Properties of Rational Numbers
Explore and apply the properties of rational numbers including closure, commutativity, associativity, identity, inverse, and distributivity.
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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 for short answer questions.
1. Which of the following statements is true regarding the closure property of rational numbers under division?
Rational numbers are always closed under division.
Rational numbers are closed under division, except when dividing by zero.
Rational numbers are never closed under division.
The closure property does not apply to division.
2. Which property is demonstrated by the equation (3/4) + (1/2) = (1/2) + (3/4)?
Associative Property of Addition
Commutative Property of Addition
Distributive Property
Identity Property of Addition
3. The product of any rational number and its multiplicative inverse is .
4. The property a(b + c) = ab + ac is known as the Property.
5. The additive identity for rational numbers is .
6. The set of rational numbers is closed under subtraction.
True
False
7. For any rational number 'a', its additive inverse is 1/a.
True
False
8. Explain the difference between the commutative and associative properties of multiplication using rational numbers as examples.
9. Provide an example to illustrate the distributive property for rational numbers.
10. Plot the following rational numbers on the number line below: -1/2, 0.75, 5/4, -2.