Properties of Real Numbers
Explore and apply the fundamental properties of real numbers including commutative, associative, distributive, identity, and inverse properties.
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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 applicable.
1. Which property is illustrated by the equation 5 + (3 + 2) = (5 + 3) + 2?
Commutative Property of Addition
Associative Property of Addition
Distributive Property
Identity Property of Addition
2. Which property states that a(b + c) = ab + ac?
Associative Property
Commutative Property
Distributive Property
Identity Property
3. The property states that changing the order of numbers in an addition or multiplication operation does not change the result.
4. The number 0 is the for addition.
5. The inverse property of multiplication states that for every non-zero real number 'a', there exists a real number 1/a such that a * (1/a) = .
6. The set of real numbers is closed under division (excluding division by zero).
True
False
7. The number line below shows the positions of various real numbers. Is the statement '√2 is between 1 and 2' true or false?
True
False
8. Explain the difference between the associative property and the commutative property.
Match each expression with the property it demonstrates.
9. 7 + 0 = 7
a. Commutative Property of Multiplication
10. 4 * (1/4) = 1
b. Inverse Property of Multiplication
11. 3 * 5 = 5 * 3
c. Identity Property of Addition
12. 2(x + 3) = 2x + 6
d. Distributive Property
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