Question 145873
Let x be the total study time of joe.

then time used for doing math homework= 1/3 of x =1/3x

 time used for preparing history exam = 2/7 of x =2/7x

 let  remaining  time be 'y'.

then, 1/3x+2/7x+ y =x

     y= x - [ 1/3x + 2/7x]
      = x - [ 7x + 6x/21]       Taking LCM OF 3 & 7 , AND SIMPLIFYING
      = X-  13x/21
      =21x -13x/21    taking LCM
      = 8x/21

ie, fraction of remaining study time  = 8/21