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 Question from Trini, a student: Can the reciprocal of a mixed number be another mixed number? Explain, and give an example.

Trini,

A mixed number has an integer part and a proper fraction part where the integer is not zero. For example

5 1/3, 2 3/4 and -4 1/5

are mixed numbers. This notation means

5 + 1/3, 2 + 3/4 and -(4 + 1/5)

Convert each to a common fraction by finding a common denominator

5 + 1/3 = 16/3, 2 + 3/4 = 11/4, and -(4 + 1/5) = - (21/5).

Notice that in each case the numerator is larger than the denominator. Why? Hence the reciprocal will have the denominator larger than the numerator. Can any of these be a mixed number? Why?

Penny

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