What's the reciprocal of 2 4/7 ?

[10 points, algebra 2]according to my answer key the restrictions are -1 and 4. but why not positive 1?

Many newspapers carry a certain puzzle in which the reader must unscramble letters to form words. how many ways can the letters of emdangl be arranged? identify the correct unscrambling, then determine the probability of getting that result by randomly selecting one arrangement of the given letters.

In trapezoid abcd, ac is a diagonal and ∠abc≅∠acd. find ac if the lengths of the bases bc and ad are 12m and 27m respectively.