Solving Proportions Problems
If you're seeing this message, it means we're having trouble loading external resources on our website. Or the ratio of 8/36 is equal to the ratio of 10 to what. Now sometimes when you see proportion like this, sometimes people say, oh you can cross-multiply. And it really comes out of a little bit of algebra. But if you don't understand it, or if it doesn't make as much sense to you at this point, don't worry too much about it. When you cross-multiply, you're saying that the numerator here, times the denominator over here, is going to be equal to, so 8 times n, is going to be equal to the denominator over here, let me just different color, the denominator over here, times the numerator over here. And we're getting n is equal to 360 divided by 8. If I write 8 times question mark is equal to 360, well, question mark could definitely be 360/8. But you could stop watching this, if you'll find this part confusing. If we want just an n here, we would want to multiply this side times 36-- I'll do that in a different color-- we'd want to multiply this side times 36 times 8, because if you multiply these guys out, you get 1. But since we're doing it to the left-hand side, we also have to do it to the right-hand side, so times 36/8.If you're behind a web filter, please make sure that the domains *.and *.are unblocked. And there's a bunch of different ways to solve this. Or another way to write 10/8, 10/8 is the same thing as 5/4. You could do that without thinking in strict algebraic terms. If I multiply these out, this guy and that guy cancel out, and it's definitely 360. But now we want to actually divide this to actually get our right answer, or a simplified answer. So let's rewrite our proportion, 8/36 is equal to 10/n. Well the easiest way to solve for n is maybe multiply both-- this thing on the left is equal to this thing on the right. These guys cancel out and we're left with n is equal to 10 times 36 is 360/8.This exercise did not ask me to find "the value of a variable" or "the length of the shorter piece".By re-checking the original exercise, I was able to provide an appropriate response, being the lengths of each of the two pieces, including the correct units of meters.I got to "grams" first when reading the exercise, so I'll put "grams" on top in my proportion.Since the relationship is given to me in terms of grams, not kilograms, I'll need to convert Jade's on-hand measure to " Ohhh!But that word "over" gives a hint that, yes, we're talking about a fraction.And this means that "rise over run" can be discussed within the context of proportions.
I'll set up the proportion, using " always the case with "solving" exercises, we can check our answers by plugging them back into the original problem.In this case, we can verify the size of the "drop" from one end of the house to the other by checking the products of the means and the extremes (that is, by confirming that the cross-multiplications match) of the completed proportion: As far as I know, biologists and park managers actually use this technique for estimating populations.The idea is that, after allowing enough time (it is hoped) for the tagged fish to circulate throughout the lake, these fish will then be evenly mixed in with the total population.To be on the safe side, though, I'll give both the "exact" (fractional) form and also the rounded (more real-world) form: If this question were being asked in the homework for the section on "percent of" word problems, then I would have the tax rate as a percentage from the info they gave me for the first property; and then I would have back-solved, using the rate I'd just found, for the value of the second property.However, since this question is being asked in the section on proportions, I'll solve using a proportion.Try always to clearly define and label your variables.Also, be sure to go back and re-check the word problem for what it actually wants.Solving proportions is simply a matter of stating the ratios as fractions, setting the two fractions equal to each other, cross-multiplying, and solving the resulting equation.The exercise set will probably start out by asking for the solutions to straightforward simple proportions, but they might use the "odds" notation, something like this: Okay; this proportion has more variables than I've seen previously, and they're in expressions, rather than standing by themselves. First, I convert the colon-based odds-notation ratios to fractional form: First, I'll need to convert the "two feet four inches" into a feet-only measurement.If you're seeing this message, it means we're having trouble loading external resources on our website.If you're behind a web filter, please make sure that the domains *.and *.are unblocked.