Solving Proportions With Mixed Numbers

Video Transcript

"So, how do you solve proportions with mixed numbers? Doesn't that make the problem that much harder? Hi, I'm Jimmy Chang. I've been teaching college math for nine years, and I'm here to address that. When you put mixed numbers into a proportion problem it does add another layer to the problem, but really, not by much. What you have to keep in mind, though, is if you turn the mixed number into an improper fraction it makes the problem actually that much easier, so here's an example. Suppose you have 1and a half over 2 equal to x over 3. Now, obviously you have a mixed number in the form of 1 and a half. You definitely don't want to solve it with it at a mixed number form. You definitely want to turn this into an improper fraction, so as long as you remember how to do that you'll be good to go. So remember, take the denominator and multiply it with the whole number, so 2 times 1 is 2, and then you add the numerator, so 1 and a half is really 3 halves. So, you have three halves over 2 equals 2x over 3. Now, where you go from there is you actually solve it the same way like you would any proportion problem, and that is by cross multiplication. Take the 2, multiply it with the x and you will have 2x, and then take the 3 and multiply it by the 3 halves. Now, 3 times 3 halves; that will give you 9 over 2 equals to 2x. Now, your objective then is to solve for x, and because the 2 is multiplied with the x just divide both sides by 2. Now, you have x on one side, but the thing is to figure out 9 halves divided by 2. Since you're dividing by a whole number and you have a fraction on top give this a fraction as well, so you have 9 over 2 divided by 2 over 1. So, as a result you'll have 9 halves, and remember from arithmetic rules if you're dividing by 2 over 1 you have to multiply by the reciprocal, one half, so you have x is equal to whatever 9 halves times 1 half is, and you will get 9 over 4 is equal to x, and then, that is your final answer. So, mixed numbers and proportion problems; they do make the problem a little bit longer, but not much more difficult than that. As long as you convert it to a improper fraction mixed numbers are just like any other problem. So, I'm Jimmy Chang, and that is how you solve proportion problems using mixed numbers."