How to Solve Problems Using Proportions

Video Transcript

"Hi. I'm Jimmy Chang and I have been teaching college mathematics for nine years. And when we think of proportions, we generally think of fractions. Now, problems involving fractions aren't our favorite in the world, however, once you actually set up the problem, it's actually fairy easy to do, though, as long as you know the strategy. Setting it up is the hard part. So, once you get past that hurdle, it's smooth sailing from there. So, here's a basic example and here we go. If 5 apples will bake 2 pies, how many apples will bake 10 pies? So, obviously the two things that you are comparing are apples and pies. Easy as pie. Now, what we have here is you have to make a decision as to which you want to be on top and which variable you want to be on the bottom. Now, because apples is mentioned first and pies second, what you might want to do is create a ratio involving apples over pies. Now, the first comparison is that you have 5 apples and 2 pies. So, basically, you have 5 for apples over 2 for pies. Now, what you're going to have here is another fraction on the other side of the equals sign. Now, how many apples? Now, since you don't know how many apples, but you do know it's on top, let's just put x for the numerator and 10 pies will be 10 at the bottom. Now, to solve any proportion problem, when you have one fraction on one side and one fraction on the other side, You simply cross multiply. What that means here is, you take one denominator and you multiply it with the numerator on the other side. So, you have 2 times x is 2x. And then you do it the same way for the other fraction. Take the other denominator and multiply it with the numerator on the other side. So, 10 times 5 is going to give you 50. All of a sudden, you have a much easier equation to work with now. All you need to do here is divide both sides by 2. So, you're left with x equals 25. That means, to bake 10 pies, you need a total of 25 apples, which is a lot of apples. But once you know how to set it up, solving it becomes easy as pie. So, I'm Jimmy, and that's how you solve problems using proportions."