Which of the following pairs of rational numbers are equivalent? 18 46 (0) 14:42 () -27 -6
The Correct Answer and Explanation is:
Correct Answer: -27 and -6
To determine which pair of rational numbers are equivalent, each pair should be converted into a simplified or reduced form to see if they represent the same value. Rational numbers are numbers that can be expressed as a fraction of two integers.
Consider the given pairs:
Pair 1: 18 and 46
18 and 46 are both whole numbers. When written as fractions (18/1 and 46/1), they clearly represent two different quantities. Neither is a reduced form of the other, and their decimal representations (18.0 and 46.0) confirm they are not equivalent. Therefore, this pair is not equivalent.
Pair 2: 0 and 14:42
Interpreting 14:42 as a time notation and not a fraction, it does not represent a rational number in its standard numerical form. However, assuming it means a ratio (14 divided by 42), then 14/42 simplifies to 1/3. On the other hand, 0 as a rational number is 0/1. Since 1/3 ≠ 0, these are not equivalent.
Pair 3: -27 and -6
Now consider the pair -27 and -6. To determine if they are equivalent, divide both numbers:
-27 ÷ -6 = 4.5
However, this gives a result rather than testing equivalence. Instead, write both numbers as fractions:
-27/1 and -6/1. Since -27 ≠ -6, at first glance they do not seem equivalent. But if one compares ratios or their simplified versions, a mistake could arise.
However, there may be a correction in interpretation: if the pair meant fractions with equal values, the rational numbers must be fractions that simplify to the same value.
Another possibility is that none of the pairs are truly equivalent unless there is a formatting or typo issue.
Upon rechecking, none of the pairs represent equivalent rational numbers. Therefore, the final answer should be:
Correct Answer: None of the given pairs are equivalent rational numbers.
