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Rational Numbers Test - 14

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Rational Numbers Test - 14
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Weekly Quiz Competition
  • Question 1
    1 / -0

    Rational numbers are closed under addition because

    Solution

    The sum of any two rational numbers is also a rational number. Therefore, rational numbers are closed under addition.

    The correct answer is B.

  • Question 2
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    Use the following information to answer the next question.

    Some statements are given as:

    I. There are finite integers between any two different integers.

    II. There are finite rational numbers between any two different rational numbers.

    III. There are infinite rational numbers between any two different integers.

    IV. There are infinite integers between any two different rational numbers.

    Which two given statements are correct?

    Solution

    Statement I: There are finite integers between any two different integers.

    For instance, the integers that lie between −21 and −30 are −22, −23, −24, −25, −26, −27, −28, and −29. There is no other integer that lies between these two integers.

    Similarly, the integers that lie between −2 and 5 are −1, 0, 1, 2, 3, 4. There is no other integer that lies between these two integers.

    Thus, statement I is correct.

    Statement III: There are infinite rational numbers between any two different integers. One can name as many decimals as one wants between any two integers. Decimals are also rational numbers.

    Thus, statement III is correct.

    Hence, statements I and III are correct.

    The correct answer is A.

  • Question 3
    1 / -0

    What is the multiplicative inverse of?

    Solution

    The given rational number is.

    The multiplicative inverse of

    The reciprocal of is.

    Therefore, the multiplicative inverse of is.

    We can note that.

    The correct answer is C.

  • Question 4
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    Which of the following relations exhibits the commutative property of rational numbers under multiplication?

    Solution

    Multiplication is commutative for rational numbers i.e., for any two rational numbers a and b, a × b = b × a.

    Thus, the commutative property of rational numbers under multiplication is exhibited by the relation.

    The correct answer is A.

  • Question 5
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    Which property is illustrated by the relation, where p and q ≠ 0 are integers?

    Solution

    In the given relation, it is seen that the sum of the rational number and 0 is again the same rational number.

    In fact, for any rational numberpq+0=pq.

    For this reason, 0 is known as the additive identity of rational numbers, which is illustrated by the given relation.

    The correct answer is D.

  • Question 6
    1 / -0

    What is the product of the additive inverse of −0.8 and the multiplicative inverse of 0.2?

    Solution

    ∴Additive inverse of −0.8 = Additive inverse of

    ∴ Multiplicative inverse of 0.2 = Multiplicative inverse of

    Thus, the product of the additive inverse of −0.8 and the multiplicative inverse of 0.2 equals the product of and 5, which is.

    The correct answer is A.

  • Question 7
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    Which of the following relations illustrates the associative property of rational numbers under addition?

    Solution

    Addition is associative for rational numbers i.e., for any three rational numbers a, b, and c, a + (b + c) = (a + b) + c.

    Thus, the relation exhibits the associative property of rational numbers under addition.

    The correct answer is B.

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