Question 757628
A number line is like a ruler, with marking for measurements.  You show marks labeled -10, -11, and -12, and there are some markings with no numbers written.  The markings between your -10 and -11 show four equal increments; this means the difference between each number, marked labeled or unlabeled, is {{{(1/4)}}}.  The reported value for F in your answer key is correct.  F sits three quarts of the way from -10 to -11.  It NEEDS to be reported as {{{(-43/4)}}}.  The negative sign is necessary.  Note that {{{-43/3}}} is the same as {{{-10&3/4}}}.


What would you call E?  It is one mark to the left of -11, and again, there are four increments between -11 and -12, so this ONE between NEGATIVE ELEVEN and NEGATIVE TWELVE is cut into increments of {{{1/4}}}.  E then sits at {{{-11&1/4}}}.  What is this as the equivalent number of {{{1/4}}}'s?


For practical purposes, an improper fraction is also a rational number.  Both a proper fraction and an improper fraction are rational numbers.