Dividing with Fractions: Missing Factor Method (1970)

[Music] Hey, hey, hey. [Music] on the great lonesome tundra of the far north and there lived a muskox named Lola. Lola was extremely smart usually. But when it came to dividing with fractions, she just couldn't. She could multiply with fractions, just multiply the numerators and multiply the denominators. She could divide whole numbers. And she even knew the connection between division and multiplication. For example, when she saw 24 / 3 equals something, she thought of the number for the box as a missing factor. She thought of the three as a given factor and 24 as a product. She thought 24 / 3 is the missing factor in the problem. 24 = 3 * something and 8 is the missing factor. So 24 / 3 is 8. Lola knew all these things, so she wasn't a dumb ox really. Then one day, her friend Arthur the Arctic Fox said, "Come on, Lola, you should be able to divide fractions. Let's look at a problem. You can use the same idea that you use with whole numbers. You just want to find the missing factor. Right? You have a product and a given factor and you must find a missing factor. You can change it to a multiplication problem. But since we're working with fractions, it will help to think of the missing factor in the form of a fraction. Then you want to find the missing numerator and denominator. Now, how do you multiply fractions? Well, you multiply numerators and then denominators. Now, what do you multiply by three to get nine? That's right. The three must go in the diamond and the triangle, right? Since 2 * 4 is 8. Now, let's go back to our problem. We want to find the missing factor. We found it was 3/4 because 3 * 34 is 9/8. So 9/8 / three halves equals 34s. Shall we do another problem, Lola? Let's try 94 / 37s. And while you're working on that, maybe everyone who is watching the film can turn off their projector and try along with you. We'll be back shortly. Let's see how we did. 94 / 37 is 3 halves. That's right. Okay, Lola. Now, we'll try one that's a little harder. That's right. Change it to a multiplication problem. Right. You must find the missing numerator. What's wrong? Oh, two isn't a factor of five. So, you don't know what number to multiply two by to get five. I'll give you a hint, Lola. Change the name of the product 56. So, it will be easy to find the missing numerator. Well, I know the value of 56 won't change when I multiply the numerator and denominator by the same number. Right? Then 5 * 2 over 6 * 2 or 10 12ths is a new name for 56 and 2 is a factor of 10. So 2 * 5 is 10 and 3 * 4 is 12. Then 2/3 * 54s is 10 12ths or 56. What about the original problem? 56 / 2/3 must be 54. That's terrific, Lola. Let's try another one. Try 7/8 / 34s. And while you're working it out, everyone watching can try, too. Now let's see how you did. 7/8 / 34s is 76. Very good, Lula. Let's try another one. And if you can do this next one, you'll be able to do any division problem with fractions. Ready? right now. We have a multiplication problem. Come on, Lola. What did you do before? Remember the last problem? What did you do? Right. You renamed 56. Now try it on this new problem. Okay, we know that three isn't a factor of 7 * 2. 2 wasn't a factor of five. But you got around that difficulty with no problem. Could you change the name of the product again? Right. You can multiply both the numerator and the denominator by three and not change the product. It's still 57ths. Now what do I do? Arthur, come on, Lola. You've done the hard part. 2 * what number = 5 * 2 * 3? Of course, 5 * 3 and 3 * 7 * 2 is 7 * 2 * 3. There you've done it. 57 / 2/3 is 15 14. Pretty pleased with yourself, Lola? I am, Arthur. Thanks to you. Do you think you can divide any two fractions now, Lola? I think so, Arthur. I'll give you some more just to make sure. Here are three problems like the three we just did. Copy them down and have fun with them. [Music]