Assistance with algebra word problem

Explain why it would be easy to interpret the picture incorrectly as showing that 4*3\5=12\20. Explain how to interpret the picture correctly, and explain why your interpretation fits with the meaning of 4*3\5

picture

http://mathhelpforum.com/image/png;b...BJRU5ErkJggg== http://mathhelpforum.com/image/png;b...BJRU5ErkJggg== http://mathhelpforum.com/image/png;b...BJRU5ErkJggg== http://mathhelpforum.com/image/png;b...BJRU5ErkJggg==

(5 rectangles divided into each whole box. 3 are shaded and 2 are unshaded in each box)

Re: Assistance with algebra word problem

If there are four whole boxes, here's how the picture could be interpreted incorrectly.

"There are 5 rectangles total for each whole box, 3 of which are filled in. When there are four such boxes, there are 20 rectangles total with 12 shaded in. Hence $\displaystyle \frac{4*3}{5} = \frac{12}{20}$"

This interpretation is incorrect because we are multiplying the number of shaded *and* unshaded boxes by 4. and so a true interpretation of the picture would be $\displaystyle \frac{4}{4} * \frac{3}{5} = \frac{12}{20}$