In this lesson, we're going to learn how to multiply fractions. Here's our first example. Five sixths times 4/15. Now, when we're multiplying fractions, just remember that we just want to multiply across and simplify. So just to remember that by multiplying cross, we mean that we're going to multiply the numerators together and multiply the denominators together. So our numerators are five and four. We multiply those, we get 20, and then we multiply across for the denominators the same way six times 15 gives us 90. And now we want to see if we can simplify our answer. 20 and 90 do have a common factor of ten and we can tell because they both end in a zero. So if we divide both the numerator and denominator by ten, this fraction simplifies to two ninths. So that's our final simplified answer. Now we're going to look at the same example, but using a slightly different strategy. And this time we're going to factor the parts of each fraction first, simplify it and then multiply. With this strategy, it's like we're simplifying the fraction first, instead of waiting until the end to simplify it. So if we take a look at that first fraction, five over six, we want to see if there's any part of that fraction that can be factored. Well, five is a prime number, so we're not going to do anything with that. But six can be factored into two times three. Then we do the same process for the second fraction. The four in the numerator can be factored into two times two and the 15 can be factored into three times five. So it will look like this. And of course, we're multiplying these fractions together. Now remember, these still represent the same fractions, the same numbers, but they're just factored out. For the next step all I'm going to do is take both of these fractions and put them together in one big fraction to show everything being multiplied together. So both numerators multiply together and both denominators multiplied together. And here's what it looks like. Now, our next step is to see if there's any factor, any number that's in the numerator and denominator. If so, those two factors will cancel each other out. So, for example, we see a five in the numerator and a five in the denominator, they will cancel each other out. And the idea is that five over five as a fraction is really just equal to one. So it would be like we're multiplying by one. That's the concept. But just remember, whenever you see a factor in the numerator and denominator, you can just cross them out and let's see what else we have. We have a two in the numerator and denominator that will cancel each other out. Now, notice, the other two in the numerator does not cancel out because we don't have another two in the denominator. So we can just cancel one of those out and then now to see what our final answer is. We want to see what's left over in our numerator and denominator. The only number that we have left in the numerator is the two and the denominator, though we have three times three. So remember, these are factors and we can multiply them together. So the three times three in the denominator will change to just nine. So we have the two that's left in the numerator and then in denominator we have three times three, which is nine. So our final answer, just like we got the other way, is two ninths. So now you have two different strategies for multiplying the fractions. But either way, we want to make sure that if the fractions that were given start off as mixed fractions, you always want to change them to improper fractions first. So that's one thing to keep in mind. If you start off with a mixed fraction, change it to an improper fraction first. And then we just multiply the numerators and multiply the denominators together, right? Just multiply across. If the fractions need to be simplified, we can either simplify the answer at the end after we're done multiplying, which we saw with the first example, or the second way was to factor every part of each fraction and cancel out any common factors that we see in the numerator and denominator and then multiply to see what our final answer will be. We have two different strategies that you can use when multiplying fractions.