Learn about Mixed numbers and improper fractions Video

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Learn about Mixed numbers and improper fractions

Learn about Mixed numbers and improper fractions We’re now going to learn how to go from mix numbers to improper fractions and vice versa. So first, a little bit of terminology. What is a mix number? Well you’ve probably seen someone write, let’s say 21/2. This is a mix number. So you’re saying, “Why is it a mix number?” Well, because we’re including a whole number and a fraction. So that’s why it’s a mix number. So a whole number mixed with a fraction, so 2 ½ and I think you have a sense of what a 2 ½ is. It’s a place half way between two and three. And what’s an improper fraction? Well, an improper fraction is a fraction with a numerator is larger than the denominator. So let’s give an example of an improper fraction. I am just going to pick some random numbers. Let’s say I had 23/5. This is an improper fraction. Why? It is because 23 is larger than 5. It’s that simple. And it turns out that you can convert an improper fraction into a mix number or a mix number into an improper fraction. So let’s start with the latter. Let’s learn how to do a mix number into an improper fraction. So first I’ll just show you kind of just the basic systematic way of doing it and it always give you the right answer then hopefully I’ll give an intuition for why it works. So, if I wanted to convert 2 ½ into an improper fraction or I want to un-mix it you could say. All I do is I take the denominator and the fraction part. Multiply it by the whole number and add the numerator. So let’s do that. I think if we do enough examples, it will—you’ll get the pattern. So 2 × 2 is 4 + 1 is 5. So let’s write that. It’s 2 × 2 + 1 and that’s going to be the numerator and it’s going to be all of that over the old denominator. So that equals 5/2. So 2 ½ is equal to 5/2. Let’s do another one. Let’s say I had 4 and 2/3. This is equal to—it’s going to be all over 3. We keep the denominator the same and the numerator is going to be 3 × 4 + 2. So it’s going to be 3 × 4 and then you’re going to add 2. Well that equals 3 × 4—order of operations, you always do multiplication first and that’s actually the way I taught it; how to covert this anyway. 3 × 4 is 12 + 2 is 14. So that equals 14/3. Let’s do another one. Let’s say I had 6 and 17/18. I gave myself a hard problem. Well, we just keep the denominator the same and the numerator is going to be 18 × 6 or 6 × 18 + 17. Well 6 × 18. Let’s see that, 60 + 48, it’s a 108. So that equals a 108 + 17, all that over 18 and 108 + 17 = 125/18 so 6 and 17/18 = 125/18. Let’s do a couple more and I’ll leave it—in a couple minutes, I’m going to teach you how to go the other way, how to go for improper fraction to a mix number. In this point, I am going to try to give you a little bit of intuition for why I am teaching you it actually works. So let’s go—let’s say 2 ¼. Well if we use the—I should call it the system that I just showed you, that equals 4 × 2 + 1/ 4. Well that equals 4 × 2 is 8 + 1 is 9. 9/4. I want to give you an intuition for why this actually works so 2 ¼. Let’s actually draw that. Let’s see what it looks like, so that’s—let’s put this back into kind of the pie analogy. So that’s equal to 1 pie, 2 pies and then, let’s say a 4th of pie, right? 2 and 4 and ignore this. This is nothing. It’s not a decimal point. Actually let me erase it so it doesn’t confuse you even more. There you go. Okay. So go back to the pieces of the pie. So there is 2 ¼ pieces of pie. And we want to rewrite this as just how many fourths of pie is their total. Well, if we take each of these pieces—oh oops, I need to change the color. If we take one each of these pieces and we divide it into fourths, we can now say, how many total fourths of pie do we have? Well we have 9/4. It makes sense right? 2 ¼ is the same thing as 9/4 and this will work with any fraction. So let’s go the other way, let’s figure out how to go from an improper fraction to a mix number. Let’s say I had 23/5. So here we go in the opposite direction. We actually take the denominator. We say how many times does it go into the numerator and then we figure out it’s the remainder. So let’s say, 5 goes into 23. Well, 5 go into 23. 4 × 5 is 20 and the remainder is 3. So 23/5, we can say that’s equal to 4 and then the remainder 3/5. So, it’s 4 3/5. Let’s review what we just did. We just took the denominator and divided into the numerator. So 5 goes in the 23 four times and what are left over is 3. So 5 go into 23 4 3/5 times or another way of saying that is 23/5 is 4 3/5. Let’s do another example like that. Let’s say 17/8. What does that equal as a mix number? You can actually do this in your head but I’ll write it out just so you don’t get confused. 8 goes into 17 two times. 2 × 8 is 16. 17 - 16 is 1; remainder 1. So, 17/8 = 2; that’s this 2 and 1/8, right? Because we have 1/8 left over. Let me show you kind of a visual way of representing these two so it actually makes sense how this conversion is working. Let’s say I had 5/2, right? So that literally means I have 5/2 or if we go back to the pizza or the pie analogy, let’s draw my 5/2 of pizza. So let’s say I have ½ of pizza here and let’s say I have another half of pizza here. I just flipped it over. So that’s 2. So it’s 1 ½, 2/2, so that’s 3/2 and then I have a 4/2 here, right? These are halves of pizza and then I have a 5/2 here, right? So that’s 5/2. Well, if we look at this, if we combine this 2/2, this is equal to 1 piece. I have another piece and then I have half of piece, right? So that is equal to 2 ½, I guess we could say piece of pie. Hopefully that doesn’t confuse you too much. And if we wanted to do this kind of the systematic way, we could have said 2 goes into 5. Well 2 goes into 5 two times and that 2 is right here. And then 2 × 2 is 4. 5 -4 is 1. So the remainder is 1 and that’s what we use here. And of course we keep the denominator the same. So 5/2 = 2 1/2. Hopefully that gives you a sense of how to go from a mix number to an improper fraction and vice versa from an improper fraction to a mix number. And if you’re still confused, let me know and I might make some more modules. Have fun with the exercises.

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Learn about Mixed numbers and improper fractions

We’re now going to learn how to go from mix numbers to improper fractions and vice versa. So first, a little bit of terminology. What is a mix number? Well you’ve probably seen someone write, let’s say 21/2. This is a mix number. So you’re saying, “Why is it a mix number?” Well, because we’re including a whole number and a fraction. So that’s why it’s a mix number. So a whole number mixed with a fraction, so 2 ½ and I think you have a sense of what a 2 ½ is. It’s a place half way between two and three.

And what’s an improper fraction? Well, an improper fraction is a fraction with a numerator is larger than the denominator. So let’s give an example of an improper fraction. I am just going to pick some random numbers.

Let’s say I had 23/5. This is an improper fraction. Why? It is because 23 is larger than 5. It’s that simple. And it turns out that you can convert an improper fraction into a mix number or a mix number into an improper fraction.

So let’s start with the latter. Let’s learn how to do a mix number into an improper fraction. So first I’ll just show you kind of just the basic systematic way of doing it and it always give you the right answer then hopefully I’ll give an intuition for why it works.

So, if I wanted to convert 2 ½ into an improper fraction or I want to un-mix it you could say. All I do is I take the denominator and the fraction part. Multiply it by the whole number and add the numerator.

So let’s do that. I think if we do enough examples, it will—you’ll get the pattern. So 2 × 2 is 4 + 1 is 5. So let’s write that. It’s 2 × 2 + 1 and that’s going to be the numerator and it’s going to be all of that over the old denominator. So that equals 5/2. So 2 ½ is equal to 5/2.

Let’s do another one. Let’s say I had 4 and 2/3. This is equal to—it’s going to be all over 3. We keep the denominator the same and the numerator is going to be 3 × 4 + 2. So it’s going to be 3 × 4 and then you’re going to add 2. Well that equals 3 × 4—order of operations, you always do multiplication first and that’s actually the way I taught it; how to covert this anyway. 3 × 4 is 12 + 2 is 14. So that equals 14/3.

Let’s do another one. Let’s say I had 6 and 17/18. I gave myself a hard problem. Well, we just keep the denominator the same and the numerator is going to be 18 × 6 or 6 × 18 + 17. Well 6 × 18. Let’s see that, 60 + 48, it’s a 108. So that equals a 108 + 17, all that over 18 and 108 + 17 = 125/18 so 6 and 17/18 = 125/18.

Let’s do a couple more and I’ll leave it—in a couple minutes, I’m going to teach you how to go the other way, how to go for improper fraction to a mix number. In this point, I am going to try to give you a little bit of intuition for why I am teaching you it actually works. So let’s go—let’s say 2 ¼.

Well if we use the—I should call it the system that I just showed you, that equals 4 × 2 + 1/ 4. Well that equals 4 × 2 is 8 + 1 is 9. 9/4. I want to give you an intuition for why this actually works so 2 ¼. Let’s actually draw that. Let’s see what it looks like, so that’s—let’s put this back into kind of the pie analogy. So that’s equal to 1 pie, 2 pies and then, let’s say a 4th of pie, right? 2 and 4 and ignore this. This is nothing. It’s not a decimal point. Actually let me erase it so it doesn’t confuse you even more. There you go. Okay.

So go back to the pieces of the pie. So there is 2 ¼ pieces of pie. And we want to rewrite this as just how many fourths of pie is their total. Well, if we take each of these pieces—oh oops, I need to change the color. If we take one each of these pieces and we divide it into fourths, we can now say, how many total fourths of pie do we have? Well we have 9/4. It makes sense right? 2 ¼ is the same thing as 9/4 and this will work with any fraction.

So let’s go the other way, let’s figure out how to go from an improper fraction to a mix number. Let’s say I had 23/5. So here we go in the opposite direction. We actually take the denominator. We say how many times does it go into the numerator and then we figure out it’s the remainder. So let’s say, 5 goes into 23. Well, 5 go into 23. 4 × 5 is 20 and the remainder is 3. So 23/5, we can say that’s equal to 4 and then the remainder 3/5. So, it’s 4 3/5.

Let’s review what we just did. We just took the denominator and divided into the numerator. So 5 goes in the 23 four times and what are left over is 3. So 5 go into 23 4 3/5 times or another way of saying that is 23/5 is 4 3/5.

Let’s do another example like that. Let’s say 17/8. What does that equal as a mix number? You can actually do this in your head but I’ll write it out just so you don’t get confused. 8 goes into 17 two times. 2 × 8 is 16. 17 - 16 is 1; remainder 1. So, 17/8 = 2; that’s this 2 and 1/8, right? Because we have 1/8 left over.

Let me show you kind of a visual way of representing these two so it actually makes sense how this conversion is working. Let’s say I had 5/2, right? So that literally means I have 5/2 or if we go back to the pizza or the pie analogy, let’s draw my 5/2 of pizza.

So let’s say I have ½ of pizza here and let’s say I have another half of pizza here. I just flipped it over. So that’s 2. So it’s 1 ½, 2/2, so that’s 3/2 and then I have a 4/2 here, right? These are halves of pizza and then I have a 5/2 here, right? So that’s 5/2. Well, if we look at this, if we combine this 2/2, this is equal to 1 piece. I have another piece and then I have half of piece, right? So that is equal to 2 ½, I guess we could say piece of pie. Hopefully that doesn’t confuse you too much.

And if we wanted to do this kind of the systematic way, we could have said 2 goes into 5. Well 2 goes into 5 two times and that 2 is right here. And then 2 × 2 is 4. 5 -4 is 1. So the remainder is 1 and that’s what we use here. And of course we keep the denominator the same. So 5/2 = 2 1/2.

Hopefully that gives you a sense of how to go from a mix number to an improper fraction and vice versa from an improper fraction to a mix number. And if you’re still confused, let me know and I might make some more modules. Have fun with the exercises.

Transcription by: Scribe4you Transcription Services