 So when we multiply fractions, we're just going to multiply straight across the top and straight across the bottom. And then we'll simplify if we need to. And we'll also talk about the fact that sometimes we can simplify before we multiply if the numbers are kind of big. So if we look here, we're going to multiply straight across. So 4 times the 2 gives us 8, and then 7 times the 11 gives us 77, and you can't reduce that one. So we are ready to say we have 8 over 77. Now in this one, we multiply straight across and we have 110 when we multiply 10 times 11, and we have 220 when we multiply 10 times 22. But they're both divisible by at least 10 because we see these zeros here. So let's divide off the 10 from both and we end up with 11 over 22. And then when we look at those, well they're both divisible by 11, so this would be 1 times 11 and 2 times 11, so it reduces to 1 half. Now I was saying to you that sometimes you can reduce ahead of time because remember if you have a common factor top and bottom, you can reduce them. And I have a common factor of 10 here. There's a 10 on the top here and a 10 on the bottom, so they really kind of cancel each other out. There's a factor of 1, and I'm left with the problem of 11 over 22, which is a lot easier to simplify. I don't have to worry about the 10 or else finding a really big number that goes into both of them. When I have mixed fractions, then we have to make them into improper fractions. So remember how you do that. You take the big and then you multiply by the bottom and then you add the top. And that number is going to be over whatever the bottom number was. Remember that's how we fix those. So we want to know how many thirds in this first fraction. So 2 times 3 would be 6 plus 2 more would be 8 thirds. And we want to know how many fourths we have here. So 3 times 4 is 12 and then plus the 3 would be 15. Yuck. 8 times 15, I'm not even sure I know what that is. But we'll do this from the long way and the short way and see which way we like. 8 times 15 I believe it's 120 and then 3 times 4 would be 12. So it's not too bad to reduce. It just wasn't fun to multiply. So this is going to be 12 times 10. So I can see that I can cancel out my 12's and I'm just left with 10. It's really over 1 or you can just say 10. I could have come in here and said oh look 8 and 4 top and bottom. 8 would be 4 times 2 so I could get rid of the 4. And then you could look and see if there's any numbers, other numbers that would reduce. Oh this is 3 times 5 for 15 and that's a 3. So that'll cancel this 3 after I've taken care of my 15 and what do I have? I have a 2 times 5 and that's all I have left. So I get the 10. Sometimes we don't see that you can reduce and you just on a roll so you want to multiply across. It's fine. So a reciprocal, when I multiply a number and it's reciprocal I get 1. And that will be very helpful when I want to divide. I can use this fact and then I can actually make my division become a multiplication. So when I want to find the reciprocal let's start here at 6 over 7 because it's a little easier. When I start at 6 over 7 the reciprocal is, if you look up here the C was first. It was on top and now it's on the bottom. The D was on the bottom and now it went to the top so you just flip it over. 7 over 6 instead of 6 over 7. Well what do you do with a whole number? Well remember that it's really 3 over 1. So the 3 goes on the bottom of my fraction and the 1 goes on top so the reciprocal of 3 is 1 third. So how do we use that to divide? We're going to take the second fraction, not the first one. It has to be the second fraction and we're going to take its reciprocal and then we'll multiply. So we take this first fraction like it is and then we're going to multiply by the reciprocal. So these switch places. The 36 comes on top and the 14 comes on the bottom and I am looking at that one and saying yuck. I can quickly see that 7 and 14 hasn't been in common. I bet 15 and 36 do but I can at least start reducing this a little bit by saying that this is 7 times 1 and this one here is 7 times 2 and the 7's cancel. That is a 1 not a 7. So that gives me 1 times 36 or 36 and 15 times 2 so that gives me my 30 and now that's a little bit easier to reduce. 36 and 30 look like they have 6 in common. 6 times 6 would be 36 and 6 times 5 would be 30. So my answer is going to be 6 fifths. Second problem. Let's keep it 4 over 7 but we're going to multiply by the reciprocal. Remember this is 8 over 1 so it will become 1 over 8 when we multiply. Here's a nice problem for us. We can say 1 times 4 is 4. 7 times 8 is going to be 56 and 4 does go into 56 because we could have reduced here with the 4 and the 8. So 4 times 1 would be 4 and 4 times 14 would be 56 so we have 1 over 14 to reduce it. And finally I have this 6 and you can leave it 6 but when we're multiplying fractions it's kind of nice to make whole numbers into fractions. I'm not making the reciprocal because that's the first fraction. Now I want to multiply by the reciprocal of this one. So we're going to have 15 on the top and 12 on the bottom. Again this one would reduce nicely. And then we can see that this would be 6 times 2 and then the 6 cancels the 6. And we end up with 15 on the top and 1 times 2 or 2. Now let's do that one the long way just in case you hadn't seen that. 6 times 15 happens to be I believe 90. And 1 times 12 is going to be 12. Well now I have to reduce them. And I think that 6 probably goes into both of them. And when I take 6 times 15 I know it goes into 90 because I started that way. And this is going to be 6 times 2 instead of 12. So the 6's cancel each other out and we're left with 15 over 2.