Properties of Rational Numbers - Grade 10
Explore and apply the properties of rational numbers including closure, commutativity, associativity, identity, and inverse for addition and multiplication.
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Properties of Rational Numbers
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Read each question carefully and answer to the best of your ability. Show all your work where necessary.
1. Which of the following numbers is NOT a rational number?
0.75
-5
√2
1/3
2. The set of rational numbers is under addition, meaning that the sum of any two rational numbers is always a rational number.
3. The identity for multiplication is 1, because any rational number multiplied by 1 remains unchanged.
4. The associative property of multiplication states that for any rational numbers a, b, and c, (a × b) × c = a × (b × c).
True
False
5. Explain the concept of the additive inverse for rational numbers. Provide an example.
Match each property with its description.
6. Commutative Property of Addition
a. Changing the grouping of numbers does not change the sum or product.
7. Associative Property
b. The order of numbers in addition or multiplication does not affect the result.
8. Distributive Property
c. A number outside parentheses can be multiplied by each term inside the parentheses.
9. Plot the rational number -3/4 on the number line below.
10. Demonstrate the distributive property with the rational numbers 1/2, 3/4, and 2/3. Show all steps.