

  2. Commutative Properties • Changing the order of the numbers in addition or multiplication will not change the result. • Commutative Property of Addition states: 2 + 3 = 3 + 2 or a + b = b + a. • Commutative Property of Multiplication states: 4 • 5 = 5 • 4 or ab = ba.

  3. Associative Properties • Changing the grouping of the numbers in addition or multiplication will not change the result. • Associative Property of Addition states: 3 + (4 + 5)= (3 + 4)+ 5 or a + (b + c)= (a + b)+ c • Associative Property of Multiplication states: (2 • 3) • 4 = 2 • (3 • 4) or (ab)c = a(bc)

  4. Distributive Property • Multiplication distributes over addition.

  5. Additive Identity Property • There exists a unique number 0 such that zero preserves identities under addition. a + 0 = a and 0 + a = a • In other words adding zero to a number does not change its value.

  6. Multiplicative Identity Property • There exists a unique number 1 such that the number 1 preserves identities under multiplication. a∙ 1 = a and 1 ∙a = a • In other words multiplying a number by 1 does not change the value of the number.

  7. Additive Inverse Property • For each real number a there exists a unique real number –a such that their sum is zero. a + (-a) = 0 • In other words opposites add to zero.

  8. Multiplicative Inverse Property • For each real number a there exists a unique real number such that their product is 1.

  9. Let’s play “Name that property!”

  10. State the property or properties that justify the following. 3 + 2 = 2 + 3 Commutative Property

  11. State the property or properties that justify the following. 10(1/10) = 1 Multiplicative Inverse Property

  12. State the property or properties that justify the following. 3(x – 10) = 3x – 30 Distributive Property

  13. State the property or properties that justify the following. 3 + (4 + 5) = (3 + 4) + 5 Associative Property

  14. State the property or properties that justify the following. (5 + 2) + 9 = (2 + 5) + 9 Commutative Property

  15. 2. Which Property? 3 + 7 = 7 + 3 Commutative Property of Addition

  16. 3. Which Property? 8 + 0 = 8 Identity Property of Addition

  17. 5. Which Property? 6 • 4 = 4 • 6 Commutative Property of Multiplication

  18. 11. Which Property? 5 • 1 = 5 Identity Property of Multiplication

  19. 25. Which Property? 51/7 + 0 = 51/7 Identity Property of Addition

  20. 40. Which Property? a + (-a) = 0 Inverse Property of Addition

  21. Properties of Real Numbers Commutative Associative Distributive Identity + × Inverse + ×

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