Properties of Integers Worksheet
Explore and apply the fundamental properties of integers including commutative, associative, distributive, identity, and inverse properties.
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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 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 expression demonstrates the Distributive Property?
7 + 0 = 7
4 × 1 = 4
2 × (3 + 5) = (2 × 3) + (2 × 5)
6 + (-6) = 0
3. The Property states that changing the order of the numbers in an addition or multiplication problem does not change the result.
4. The additive inverse of 10 is because their sum is 0.
5. The Identity Property of Multiplication states that any number multiplied by 0 equals 0.
True
False
6. For any integer 'a', a × 1 = a demonstrates the Multiplicative Inverse Property.
True
False
7. Use the number line below to show the sum of -4 and 7. What property allows you to add in any order?
Match each property with its example.
8. Commutative Property of Multiplication
a. (a × b) × c = a × (b × c)
9. Associative Property of Multiplication
b. a × 1 = a
10. Identity Property of Multiplication
c. a × b = b × a
11. Inverse Property of Addition
d. a + (-a) = 0
12. Explain how the Distributive Property can simplify the calculation of 8 × 23.