Visualizing Ratios to Scale Least Common Multiples
Date: 10/02/2010 at 08:18:03 From: Louie Subject: ratio In my flock of sheep, there are three breeds: Cotsworlds, Swaledales and Leicester Longwools. The ratio of Cotsworlds to Swaledales is 3:5 and the ratio of Swaledales to Leicester Longwools is 7:4. a) What is the ratio of Cotsworlds to Leicester Longwools? b) There are more than 100 sheep in my flock. What is the smallest number of sheep there could be? I know that C:S is 5:2, S:L is 7:4, and LCM of 5 and 7 is 35. I tried to make it equivalent and got that C:S is 21:35 and S:L is 35:20. Is C:L therefore 21:20? There are (21 + 35 + 20 =) 76 parts all together; so if there are more than 100 sheep, as it says in the second question, would I multiply 76 by 2 to get 152 as the answer? Please help.
Date: 10/03/2010 at 10:45:38 From: Doctor Ian Subject: Re: ratio Hi Louie, The way I think about this is, I imagine that I have some C's and some S's next to each other, in the right ratio: C C C S S S S S And I have some S's and L's next to each other, also in the right ratio: C C C S S S S S S S S S S S S L L L L Then I think about how I could scale those to get the same number of S's in both groupings. The smallest number divisible by both 5 and 7 is 35, as you wrote. So I could have 7*3 C's 7*5 S's 5*7 S's 5*4 L's or 21 C's 35 S's 20 L's And the actual numbers would have to be some multiple of that grouping, wouldn't it? It's basically the same sort of thing you're doing, but I find that the pictures help me keep track of what I know, and how each thing relates to everything else. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 10/03/2010 at 11:48:10 From: Louie Subject: Thank you (ratio) Dear Dr. Ian, Thank you so much for your answer. I hadn't thought of using the pictures before. Great idea. Will help me a lot in dealing with ratio problems in the future. Thank you again. Louie
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