a) 2/3 x 3/4 = 1/2
This reads as two thirds of three quarters. So the referent whole for the 2/3 is the 3/4 and the referent whole for the 3/4 is a whole one. The answer 1/2 refers to the whole one. For example: If Joe ate 2/3 of 3/4 of a pizza that was leftover from lunch, he ate 1/2 of the whole pizza. Two thirds refers to the leftover portion of the pizza, while 3/4 and 1/2 refer to the original whole pizza.
b) (1/2)/(3/4) = 2/3
This could be read as how many 3/4 in 1/2. It is the inverse of the multiplication problem. So the referent wholes are the same as in the multiplicaiton problem. Joe ate half of the whole pizza. If only 3/4 was leftover from lunch, then Joe ate 2/3 of the leftover pizza.
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