Properties of Integers Worksheet

Explore and apply the fundamental properties of integers including closure, commutativity, associativity, identity, and inverse for addition and multiplication.

Grade 10 Math Number SenseProperties of Integers

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Includes

Multiple ChoiceFill in the BlanksTrue / FalseShort AnswerMatching

Standards

CCSS.MATH.CONTENT.7.NS.A.3CCSS.MATH.CONTENT.HSA.APR.A.1

Topics

integersnumber sensepropertiesgrade 10math

7 sections · Free to use · Printable

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Properties of Integers

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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 states that the order in which two integers are added or multiplied does not affect the result?

Associative Property

Commutative Property

Distributive Property

Identity Property

2. What is the additive inverse of -15?

-15

1/15

3. The property states that for any integers a, b, and c, (a + b) + c = a + (b + c).

4. The multiplicative identity for integers is .

5. The set of integers is under subtraction, meaning that subtracting two integers always results in an integer.

6. The set of integers is closed under division.

True

False

7. The distributive property allows us to multiply a sum by multiplying each addend separately and then adding the products.

True

False

8. Explain the difference between the additive identity and the multiplicative identity for integers.

9. Provide an example to illustrate the associative property of multiplication with three integers.

Match each property with its description.

10. Commutative Property

a. The sum of an integer and its opposite is zero.

11. Associative Property

b. The grouping of integers in addition or multiplication does not affect the result.

12. Additive Inverse Property

c. The order of integers in addition or multiplication does not affect the result.

13. Multiplicative Identity Property

d. Any integer multiplied by one remains unchanged.