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Three people are coloring the same piece of 8 1/2 by 14 paper. Abby starts on the left side and painted 1/2 of the paper red. Ben starts on the right side and painted 3/4 of the entire paper green. Cathy starts in the middleand painted 1/3 of the entire paper, evenly on either side of the centre line, using blue color. What fraction of the paper has all three color painted on it?

 May 24, 2021
 #1
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Is it not clear that the three colors overlap on the(in the) region I have painted yellow? The \(\frac{1}{6}\) of the entire sheet immediately to the left of the midline?

 May 24, 2021
 #2
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The easiest way is to to determine what is the smallest common multiple of 2,3, and 4  (the numbers on the bottom)

 

They all go into 12  so 12 is the magic number

 

\(\frac{1}{2}=\frac{ \square }{12}\\ \frac{3}{4}=\frac{ \square }{12}\\ \frac{1}{3}=\frac{ \square }{12}\\\)

 

Now draw it.  Divide your rectangle into 12 strips.

Put R in the red strips, G in the green strips and B in the blue strips.

 

Now answer the question.

 May 24, 2021

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