Learn about Multiplying fractions

Khan Academy Presents: Learn about Multiplying fractions

Welcome to the presentation on multiplying fractions. Well, I think today you’ll be very happy because you’ll find out that this is one of the few times we’re multiplying something that is easier than adding it, I think, or subtracting it for that matter. And if you don’t believe me, let’s do some problems. Okay, let’s get it started. Let’s start with ½ times ½. So when you multiply fractions, it’s very straight forward. Its essentially just 2 separate multiplication problems. You multiply the numerators. So you get 1 times 1. And you multiply the denominators, 2 times 2. 1 times 1 is 1, 2 times 2 is 4. So ½ times ½ is equal to ¼. And that makes sense. It’s just like saying ½ of ½ is ¼ which makes sense. What if we had negative numbers? Well ½ times -1/2, when you have a negative fraction, its good to describe the negative number, I tend to describe the negative number to the numerator, -1 over 2. You realized that -1/2 is same thing as -1 over 2. Hopefully that makes sense. So ½ times -1/2, that’s just the same thing as 1 times -1 over 2 times 2 which equals -1 over 4 which is the same thing as -1/4. What if I had different denominators? When you’re adding and subtracting fractions, that has to make things difficult. Not necessarily the case here. If I had 2/3 times 1/2, just multiply the numerators, 2 times 1 and you multiply the denominators, 3 times 2. So you get 2 times 1 is 2, 3 times 2 is 6. And 2/6, we know for a cooler fractions the same thing as 1/3. That was an interesting problem. Lets do it again and I will show you a little trick here. So 2/3 times ½, as you said, any multiplication problem you just multiply the numerator and multiply the denominators and you have your answer. But sometimes yet there’s a little trick here where you can say, you can cancel out, you can divide numerators and denominators by a number. Because you know this is going to be the same thing as 2 times 1 over 3 times 2 which is the same thing. I’m just switching the order on top is 1 times 2 over 3 times 2. All I did was switch the order on top coz you can multiply in either direction and that’s the same thing as 1/3 times 2/2. Well that just says 1/3 times 1 which is equal to 1/3. And why did I do that? Well I want to show you that these 2s, all I did is switch the order but at all times we had one 2 at the numerator and had one 2 at the denominator. If I wanted to, this is kind of a trick for doing multiplication fast, so you don’t have to reduce the final fraction too much. You get 2/3 times 1/3, 2/3 times ½ sorry. You see I have 2 at the numerator, 2 at the denominator. Let me divide it both by 2, that equals 1/3. Just a fast trick. I hope I didn’t confuse you. Lets do a couple more problems and I’ll do both with the trick and without the trick. What if I had 3/7 times 2/5. Well multiply the numerators, 3 times 2 is 6, 7 times 5 is 35, that’s it. Let’s do some negative numbers. If I had -3/4 times 2/11. Well that’s -6/44 which is the same thing as -3/22. Okay now there’s a cross dividing trick here. Lets do it again with the cross, times 2/11, you say, oh 2 and 4 they’re both divisible by 2 so lets divide them both by 2. so 2 becomes 1, 4 becomes 2 and then our answer becomes -3/22, right, -3 times 1 is -3, 2 times 11 is 22. Let’s do another one right here. If I had -2/5 times -2/5, well that’s just equal to -2 times -2 is positive 4 and 5 times 5 is 25, so 4/25. And that’s just refer, negative times a negative is positive which makes sense. Lets just a couple more problems since we have a lot of time. But I think you probably got this by now. You’re probably realizing that multiplying fraction is a lot easier than adding or subtracting them, hopefully. This is not a bad thing if you find that adding or subtracting fractions is easy as well. Let’s do, I’m just making up numbers now. 2/9 times 18/2, well here we could, well we have a 2 in the numerator and 2 in the denominator, and let’s divide them both by 2. So they become 1. And we have an 18 in the numerator and a 9 in the denominator, well they both are divisible by 9 so let’s divide them both by 9. So 9 becomes a 1 and 18 becomes a 2. So we have 1 times 2 over 1 times 1 well that is equal 2/1 which equals 2. That was pretty straight forward. We could have done it, I guess you got the hard way. If we said 2/9 times 18/2, 2 times 18 is 36, 9 times 2 is 18, and 36 divided by 18 and we can see 18 goes to 36 2 times. That also equals 2. Either way is fine. If you dint feel comfortable doing this trick right now, you don’t have to. All that does is it makes it easier, you won’t end up with huge numbers in your product that you’ll have to figure out if they can be reduced further. Let’s do 2 more problems. -5/7 times 1/3. -5 times 1 is -5, 7 over 3 is 21, that’s it. Let me do one of the cross with the trick I showed you. Say if I had 15, here I think you’ll see why the trick is useful, over 21 times 14/5. Well clearly if we multiply this out, we end up with pretty big numbers. I think its 220/105 and you have to reduce those, becomes a big mass. We can see that 15 and 5 are both divisible by 5s so let’s divide them both by 5. So 15 divided by 5 is 3, 5 divided by 5 is 1. 14 and 21, they’re both divisible by 7. 14 divided by 7 is 2, 21 divided by 7 is 3. And so we get 3 times 2 is 6 over 3 times 1 is 3 which equals 2. and that’s the same thing as when I said before if we have multiplied 15 times 14, that would have been 210, yeah 15 times 14 is 210, and 21 times 5 would have been 105 and you would have to say, I guess in this case, its kind of obvious that 210 is 2 times 105. And you got 2 as well. So hopefully I didn’t confuse you too much with that last problem. But I hope your multiplication is pretty straight forward. Just multiply the numerators. You multiply the denominators. And then if you have to reduce, you reduce. But you’re pretty much done. I think you’re ready now to try the multiplication module. And I hope you have fun.