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Which number can be multiplied by a rational number to illustrate that the product of two rational numbers is rational?

A. (aπ) / 3

B. (-218)

C. (31 / -3)

D. (5 / 3)

1 Answer

4 votes

Final answer:

Any of the options B, C, or D can be multiplied by a rational number to illustrate a rational product as they are all rational numbers. However, option B (-218) is the simplest choice.

Step-by-step explanation:

The question asks which number can be multiplied by a rational number to illustrate that the product of two rational numbers is rational.

To answer this, we need to remember that a rational number is any number that can be expressed as the quotient or fraction ⅟ where p and q are integers and q is not equal to zero. Now, let's examine the options:

  1. A. (aπ) / 3 - This option includes π (pi), which is an irrational number, so it can't be the answer.
  2. B. (-218) - This is an integer, and all integers are rational numbers because they can be expressed as a fraction where the denominator is 1. So this could potentially be the answer.
  3. C. (31 / -3) - This is a fraction of two integers, thus it is also a rational number.
  4. D. (5 / 3) - Similar to option C, this is a fraction made of integers, which is a rational number.

Since we are looking for a number that will result in a rational number when multiplied by another rational number, options B, C, and D are all valid, as they are all rational numbers.

Multiplying any of these numbers by another rational number would indeed give a rational product. However, if the question implies that we need to choose just one, option B. (-218) is perhaps the simplest choice to demonstrate the rule because its multiplication is straightforward.

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