Setting Up Proportions

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When setting up proportions, it's important to remember to do so in a fraction problem. Decide where to put variables when setting up proportions with help from a math teacher in this free video on proportions in math.

Part of the Video Series: Fractions & Proportions
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So, how does one set up proportions? Hi, I'm Jimmy Chang. I've been teaching college math for nine years, and setting up proportions, is a fraction problem, and I know we don't work too well with fractions overall, but once you identify what two things are being compared, setting them up is actually a relatively straightforward exercise, as long as you're consistent with the decisions that you make, so here's a basic example, and we'll set up the problem together. If 7 cups of water are needed for three cups of sugar, how many cups of water are needed for 8 cups of sugar? So what you have to decide is, you have a proportion to make, but you have to decide what thing you want to be the numerator, and what you want to be for the denominator. Now, since water is mentioned before sugar, one easy way you can form a proportion, is to put water over sugar, and then put the numbers in that way, but once you've made that decision, you need to stick with it, throughout the entire problem. Now, because 7 cups of water, you will have 7 in the numerator, and because you have 3 cups of sugar, you'll have three in the denominator, and then on the other side, because you want to know how many cups of water are needed, because water you decided is the numerator, you would put x on top, and then 8 cups of sugar, you'll have eight on the bottom. Now, if you had made the decision to put sugar on top of water, then it's the same exact idea, but you must be consistent on both ends, so for example, sugar for the first comparison, is 3 cups, so you have 3 over, the cups of water needed, is 7, and then on the other side of the equation, because you have eight cups of sugar, that will be your numerator, and the number of cups of water needed is x on the bottom. Whatever decision you make, you will get the same exact answer, but as long as you're consistent with your decision on both ends, you will be just fine, so I'm Jimmy, and that's an example as to how you set up proportions.

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