How to Find Equivalent Fractions

0:00 Welcome to Math Academy. Hi everybody. Welcome to Math Academy. Today we're going to be talking about equivalent fractions. Let's start off with uh 2/3. Okay. And uh in 2/3, you know that what that means is that is two parts of the three parts. Okay. So if we were to draw a rectangle right here and break that up into three parts, and then shade in two of those parts. Okay, that is going to be 2/3 or two out of three parts. So the blue right is up here is the numerator and the red the

0:46 total amount in the three parts is the denominator. Okay, so um let's find an equivalent fraction into 2/3. So 2/3 if we multiply the numerator and denominator by the same number. So let's let's multiply the the numerator by two. We'll multiply the denominator by two. All right. So when we multiply the numerator we get 2 × 2. And that's going to get us four. And then when we multiply the denominator 3 * 2 we get 6. So that tells us that 2/3 is equivalent or an equivalent fraction. 2 4 6. Well, let's check that. Right. So, um let's draw another

1:32 uh rectangle of the same size. Uh well, almost the same size here. Um and then uh well, let's break up into three parts. And now we're going to break each of those parts in half. Uh so that we have a total of six parts like that. And if we were to shade in now four, see this uh we were to shade in four of the parts. 1 2 3 4. You can see that these two are equal. So 2/3 um is an equivalent fraction to 46. Okay? And you you don't have to just multiply the numerator denominator by like two uh by both by two. You can multiply them by 3 or 3, 4 over 4,

2:18 etc. Um as long as you multiply them both by the same number, you're going to get an equal fraction. Um, and you could also uh uh divide as well. So, let's quickly just take a look. And we took 46 at this point. Uh, here. Let's just grab a different color. So, you know, we're going to bring the 4 six down here like that. And let's go 4 six. We'll bring it right down here. Now, if we were to say divide instead of multiply, we could divide this by, right? Divide by two. Divide by two. And that's going to get us uh four divided by two gets us two and six divided by two gets us three. It gets us back to our original number, right? And that makes sense. Um all right, so let's jump um over to

3:05 um a new uh number here. Let's do uh 3 fifths. So we'll put 3 fifths right here. All right. So now last time uh in our example with 2/3, we multiply the numerator and denominator by 2 over2. So let's try multiplying three fifths. Now let's just do I don't know um let's do five and five. So you know five fifths, right? So 3 × 5 gets us 15. So we multiply the numerators 5 uh 3 × 5 is 15 and then 5 × 5 is 25. So that means 3 fifths is an equivalent fraction of 15 25ths. That means they equal each other. So 3 fifths equals 15 25ths. They are equivalent

3:54 fractions. Okay. Now uh three the 15 25ths is not the only equivalent fraction to 3 fifths. So up here as you can see we multiplied um both of them by five. But what if we multiplied them by a different number? Right? So so let's bring three fifths back right here. Okay. Instead of multiplying by five, let's just multiply by four this time. Okay? So, we multiply the numerator, the three by four, we get 12. Multiply the denominator by 4 and we get 20. Okay? And now we have 20 uh 12 20ths. Well, guess what? 12 20ths is also an equivalent fraction to 3 fths

4:40 and it's also equivalent to 15 25ths at this point. Um, so there's a lot of fractions equivalent to 3 fths. All right. So you it you can multiply or you can divide. Um, and I the last thing I want to quickly say is why does that work though? Why why can you multiply the numerator by by uh the same number as denominator and get an equivalent fraction? Well, ultimately what we did here is when we multiplied the when we multiplied the 3 fifths by uh 4 over 4, right? We were multiplying by a 44s, right? And um 4/4s or any uh anytime the numerator and denominator are the same number, right? Like this

5:27 4/4s, that's 4 / 4, which is equivalent to 1. Okay? So that's a one. So any anything over itself, anytime you have the numerator and denominator is the same number, you're going to get a one. So uh um so 3 fths × 1 is 3 fifths. But when it's, you know, 4 over 4, now you're just going to get something that is itself. It's just, you know, going to look different, but it's an equivalent fraction. So that's that's one of the reasons why it works. Um all right, until next time. We'll see you at math.