Final answer:
No, the statement that a mixed number and its reciprocal are equivalent fractions is false. Mixed numbers and reciprocals have different values, except for the special cases of 1 and -1.
Step-by-step explanation:
The question "A mixed number and its reciprocal are equivalent fractions." is false. A mixed number consists of a whole number and a fraction, while its reciprocal is obtained by inverting the fraction part and changing the sign of the whole number, if present. For instance, the reciprocal of the mixed number 2 ½ is ¼described by flipping the fraction to get ¾two-and taking the reciprocal of two, which is ½, combines both to form ¼-½. These two numbers are not equivalent as their values are not the same. It's a common mistake to assume that any two numbers that are reciprocals of each other must be equivalent, but this is only true for the number 1 and -1 because they are the only numbers whose reciprocal is equal to itself.
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