Math Ratio Problem

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  1. Joe cut a 20 feet board into 2 pieces. The ratio of the shorter side to the longer side is 2:3. How long, in feet, is the longer board?

2+3 = 5 → 20/5 = 4 → 4*3 = 12 feet

  1. Jill split a 12 inch cake into 6 pieces. The ratios of the first 3 pieces to the last 3 pieces was 2:4. What's the length in inches of one shorter piece?

2+4 = 6 → 12/6 = 2 → 2*2 = 4
one piece → 4/3= 0.75 inch

Is this rational correct? Please give an explanation as to why or why not. Thank you for your help

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I meant to write “Two Math Ratio Problems, Is the rational correct?” for the title^

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4/3 is not 0.75. This is the only error that I have noticed.

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This is a really poorly worded problem. Cakes are traditionally shaped lie a circle. Is this cake instead shaped like a board, so length is the only relevant dimension? And does 12 inches refer to that length? Are the 3 pieces all of equal size? Why express the ratio as 2:4, rather than 1:2? Who makes {1.33 in x small} cake slices? I expect they want the answer 4/3 = 1.33… (not 0.75), but technically the correct answer is unable to determine.

You might skip a listed step with reasoning like 1:2 ratio, so divide by 3 for smaller. 12/3 = 4. 3 pieces of equal size, so divide by 3 again. 4/3 = 1.33…