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Properties of Real Numbers Worksheet

Explore and apply the fundamental properties of real numbers including commutative, associative, distributive, identity, and inverse properties.

Grade 11 Math Number SenseProperties of Real Numbers
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Multiple ChoiceFill in the BlanksTrue / FalseShort AnswerCustomLong Answer

Standards

CCSS.MATH.CONTENT.HSA.APR.A.1CCSS.MATH.CONTENT.HSN.RN.B.3
8 sections · Free to use · Printable
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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 work where applicable.

1. Which property is illustrated by the equation 5 + (3 + 2) = (5 + 3) + 2?

a

Commutative Property of Addition

b

Associative Property of Addition

c

Distributive Property

d

Additive Identity Property

2. The property a(b + c) = ab + ac is known as the:

a

Commutative Property

b

Associative Property

c

Distributive Property

d

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.

T

True

F

False

6. The commutative property applies to subtraction of real numbers.

T

True

F

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

-5 -2.5 0 1.75 4 5

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.