 Alright, well let's take a look at some algebraic problems that involve fractions, and as it turns out, the best way of solving these algebraic problems that involve fractions is to not actually use algebra, but just to draw the representation of our fractions. So, for example, let's take a typical problem after construction, and a parking lot was reduced in size by one-fifth, and there's eight thousand spaces remaining, and we want to find out, typical question, how many are present before the construction, and we'll go and use this using a tape diagram, area model, bar model, the terms are pretty much interchangeable. So, let's go ahead and draw that. So, we can represent the situation. Well, here's our parking lot. And we're going to lose one-fifth of those spaces, so we'll divide our parking lot into five pieces, and we'll lose one-fifth of them, so those are gone, you can't park there, but you can park in the remaining spaces here. Now, we're told that there's eight thousand parking spaces, so that means that if these represent eight thousand spaces, then each of these blocks represents two thousand spaces. And also, because we divided the parking lot into five equal pieces originally, this block here also represents two thousand pieces. And so, if I think about this, this was my original parking lot before construction, took out this section, then there's two, four, six, eight, ten thousand spaces originally in the parking lot. And we'll go ahead and give our answer to that, the parking lot originally had ten thousand spaces. Now, if you're uncomfortable with drawing the tape diagram, you could actually express this as an algebraic problem, but it's actually a somewhat difficult problem to write down for a number of reasons, not the least of which is that it is a very common mistake to try and solve this problem, and to find out, for example, if I reduce the size by one-fifth, then I might find out that the parking lot had six thousand four hundred spaces before construction. And that's not true, because if it only had six thousand four hundred spaces and lost one-fifth of them, it can't have had eight thousand afterwards. And there are other varieties of wrong answer that are caused by not reading the actual situation correctly, and the easiest way of ensuring that you have read the situation correctly is if you actually draw the picture that shows your parking lot losing one-fifth of its spaces. Again, another classic problem, the jacket's price was increased by one-quarter to one-hundred dollars, what was the original price? And again, we can solve this algebraically, and the most common wrong answer to this is to say that the original price was seventy-five, and the reasoning is something along the lines of a quarter of a hundred is twenty-five, so the jacket's price increased by twenty-five dollars and so on. That's not correct, though, and we'll see why by using a tape diagram. So we'll go ahead and let the tape represent the jacket's original price, and we're increasing that price by one-quarter. So what does that mean? Well, I'm going to take one-quarter, and it's an increase. So this is the original price. If I want to increase it, I don't lose any of these pieces, I actually get one more. So I'm going to take one of these pieces and clone it, and that's my increase in price. Now we do know the new price is one-hundred dollars, so if this amount here represents one-hundred dollars, then there's one, two, three, four, five of these pieces. Each of these individual pieces must represent twenty, which says that the original price of the jacket, just the green, is eighty. And so the original price of the jacket, eighty dollars.