different type of fraction problem
- Thread starter bmathew
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You'll need to be more specific. Is there an actual problem statement you can provide?
Your example equation has two question marks in it. If these represent two different variables, it will not be possible to solve for those variables with just one equation.
If you're trying to set up some ratios that model some unspecified problem, such as similar triangle leg proportions, the equation would look something like the example you've provided.
mmm4444bot
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bmathew said:
A/20 = 5/B
A * B = 20 * 5
A * B = 100
A and B can be any pair of Real numbers whose product is 100.
see that's the thing this question was on an entrance exam for a program im trying to get into and this is the first time ive ever seen this problem. they dont tell you anything that going to be on the test. they just tell you to get a GED practice text and study that. sorry i dont have a specific example.
mmm4444bot
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bmathew said:
Hooboy. :roll:
If that's their idea of an exam question, then I might be looking for a different institution from which to learn programming.
My best guess is that they want you to be aware of the following relationship between two ratios.
Given: A/B = C/D
You may rewrite as: A * D = B * C
Some people refer to this as "the product of the means equals the product of the extremes". (Please do not ask me why the numbers A and D are called "means" and the numbers B and C are called "extremes".)
Some people refer to this as "criss-cross multiply", or simply "cross-multiplication".
It's a common way to eliminate the fractions from a proportion (i.e., two ratios set equal to one another).
Click HERE to see a post where it's suggested.
Let me know if you're still uncertain about anything.
> ?/20 = 5/?
If you assume that the question mark represent a single variable, then it is the same as... solve for x when x/20 = 5/x. As has been said in prior posts, the product of the means equals the product of the extremes giving us x[sup:friz1p7a]2[/sup:friz1p7a]=100. Solving for x, we see that x = 10 or x = -10.
As for why the means and the extremes are so named, the original notation for a proportion was as follows:
a:b::c:d. The "::" meant "equals" and was replaced by "=" giving us a:b=c:d. The b and c are in the middle and were named the "means". The a and d were on the ends and were named the "extremes". When the more recent notation of a/b=c/d or \(\displaystyle \frac{a}{b}=\frac{c}{d}\) the names held.
Many consider the rule "the product of the means is equal to the product of the extremes" to be outmoded. I guess it is too difficult to learn the proper names of the four positions. It seems to be fashionable to say "cross multiply" or "criss-cross". Without proper exposure to working with proportions as opposed to adding and subtracting fractions, I have seen students cross multiply a problem such as \(\displaystyle \frac{2}{3}+\frac{5}{7}\) and get 14/15.
If you assume that the question mark represent a single variable, then it is the same as... solve for x when x/20 = 5/x. As has been said in prior posts, the product of the means equals the product of the extremes giving us x[sup:friz1p7a]2[/sup:friz1p7a]=100. Solving for x, we see that x = 10 or x = -10.
As for why the means and the extremes are so named, the original notation for a proportion was as follows:
a:b::c:d. The "::" meant "equals" and was replaced by "=" giving us a:b=c:d. The b and c are in the middle and were named the "means". The a and d were on the ends and were named the "extremes". When the more recent notation of a/b=c/d or \(\displaystyle \frac{a}{b}=\frac{c}{d}\) the names held.
Many consider the rule "the product of the means is equal to the product of the extremes" to be outmoded. I guess it is too difficult to learn the proper names of the four positions. It seems to be fashionable to say "cross multiply" or "criss-cross". Without proper exposure to working with proportions as opposed to adding and subtracting fractions, I have seen students cross multiply a problem such as \(\displaystyle \frac{2}{3}+\frac{5}{7}\) and get 14/15.