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:
- A. (aπ) / 3 - This option includes π (pi), which is an irrational number, so it can't be the answer.
- 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.
- C. (31 / -3) - This is a fraction of two integers, thus it is also a rational number.
- 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.