Question

Frank has two same size rectangles divided into the same number of equal parts. One rectangle has 3/4 fourths of the parts shaded and the other has 1/3 third of the parts shaded.

Part A
Into how many parts could each rectangle be divided?

Part B

Is there more than possible answer to Part A? If so find the least number of parts in which bot rectangles could be divided? EXPLAIN your reasoning.

Answer 1

Both rectangles need to be divided into a number of of parts that is divisible into both 3 and 4 parts. Since 3 and 4 don't have any factors in common, it has to be divisible by both 3 and 4, so it has to have minimally 3*4=12 parts (answer to A and B!) but it can be any multiplication of 12, such as 24, 36, etc.