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**Mastering Real Number Properties** Uncover the intricacies of commutative, associative, distributive, and identity pro

Explore the key properties of real numbers like commutative and associative, and understand how they affect addition and multiplication. Discover the identity properties and the concept of inverses in this engaging learning experience.

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**Mastering Real Number Properties** Uncover the intricacies of commutative, associative, distributive, and identity pro

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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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