2.Topic 1-Video 2

In this video, we're going to take a look at equivalent fractions. And, if you understand equivalent fractions, working with fractions is pretty easy. For what are they? So, here you have two fractions. One half and two fourth. And, they're naming same part of that circle. One half, two fourth, are equivalent fractions. They are naming the same thing. ...which states that any number times 1 will give you that same number. It's identity doesn't change. For example, if you multiply 6 times 1, you're still going to get 6. The 6 doesn't change. If you multiply one half times 1, you're going to get one half. If you multiply anything by 1, it's identity won't change. You'll end up with the original number. Well, that's real important. All of these fractions here, are equal to 1. Eleven elevenths and five fifths, and so on. All of these equal 1, which means if we multiply something times these fractions, it won't change the identity of that number. For example, if we took two thirds, all of these fractions right here are the same, and is 1. It's like you're multiplying times 1 which means you're not changing the identity of the original number. Two thirds is equal to 22 over 33. Two thirds is equal to fourteen twenty firsts. 2 times 7 is 14, 3 times 7 is 21. These are equivalent fractions. If you multiply 2 times 5 and get 10, 3 times 5 and get 15, two thirds and ten fifteenths are equivalent fractions. And, that last example, when you're multiplying by three thirds, it's like you're multiplying by 1. You're really not changing the identity of two thirds. Two thirds is equal to six ninths. In fact, all these fractions, down here, that we have created, they're all equivalent fractions. They are naming the same thing. So, if your teacher asks you to write four different equivalent fractions for three eighths, it'd be easy. We could multiply it, three eighths times 2 over 2, which is just like multiplying by 1. We're not changing three eighths' value. 3 times 2 is 6. 8 times 2 is 16. Six sixteenths is an equivalent fraction to three eighths. What about if we multiply it times 4 over 4? 3 times 4 would be 12. 8 times 4 would be 32. Twelve thirty seconds is an equivalent fraction to three eighths. What if we did 10 over 10? ...which is the same as 1. That would be 30 over 80. Three eighths and thirty eightieths are equivalent fractions. Now, what about if we did...how about 10,000 over 10,000? ...which is equivalent to 1. It's like multiplying times 1. That would give us 30,000 over 80,000. That's an equivalent fraction to three eighths. So, we just made four fractions that are equivalent to three eighths. Really easy. Now, let's take a look at these equivalent fractions, and, see if we can find the missing numerators and denominators. So, if we look at the first one, 9 times 8 would give you 72. If you multiply 7 times 8, that would give you 56. The missing numerator would be 56. 4 times 5 is 20. And, 7 times 5 would be 35. That's your missing denominator. 8 times 7 is 56. Something times 7 is 21. It would be 3. 2 times 9 is 18. Something times 9 is 45. It would be 5. Now, there's a couple of different ways you can tell if... if two fractions are equivalent. And, we'll look at both methods. 4 times 3 will give you 12. Is 7 times 3, 28? No. Those are not equivalent fractions. 5 times 8 is 40. Is 6 times 8, 48? Yes, it is. Those are equivalent fractions. The name the same thing. We'll do a different method on this next one. First, 7 times 3... 3 times 7 is 21. Is 10 times 7, 30? No. Now, there's another way you could tell if these were equivalent? If you cross multiply, you should get the same product. So, 10 times 21 is 210. 30 times 3 is 90. These are not the same. That isn't... Those are not equivalent fractions. I'll solve it... this last example. 6 times 6 is 36. Is 9 times 6, 54? Yes, it is. Those are equivalent fractions. Now, this is an interesting question.. And, equivalent fractions can help you to answer it. Are there any numbers between one third and two third? Wow! When you first look at that, you say, no, there is nothing in between one third and two third... two thirds. Well, that's... it's not true. And, we can use equivalent fractions to help us. If you took one third and you multiplied it times 8 over 8, which is like multiplying times 1, you will get an equivalent fraction of eight twenty fourths. If we did the same thing to two thirds, multiplied it by 8 over 8, we would end up with 16 over 24 which is... is also an equivalent fraction to two thirds. So, instead of asking you, are there any numbers between one third and two third? ...two thirds? I asked you, are there any numbers between eight twenty fourths which is the same as one third, and sixteen twenty fourths which is the same as two thirds. You'll say, yes, sure, there are. There are quite a few things between eight twenty fourths and sixteen twenty fourths. And then... there's actually a lot more than that as well, but... You can use equivalent fractions that can help you in so many different ways, when you're working with fractions.