Hi, my name is Bassem Saad. I'm a Math Ph.D. candidate at U.C. Davis, and I'm here today for About.com to show you how to solve proportions.Remember proportions are equations with ratios on either side of the equal sign. Often, the most interesting proportions have variables inside of them. So there are a few different methods to solving proportions, but I'll show you how to solve proportions using basic algebraic manipulation.Let's take a look at our first example: 3/10 equals 12/x. The first thing you want to do is identify the variable you're solving for; in this case, it's x. And what you need to do is get x by itself on one side of the equation, on top, and everything else to the other side. Well, in order to get x on top, you have multiply both sides of this equation by x. So, we can multiply an x here and an x here. The x on this side cancels with the x on the denominator, and we end up with 3x/10 equals 12.Next thing we want to do is get rid of this ten, so we want to multiply both sides by ten. We can do that simply by multiplying a ten right here, and multiplying a ten right here. The tens on this side cancel and you're left with 3x equals 120. Now you just want to get x by itself so that means you want to get rid of this three. Well, that's easy! You just divide both sides by three. Threes cancel and you're left with x equals 40 – that's you're answer.Being able to solve proportions is an essential life skill. Anytime you wish to calculate your finances, or use a scale on a map or blueprint, or modify a recipe, you'll need to calculate some proportions. Mechanics, or really any technicians, must be able to calculate proportions on a regular basis; and even pharmacists use proportions to calculate the correct medical dosage for their patients.Thanks for watching, and to learn more, visit us on the web at About.com.