 Okay, so let's do this. Let's play with fractions. We'll start simply by adding fractions so going over the notes and when we have one third plus two-thirds If the denominator is the same It stays the same It's already done it and then we can just add the two numerators together one plus two is three and If we have three out of three it is also known as a whole number one So that's when the denominators are the same What if they're different? What do we do if they're different? So let's say it's one over three and Two over four and we needed to add them together. What's the strategy there? We can't add them unless these two denominators are the same So we need to convert them and we do this by what I call ratio so we need to find the lowest common Multiple LCM of both of these fractions or both of these denominators So the lowest common multiples go like this What do both of these numbers multiply? Together with that is the same number. All right, so let's go through our multiples of three one times three Three. Yeah, two times three six three times three equals nine four times three Equals twelve. Let's leave it at twelve and here's why Well, let's do number let's do the four so one times four equals four two times four equals eight three times four equals twelve now Can you see that here and here? We have both twelve that is the lowest common multiple So we can convert one over three plus two over four two Over twelve here and over twelve here and we're adding them together We know that it's going to equal twelve as the denominator but We can't just add one plus two because we've scaled up both of these fractions So we need to learn now how to scale the numerators up and here's how you do it, okay? Firstly, and this is will help you with your ratios two three Times something equals twelve now when we were doing it back here We figured out that three times something or something times three, which is the same equals twelve We go down. Oh, here it is the magic number is four So three times four equals twelve now with these fractions and ratios We have to do the same thing to the top as we did to the bottom. So it's going to be one multiplied by four one multiplied by four is four So four over twelve is the same as saying one over three. It's the same ratio. Yeah So if you were to ask if you were to get asked to simplify four over twelve to a simpler fraction The answer would actually be one over three But this time we're making a bigger so that we can Add these two fractions together, right? Let's do the next one What is four? multiplied by to get twelve Did you have three as the answer you're correct? So four times three equals twelve and again Whatever you do to the bottom you have to do to the top so two times by three will equal Six so we've got six Right, we're done. Where are we done? Let's add these two together to get our final answer four plus six equals ten and There we have it Ten over twelve, but let's simplify it. How do we simplify ten over twelve? We need to make it into a smaller number the way that I go about it is work through my Singular numbers. We don't use one because one divided into ten is ten. Nothing's happened One divided to twelve is twelve, okay What about two two can two divide into ten? The answer is yes because ten is an even number. How many times does two go into ten? Let's go old-school. We can even use fingers here ten two four six eight ten Five is your answer. So we have five What about twelve? Let's use our fingers again two four six eight ten twelve six So the answer is six and that's how you add Numbers or fractions that have a That don't have a common denominator So step one find the lowest common multiple L C and remember that and Then you can add them once you add them make sure that you scale The fractions the same way as you do with the denominator to the numerator and that's how you do it Okay next bit next bit Now again, if that's going too quick, you can always pause it rewind the video and watch it again Okay So what about subtraction? Let's say we have four fifths Take away three fifths If the denominator is the same The denominator stays the same and we can do four take three. Yeah Taken away the numerators four take three equals one One over five is the answer. That's easy, but it's been in high school. We need to get a little bit more challenging Let's make it Four over five take away Three over Let's go with six Three over six four over five takes three over six Yeah, so first thing we need to do is we need to make these two numbers the same We need to make a lower cop find the lowest common multiple of the denominates. So let's do that one times five five two times five ten three times five 15 Four times five because 20 who's getting a bit of a recall from private school. We're doing our times tables. This is why five times five 25 And then six times five equals 30 now I could just keep going if I wanted to but let's stop at six Okay, let's do about six times tables one times six six two times six twelve three times six 18 four times six 24 five times six 30 ah There it is There's our number now. I purpose purposely stop at 30 because I know that's the lowest common multiple But I've been doing this forever. I'm old So let's have a look. Let's convert this to 30 here take away 30 here and then we'll have our answer here over 30 What are our numerators going to be? Well, let's have a look. How do we get from five to six? Sorry five to 30 we multiplied by six Whatever we do to the bottom we do to the top Four times six. Oh, we got that here. This is an easy answer 24 That was easy. Yeah What about this one? Oh six to 30. How do we get from six to 30? Oh, we multiply by five five times six equals 30 and Then we have to multiply this one by five Don't get confused because that's the six that we use and we multiply by five That's sound number so times five and whatever we do to this one. We do to the top as well. So times by five That's where we get the number from three times five equals 15 Excellent. So that is the same as that but with common denominators Let's finish the problem 24 take 15 is Well, let's have a look. Let's do it here just in case you forgot how to subtract Four take five. You can't do borrow the one carry the four fourteen take five equals nine And then one take one equals zero our answer is nine So our answer here is nine over 30 Now, can we simplify that fraction? Let's go. We're going to ignore the one. We're going to go to the two. Can two divide evenly into nine? No, it can't. Can three divide evenly into nine? Yes, it can and Before we continue, we're going to make sure that three can divide into 30 evenly as well Yes, it can. How many times? Let's use our fingers Three goes into nine three six nine three There's the first one what about 30 Three six nine twelve fifteen eight and twenty one twenty four twenty seven thirty Ten there's our answer three over ten Okay, we've done it. We've done it. We've got our answer. Yay Okay, so now we've done that We're going to look at the next stop Okay, the next problem you're going to get a problem that Looks like this now I'm gonna go a little bit quicker and skip the finding the lowest common denominator. Okay, so let's say we have five Over six plus and then in brackets. What's the number that I've set up? Negative seven over nine. Okay now What we can do here is first that we need to find the lowest common multiple I'm going to skip a step and I'm going to tell you straight away that that equals two over 18 over 18 over 18 Okay, and the top two numbers are going to be 15 and and 14 Okay, 15 and 14 So from here, we need to know what the middle bit is now Because we have a plus and a minus We need to convert that now when we're adding a negative. We're actually subtracting. Okay, so We have 15 and 14 The plus and minus if you remember your integers from year seven is actually a takeaway So we have a takeaway here. So the answer is one over 18. Okay, done done That's the first one. Now another way to do that is Let's say let's say We have a common. Let's say we have a common denominator Okay, let's make it a little bit easier. Let's say we have three over five Plus and then brackets minus one over five So it's a minus altogether. Yeah, so a lot same thing now Quick tip minus one over five equals minus one over five like this equals one over minus five They're all the same. Okay, but Let's make it the top one. Let's use this one as an example. Okay So we're going to rewrite this like this so three Over five plus negative one over five and then when it comes to our Coding let's call it coding. It actually looks like this Three plus negative one over five because When we have a common denominator, remember it stays the same and then we have three plus negative one When we're adding a negative, we're actually taking it away. This here becomes a negative Three take one is two over five And that's your final answer Okay done next bit next bit next bit All right now. This is my favorite bit. I prefer this over the addition and subtraction. All right, let's erase this Let's go for the Multiplication. I'm just gonna check if we still got time for this recording. Yes plenty of time We're 14 minutes in and if you're ready stuck feel free to go back and try again We're gonna go with multiply first Multiply okay with multiplying fractions. There's actually less work involved. Okay, so let's say we have three over five multiply by two over four okay, all you have to do is multiply both Numerators and in brackets, I'm gonna put top and then also multiply both denominators Which is the bottom numbers Now if you're still quite confused with what all those words are Let's label it a half That's the numerator numerator and that's the denominator Okay, I probably should have done that at the very beginning of the lesson But here we go. We've unlocked it now if you're less confused you can go all the way back to the start and go for it Okay, so multiply both numbers the top so we're gonna multiply these two together Okay, anytime you see this set up three times two is six. That's the top number and then four times five or five times four is 20 There's our number. Let's simplify it how many times there's two going to six three and How many times there's two going to 20? Okay, so there's our first one. Let's say multiply. That's it the end the end I'm going to do one more for negatives. I'm going to do one more for negatives. Okay, so for the negatives Let's say we have negative one over five multiply by two over three Okay, now remember one over five Negative is equal to negative one over five as well. So let's write it like that. Let's make that a little bit easier Let's get rid of this and do that we can do that We're allowed to do that now remember from the notes here if you didn't write them down Rewind this about a minute and copy those notes down. That's the video video We multiply the top two together now negative one times two. What do you think the answer is? It's actually negative two Okay, now a Here's some more notes for you if you haven't figured it out a negative Multiply by a positive Will give you a negative and also the other way around because remember three times four is also four times three So therefore positive Times a negative is also a negative There are two more. Can you figure them out? Pause the video and see if you can write them down and unpause negative times a negative Is actually a positive Okay, it's like two wrongs make a right sort of thing and then a positive times a positive positive equals a positive Remember those those will be with you throughout your maths career all throughout high school. There it is Now let's go back to this. That's correct because negative one negative times a Positive now we know that's a positive because there's no pluses or minuses in front of that We don't need to put a plus and then because we're automatically going to know that it's positive. That's the rule Okay, positive equals a negative. That's why we wrote negative two and we know our ones times tables We know our two times tables one times two is two and that's where we put the negative there Right next one five times three five as a positive Times three. That's also a positive. Oh, that's not it positive positive positive So the answer is gonna be a positive five times three is 15 We're done. That's our answer and you can do that in any way whether it's here whether it's here Anyway, just as long as you follow these laws. Okay, right last one. Let's do divide divide Isn't that much harder, but you have to remember three words Keep change and flip So let's have a look at this problem one divide one over five divided by two over three Now here's where the words come in label this keep Which means? leave it Alone Leave it alone. Don't do anything. This one is Change, what are we changing it to? To multiply Change to multiply so from this To this okay, and then this last one Flip They're the three magic words keep change and flip we can also Use the word swap Swap over swap around rotate whatever words you want to use So the two and the three become the three and the two Okay, let's write all of that Here based off of what you just learned So first step first number one over five. What does it tell me keep leave it alone? Okay, I'll leave it alone. I'll keep it like it is one over five. What's the next step? Change to multiply. Oh, we've got to change this. Oh this to this. Okay, I'm gonna write that here done Last one flip swap over two over three. Oh Three over two. See how we've just rotated them around Done. Oh, I know how to do this. This is just multiply You just multiply the tops and the bottoms one times three is three Five times two is ten done drop the mic. We're finished How are we cool? Let's move on. Yeah Okay, the last one last one and I'm going to do negatives. Okay, I'm gonna do negatives and a vision This is as hard as it gets for now. Let's use Some different numbers Let's go with over eight. Let's make it a negative eight. Let's make it. Let's make it and then we'll go negative three over four. So what do we do here? Keep leave it alone. Okay. I'll just write it again. That was easy Change to multiply. Oh, that was easy Flip swap over. Okay, negative three and four. So the four now goes on top and the negative three goes to the bottom again We've just rotated and now let's do it. Oh We have to just multiply the top and the bottom two times four. That's easy Eight What about negative eight times negative three? Oh, what happens if you don't know if you're not sure rewind it a few minutes Go back to when I had the positive and negative notes But if you've written them down well done So, you know that now a negative times a negative equals a positive so eight times three eight sixteen twenty four There's our answer Can we convert this? Yeah, we can. Two goes into eight. How many times? four Two goes into eight. Uh, two goes into 24. How many times? 12 Can we convert that? Absolutely. Two goes into four. How many times? Twice. Two goes into 12. How many times? Six. Can we convert that? Oh Yeah, why not? Why not? Why not? Two goes into twice Sorry, two goes into twice once Two goes into six times three times One third. Could we have done this quicker instead of doing these? Yes, this is how. What goes into eight and what goes into 24 evenly? The number four. How many times does four go into eight? Twice. How many times does four go into 24? Six times. So we could skip that step. Okay, and then they're both even still so two goes into two one Two goes into two three times. Ladies and gentlemen, we are done with fractions. That's how you do it Thank you for tuning in. You've been a wonderful audience. Good night