You’ve probably noticed that we’ve been talking an awful lot about fractions around here lately. Well, now I’m going to tell you something you can do with fractions that’s really easy. No, no… not juggling fractions. [circus music] Although that is pretty easy… for me. I’m talking about something even easier than that. I’m talking about multiplying fractions. Multiplying fractions is super easy. In fact it’s easier than adding fractions, and that’s why we’re going to learn it first. The reason it’s easier is because fractions are really just division problems. And multiplication and division get along much better than addition and division. Now since fractions are division, that means if I have the problem one-fourth times two-thirds, it’s the same as the problem: 1 divided by 4 times 2 divided by 3. That means I’ve got both multiplication and division in the same problem. And because they get along so well, that means I can just rearrange our problem to look like this. Now it looks like two multiplication problems that are being divided. And… it looks just like a fraction. In fact, if we go ahead and do the multiplications… 1 times 2 equals 2 and 4 times 3 equals 12 Then we do have a fraction, and it’s the answer to our problem. So, what does this all mean? Well, it means that to multiply fractions, all you have to do is multiply the top numbers, and then multiply the bottom numbers, and Tada!… There’s your answer! As always, let’s see an example or two. Let’s try this problem: two-thirds times four-fifths Now we could re-write the problem like we just saw, but that’s not necessary as long as we remember the procedure. First, we know our answer is going to be a fraction, so let’s go ahead and write a new fraction line for it. Next, we multiply the top numbers: 2 × 4 = 8 So 8 is the top number of our answer. Last, we multiply the bottom numbers: 3 × 5 = 15 So 15 is the bottom number of our answer. There we have it: 2/3 times 4/5 equals 8/15 See how easy that was? …and FUN too! …even funner than video games!! [coo-coo clock sound] Okay …time for another example. Let’s try 6/11 times 7/8 From our multiplication table, we know that 6 × 7 = 42, so 42 is the top number of our answer. And on the bottom, we have 11 times 8 which is 88. So, 6/11 times 7/8 equals 42/88 Oh, now some of you might see that this answer could be simplified, but we’ll save simplifying fractions for another video. Alright, let’s see one last example. Here it is: 1/2 times 4/3 times 3/5 Wait a minute! This has three fractions multiplied together, and that middle one looks like an “improper” fraction cuz its top number is bigger than its bottom number. Does our procedure work for this problem too? Yep! All we have to do is multiply all the top numbers together and then multiply all the bottom numbers together and we’ll have our answer. And this will work no matter how many fractions we have to multiply. So, on the top we have: 1 time 4 is 4 …and 4 time 3 is 12. And on the bottom: 2 times 3 is 6 …and 6 times 5 is 30. That means our answer is 12 over 30 So, there you have it… Multiplying fractions is easy because fractions are just another way of writing division problems. But, remember, there’s another way to think about fractions. We can also use fractions to represent parts of things like half of a pizza for instance. But does it make sense to multiply half a pizza by another half? Actually, it does! If you are thinking of fractions as ‘parts of something’ them multiplying fractions is really like taking part of another part. For example, here’s half of a pizza. You can see that if I take one-half of that half, then I get one-fourth of a pizza. And if we do the multiplication: 1/2 times 1/2, you see that we DO get 1/4. So that’s why you can think of multiplying fractions as taking part of another part. In fact, sometimes, especially in word or story problems, you’ll see multiplying fractions written using the word “of” instead of “times”. They may ask, “What’s three-fourths OF two-thirds?” And now you’ll know they just mean, “What’s three-fourths TIMES two-thirds?” So, whether you think of fractions as parts of something or as division problems, the procedure for doing the multiplication is exactly the same! Let’s do a quick review of what we’ve learned. Multiplying fractions is even easier than adding fractions. It’s easy because ‘Order of Operations’ says that we can do the multiplication before the division. The procedure for multiplying fractions is to multiply the top numbers to get the answer’s top number, and multiply the bottom numbers to get the answer’s bottom number. If you think of fractions as parts of something, then multiplying a fraction by another fraction is the same as taking a part of a part. And sometimes, especially in word problems, you might see the word “of” instead of the word “times”. Even though multiplying fractions is so easy, it’s a good idea to practice. So be sure to do the exercises, and I’ll see ya next time. Learn more at www.mathantics.com
