Properties of Real Numbers Worksheet
Explore and apply the fundamental properties of real numbers including commutative, associative, distributive, identity, and inverse properties.
Includes
Standards
Properties of Real Numbers
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Read each question carefully and answer to the best of your ability. Show all 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
Additive Identity Property
2. The property a(b + c) = ab + ac is known as the:
Commutative Property
Associative Property
Distributive Property
Inverse Property
3. The property states that for any real number a, a + 0 = a.
4. The multiplicative inverse of a non-zero real number 'a' is , such that a * (1/a) = 1.
5. The set of real numbers is closed under division by zero.
True
False
6. The commutative property applies to subtraction of real numbers.
True
False
7. Explain the difference between the associative property and the commutative property.
8. Provide an example of the distributive property in action with numbers.
9. Plot the following numbers on the number line below: -2.5, 0, 1.75, 4
10. Discuss how the properties of real numbers are essential for simplifying algebraic expressions and solving equations. Provide specific examples for each property you mention.
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