Properties of Real Numbers - Grade 12
Explore and apply the fundamental properties of real numbers including commutative, associative, distributive, identity, and inverse properties.
Includes
Topics
Properties of Real Numbers
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Read each question carefully and answer to the best of your ability. Show all your work where necessary.
1. Which property of real numbers is demonstrated by the equation 5 + (3 + 2) = (5 + 3) + 2?
Commutative Property of Addition
Associative Property of Addition
Distributive Property
Identity Property of Addition
2. The product of any real number and its multiplicative inverse is:
0
1
-1
The number itself
3. The Property states that a(b + c) = ab + ac.
4. The additive inverse of a real number 'a' is .
5. The number 0 is the identity for addition.
6. All rational numbers are also irrational numbers.
True
False
7. The set of real numbers is closed under subtraction.
True
False
8. Explain the difference between the Commutative Property and the Associative Property of Addition. Provide an example for each.
9. Use the Distributive Property to simplify the expression: 3(2x - 5).
10. Plot the following real numbers on the number line below: -2.5, 0, 1.75, 4.
Match each property with its example.
11. Commutative Property of Multiplication
a. 7 + 0 = 7
12. Identity Property of Addition
b. 4 * (1/4) = 1
13. Inverse Property of Multiplication
c. 6 * 3 = 3 * 6
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