 All right, today we are going to talk about fractions. It seems like no matter what math class I teach, algebra, trigonometry, calculus, all the students struggle with fractions. All right, so first rule is simplifying fractions. If you have a fraction like, let's say, 3 over 43, now just because they both have a 3 in them doesn't mean you can magically cancel those 3s, okay? Just like for example, if we had, I don't know, like x minus 2 over x plus 4, because these both have x's in them, you can't magically cancel those. You need to build a factor of things and then you can cancel stuff. So better examples then would be like 3 over 15, okay? That one you can actually reduce because you can factor a 3 out of that denominator. So this would be like 3 over 3 times 5, cancel those 3, so you'd end up with 1 5th, okay? In a similar way then, if you had x's in there, if you had like x minus 2 over x squared, minus 4, so similar to what I had up here, but I changed it just a little bit, you can factor that denominator, right? So you could factor that denominator as x minus 2 and x plus 2 and then we can cancel those factors out, so we're going to end up with 1 over x plus 2, okay? So that's simplifying fractions. So just because they have something in common does not mean you can magically cancel it. You can only cancel factors. All right, so then adding fractions, how do we do that? Well, remember you've got to have a common denominator. So let's say we had, I don't know, how about 1 5th plus 2 3rds, for example, okay? So fractions sometimes end a common denominator, sometimes they don't. So adding and subtracting they do, we're going to do an example with multiplying where they don't, okay? So here you need to find the common denominator between these two. That would be 15 because obviously these are both prime numbers, so nothing else will go into them. So we can change this into, let's see, multiply this one by 3 over 3, multiply this one by 5 over 5, so we end up with 3 15ths plus 10 15ths, which now that we've got the common denominator we can now combine like terms basically, okay? So combine those numerators together, we end up with a grand total of 13 15ths, okay? So first thing we did was simplifying, second thing we did was adding, third thing we're going to do here then is multiplying, okay? So let's say we're going to multiply these same two fractions. Multiplying is actually a lot easier, believe it or not. Multiplying you can just multiply straight across, okay? So that's going to end up giving us 2 15ths, and then maybe we can look at that and see if we can reduce it, but obviously 2 won't go into 15, so that's going to be our final answer. So we've got final answer here, final answer here, okay? Last thing we want to look at then is dividing. So dividing is very similar to this, but there's one more step. So that's going to be if we wanted to divide these two fractions, okay? Well dividing you've got to do the multiplying and then you've got to change it to a reciprocal or you've got to invert it, you've got to flip it, whatever word you want to use there. So that's going to give us 1 5th times 3 halves, and then again you can multiply straight across, so that's going to give us a grand total of 3 10ths. Again, 3 will not go into 10, so we are done with that fraction too. All right, this is a crash course on fractions, but watch this video whenever you're doing something more complicated, because then you can always go back to the simple ideas. Thank you for watching.