Bob Tina and Hadley went running. Bob ran for 3/8 hour, Tina ran for 3 4/9 hours, and Hadley ran for 4 19/29 hours. Which running times can be written as improper fractions

An improper fraction is one in which the numerator is bigger than the denominator, which means the value of the fraction is more than ' 1 ' .

Bob petered out after only 3/8 of an hour. This number is less than ' 1 ', so if it's left in the form of hours, it can't be an improper fraction.  If Bob wants his effort to look more impressive, he might try to describe his performance as 22.5 minutes. THAT number could be written as an improper fraction, (45/2 minutes), but somebody would be sure to notice his trick, and they would laugh at him.

Tina and Hadley both ran longer than 1 hour, so both of them could write their times directly as improper fractions, without any deceptive monkey business.

Tina . . . 3-4/9 hours . . . 31/9 hours

Hadley . . . 4-19/29 hours . . . 135/29 hours    

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