Properties of Integers Worksheet
Explore and apply the fundamental properties of integers including closure, commutativity, associativity, distributivity, and identity elements.
Includes
Standards
Topics
Properties of Integers
Name:
Date:
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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 integers states that the product of any two integers is always an integer?
Commutative Property
Associative Property
Closure Property
Distributive Property
2. What is the additive identity element for integers?
1
-1
0
Any integer
3. The property states that for any integers a and b, a + b = b + a.
4. The multiplicative inverse of an integer a (where a ≠ 0) is .
5. Division of integers is always closed.
True
False
6. The set of integers is associative under subtraction.
True
False
7. Give an example to illustrate the distributive property of multiplication over addition for integers.
8. Explain why the multiplicative inverse property does not hold for all integers.
9. Plot the integers -3, 0, and 4 on the number line below.
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