 In this video, I'm going to talk about solving proportions. In this case, when we solve proportions, a proportion is basically a fraction equal to a fraction. I can also say that a proportion is a comparison of two different ratios. 16 over P is a ratio, 24 over 12.9 is also a ratio. Ratio is just another name for fraction, I like to think of that. Okay, so to solve proportions, we use what's called cross. I call it cross multiply. It's also called cross product, there's a couple of different names for it. So in this case, if I want to solve for this variable, what I'm going to do is I'm going to take the numbers that are crossed from one another and multiply them. Now the cross parts is not quite accurate, it's more of a cross as in an X, not a cross as in a cross the equal sign. So what I'm going to do is I'm going to take 16 and 12.9 and I'm going to multiply them together and I'm going to take P and I'm going to take 24 and I'm going to multiply them together. Okay, so this is what we mean by cross multiply, not a cross as in a cross the equal sign but cross as in it makes an X when you multiply these numbers. So 16 times 12.9 is equal to P times 24, that's how we find that. Okay now from there this looks like a pretty simple equation for us to solve, we just have to figure out what 16 times 12.9 is, plug that into your calculator and you get 206.4 is equal to 24P, I'm going to put the 24 in front of the P because that's usually how we write variables times numbers. Okay so in this case I need to divide by 24 to solve and 206 divided by 24 is in this case 8.6 and so that is what the variable is equal to. Now if you really want to, what you can do is you can take this and plug it back into, you can plug it back in to see if it is correct, this is a little bit of a longer process to check this, you take 16 divided by 8.6, so that's the left side of this proportion and 16 divided by 8.6 is, it's a long repeating decimal, we'll just call it approximately 1.86. Now there are more decimals after that but I'm just going to leave it as 1.86. Okay and then you can also check 24 divided by 12.9 and see approximately what that is, so 24 divided by 16.9, not 16.9, 12.9, excuse me, is going to be 1.86 approximately and again there are more decimals after that but if you notice that both of these fractions are indeed the same decimal so the left and the right side are equal so that tells me that the variable that I got, the answer that I got is in fact correct. Okay so that's one example of solving proportions, let's do a couple more examples so we can get a better handle on this, for example what if you have a number with a variable, so what about 3x over 15 equals 3 over 5, okay so what if you have a number with a variable, that really doesn't change anything for us, we're still just going to do the cross product, we're still just going to cross multiply, so in this case I'm going to skip a few steps here, I'm going to take 3x times 5 which is 15x and I'm also going to take 15 times 3 which is going to be 45, okay nice I skipped a few steps there, I didn't show all my work but I'm just kind of speeding through this problem, okay so 15x is equal to 45, I'm going to divide by 15 here, divide by 15x is equal to 3, okay so the solution that I got is that x is equal to 3, okay you can check this to see if you did this correctly, so in this case if I plug it back in 3 times 3 is going to be 9 over 15 and I'm also comparing 3 over 5, well actually what you can do is this 9 over 15 you can reduce that to 3 fifths, so these two fractions are indeed the same, so that tells me that that solution is actually accurate, I did get the right answer, okay so that's one example, how about one more, let's do one more, 8 over 5x is equal to 2 over 11, okay so here's another one this time the variable is on the bottom, again it doesn't make any difference when we solve these type of equations, when we solve proportions we're still just going to use the cross product, so I'm going to take 5x times 2 and I'm going to take 8 times 11, now one question I usually get when solving this is does it matter what order you do it, you multiply these numbers, no not really, I can take 5x times 2 and I can do that first or I could have done 8 times 11, I could have done that first and so then it would have been 88 equals 10x, I could have done that but it really honestly doesn't make a difference which order I have it, as you can see it's either 88's on the left or on the right, 10 is on the left and 10 is on the right, doesn't really make a difference, anyway I'm going to solve this, divide by 10, divide by 10, love dividing by 10 all you do is move the decimal, so in this case x is equal to 8.8, so again what we're going to do is we're going to plug this back in to see if we got this correct, to see if that is in fact the correct answer, so 2 divided by 11 is going to be .18 repeating over the 1 and 8 and if you plug that into your calculator see what that is, so on the other hand if I take 8 divided by 5 times 8.8 I get 8 over 44, okay now one thing I can do is I can take 8 divided by 44 plug it into my calculator and see what kind of decimal I have or if I don't have a calculator with me I can simply just reduce this, so I know that 4 goes into both of these, so that leads me 4 goes into 8 twice and 4 goes into 44 11 times, so you now notice that this fraction is the same as what we have up here, so that tells me that the left and the right sides were in fact the same since this solution, if we have a solution of 8.8, okay so there's a couple of examples of solving proportions, the one thing you've got to remember is cross product, it's called cross product because the numbers that we multiply create a cross when we multiply them, okay so that's where the name comes from and if you can get that down all you do after the cross product is you simply just solve it just like you do it do a normal equation and you get your solution and make sure that you are always checking to see if that is the correct solution, just takes another minute or two extra couple of seconds to see if you get the correct answer.