Ratios as Fractions
Date: 01/26/97 at 01:06:06 From: Michelle Gerard Subject: Ratios I am in grade seven and I always have trouble with my math. I am particularly stuck in the area of ratios. For example, last month we started by trying to put ratios into simplest form, like 64:12 = ? Please help, Dr. Math! Thank you very much, Michelle
Date: 01/26/97 at 19:17:41 From: Doctor Mike Subject: Re: Ratios Hello Michelle, One way to look at 64:12 is as the fraction 64/12. This is what is called an "improper" fraction because its numerator is bigger than its denominator, but it is still a perfectly good fraction. You have probably had problems where you are supposed to reduce a fraction to its lowest terms. An example is that the fraction 7/14 equals 1/2. I wanted to say this so you will know this is not a completely new thing for you to learn how to do. It's just the same old fraction problem in different words. Back to your problem in fraction form: 64/12 is the same as 32/6, and that is the same as 16/3. We cannot go any farther than that. In terms of ratios, 64:12 equals 16:3. I hope this helps on the mechanics of what you are supposed to do for this kind of problem. Perhaps you need a little more info on what ratios are all about. Sometimes when a teacher is rushed she/he will do a quick explanation that everybody may not absorb completely. A few examples might help. Suppose the fast-track advanced math class has 26 girls in it and 13 boys. That is a ratio of 26:13 but it is also a ratio of 2:1. The ratio of 2:1 is easier to understand because it captures more simply the idea of "twice as many". There are twice as many girls as boys. By the way 26 + 13 = 39 students is too many for one math class! Here is another one. At age 12 you have probably spent 8 years in grades K through 7. There is a ratio there, namely, the ratio of "number of years in school" to "number of years in your whole life". For you this ratio is 8:12 or 8-to-12. You could simplify that to 4:6 and further to 2:3. The same thing can be done with the fraction 8/12 which is the fraction of your life you have spent in school (including summers). You reduce that fraction to 4/6 or 2/3. Either way, as the ratio 2:3 or the fraction 2/3, it says you have spent two thirds of your life as a person of school age. One more little warning about how you use these words. When you do ratios it is important for you (and your teacher) to be clear about WHAT is in a ratio to WHAT ELSE. In the last example I gave there are lots of ratios we could talk about: 8:12 -- school years to total years 12:8 -- total years to school years 8:4 -- school years to preschool years 4:8 -- preschool years to school years 12:4 -- total years to preschool years 4:12 -- preschool years to total years This is not something else for you to worry about learning. It's just an encouragement for everybody to try to make sense of what the numbers mean. I hope what I have said makes sense to you, and that on your next test the ratio of "your score : total points" will be 40:40 = 100:100 = 1:1 (these are all different forms of the same ratio). -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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