Shelly has a photo that is 7 1/3 inches tall. she wants to shrink it down to fit in a picture frame that is only 5 1/3 inches tall. the photo shop can only reduce photos by certin fractions. they can reduce it to 2/3 the original size, 3/4 the original size, or 5/9 the original size. which reduction should she use so the picture fills as much of the frame as possible, without being too large?

We know that 

the photo is 7 1/3 inches tall> 7 1/3=(7*3+1)/3=22/3 in > (7.33 in)
the picture frame  is 5 1/3 inches tall--> 5 1/3=(5*3+1)/3=16/3 in> (5.33 in)

a) case A reduce 2/3 the original size> (22/3)*(2/3)=44/9 in> (4.89 in)

b) case B reduce 3/4 the original size---> (22/3)*(3/4)=66/12 in> (5.5 in)
this is not solution because 66/12 (5.5 ) in >16/3 (5.33) in ( picture frame)

c) case C reduce 5/9 the original size---> (22/3)*(5/9)=110/27 in> (4.07 in)

the answer is the case A reduce 2/3 the original size> 44/9 in  (4.89 in)

Uneed to add them up 27+18+23=68