How To Multiply Mixed Fractions
Question
At the end of the equation what is the only option?
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How To Multiply Mixed Fractions

Hi, my name is Charles, and I am one of the math teachers from the Maxim workshop. I am just going to now teach you how to do some math. I am going to show you how to multiply mixed fractions. Now, the first thing we want to do is put our mixed fractions on the board. So, I am going to do that now. We have one and two-fifths multiplied by three and two-thirds, okay? So, the easiest way to multiply these particular fractions is to convert, first of all, these mixed fractions possibly into improper fractions, okay? So, if you think about what one equals, one basically equals any number divided by itself. So, we can change that into a fraction, whereby we have a number on the top and that same number on the bottom. Now, for purposes of adding these two together, the integer with the fraction, we will need to look at the denominator of this fraction here. And we can see the denominator is five, so that's the number on the bottom. So, we would need to compose our integer, which is one, as a combination of the numerator and denominator, with five. So we put five divided by five, plus two over five. And that's what this equals to. Now, we are going to try to do the same thing here. Now, if you think about what three equals, three is three times one. Okay? So, we are going to do the same procedure, but we are going to need a factor of three on top of our fraction. Okay? So, if we take a look at the denominator of this fraction, we can see that it is three. So, we want three divided by three, times three. Okay. So, this three here obviously exists because it multiplies by one to be there, and then we add two divided by three. So, if we look at this, just before we close the bracket, we want to simplify what this equals. So, three actually basically will simplify down to nine divided by three. So we can rub this out and write in nine divided by three. Now, it becomes a little bit more simple from here. What we want to do now is bring together fractions, so we've got two fractions that we can directly multiply by. So, the first one that we are going to do here is add the tops and write the same as the bottom. So, if we add the tops, we've got five plus two, which is seven. And then we write the bottom, the denominator. And again, we are going to do that with these two fractions. So, we've got nine plus two, which is eleven, and then we write the denominator. So, we've got seven-fifths multiplied by eleven-thirds. Now, that is pretty much what these two equate to. So the multiplication now is a lot easier. So we've got seven times eleven which is seventy-seven and we've got five times three, which is fifteen. Okay? Now, from here we would want to see if we can cancel anything out or possibly factorize. No, sorry, not factorize. Just basically cancel out the prime factors. So, if we think about what seventy-seven looks like, it is basically seven times eleven, which is its prime factors. So, we obtain that from here. And if we look at these two, they are the prime factors of fifteen, so we can see that there is no chance of actually factorizing anything or cancelling down. So, we have to leave it like this, as an improper fraction. The only other thing that we can possibly do with this is to convert it back to a proper fraction. Now, we would need to see how many times fifteen goes into seventy-seven. Okay? So, the ideal thing to do is to say to yourself, "How many times can I multiply out fifteen before it passes seventy-seven?" Okay? Now, straight off the top of my mind, I know it's five because five times fifteen equates to seventy-five. Okay, so, we say that fifteen goes into seventy-seven five times and we get left with a remainder of two, but that remainder of two, we still want to divide that by fifteen. So, when we multiply one and two-fifths by three and two-thirds, we arrive at the answer of five and two-fifteenths. And that's pretty much how to multiply mixed fractions