Adam drew two rectangles of the same size and divided them into the same number of equal parts. He shaded [tex]\frac{1}{3}[/tex] of one rectangle and [tex]\frac{1}{4}[/tex] of the other rectangle. What is the least number of parts into which both rectangles could be divided?
Answer (2)
The problem needed to say that when he did the shading, he only shaded WHOLE PARTS.
For the rectangle that he shaded 1/3 of, how many parts could it have ? It could have 3, 6, 9, 12, 15, 18, 21, etc. parts ... the multiples of 3.
For the rectangle that he shaded 1/4 of, how many parts could it have ? It could have 4, 8, 12, 16, 20, etc. parts ... the multiples of 4.
Both rectangles have the same number of parts. What's the smallest number on both of those lists ? It's called the "least common multiple of 3 and 4". It's the smallest number that they both go into. It's 12 .
The least number of parts into which both rectangles could be divided is 12, as this is the least common multiple of the denominators of the shaded fractions, 3 and 4.
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