>>Hi. This is Julie Harland, and I’m your Math Gal. Please visit my website at yourmathgal.com where you can search for any of my videos organized by topic. We’re going to learn how to write whole numbers as fractions. This would be helpful for doing problems like this, like 7 minus 3-2/5, for instance. So some people have trouble doing this problem, and one way of doing it is to rewrite 7 as a fraction, okay. So let’s go and talk about how could we write 7 as a fraction. Well, first of all, 7 is the same thing as 7 over 1 as a fraction. There, I’ve just done it. Why is that? Because 7 over 1 means 7 divided by 1, which is 7. So hopefully this makes sense to you that 7 is the same thing as 7 divided by 1, which could be written as 7 over 1. Okay, now once you’ve written it like that, we can make an equivalent fraction by multiplying the numerator and denominator by any number we want. So let’s say you wanted to have a denominator with a 3 in the bottom. Well, then, I can just multiply the 7 over 1 by 3 over 3, because that’s the same thing as multiplying by 1, of course, right, since 3 divided by 3 is 1, and that way my numerator would be 21 over 3. Now, again, does that make sense. Is 7 the same thing as 21 over 3? Sure, because 21 divided 3 really is 7. So hopefully this is making sense, so this also could be written as 21 over 3. So there’s another way of writing 7 as a fraction. Let’s do it a different way. How about if I wanted to have a different denominator, so you could pick anything you want for the denominator. Let’s say you wanted the denominator to be 8, okay. I would like to have an 8 in the denominator. So what would I multiply the 1 by to get that 8 in the denominator? Well, by 8. And, of course, whatever you multiply the denominator by you have to multiply the numerator by, so this, again, keep in mind what you’re really looking at. This is like saying 7 times 1, right, because 7 divided by 7 really is just a 7, and 8 divided by 8 is really just like the same one. So basically, I’m saying 7 times 1, all right. I’m going to erase that so it doesn’t get confusing here. And then what do we have in the numerator? 7 times 8 is 56. And does that make sense? Is 56 over 8 the same thing as the number 7? Remember we’re starting off with just the number 7 and we’re writing it as a fraction. So there’s different ways of writing it as a fraction. Here’s another one, because 56 divided by 8 is 7. So there’s another way of writing it as a fraction. So that’s how you could write a whole number as a fraction. Now some people think of it slightly differently. You get exactly the same answer. They say well, if I want to write 7 with a denominator of let’s say, 6, there’s two ways of thinking about it. They think, well, what divided by 6 is 7. That’s one way the getting the answer, right. So you take a whole number and you’re saying I want to write it with a 6 in the denominator, so you have to think, what number divided by 6 is 7, and they get the answer, it’s 42 divided by 6, okay. Some people have trouble with that, thinking what divided by 6, so there’s another way to do it. If you’ve got a whole number, if you want to know what divided by 6 is 7, all you do is multiply 6 times 7, and that’ll give you your answer. So there’s another fraction that equals 7. Let’s try one more like that. What if you wanted to make the denominator 10? What would go in the numerator? Well, you say 7 is what divided by 10, or you could just say, well that’s going to be 10 times 7, so 70 over 10. All right, let’s pick another number besides 7. How about 3? How come I write that with a denominator of 2? What would go in the numerator? Well, 2 times 3 is 6, and then check and see if it makes sense after you’ve written it as a fraction. Is 3 the same thing as 6 divided by 2? Certainly. Now remember, the first way I showed you to do is you could write 3 as 3 over 1, and say I want to end up with a 2 in the denominator, so I just multiply it by 2 over 2. All right, so that I get a 2 in the denominator, and you still are going to get 6 over 2. So you kind of have to pick which way is easier for you to do it. Is it easier for you to write it as 3 over 1 and then do you multiply by 2 over 2, or can you go directly to this, 3 equals what over 2 and pick that number at the top by multiplying the 2 times 3. Let’s do another one. How about 5. 5, let’s see, could you do this one? What would go in the numerator if I wanted to have a, let’s say 7 in the denominator. What would go in the numerator? Well, 7 times 5. Does that make sense? Is 5 the same thing as 35 divided by 7? Yes. All right, why don’t you try this one. How about the number 11? Now, what I want you to do, I’m going to leave off the equal sign here because I don’t know which way you’re going to do it. I want you to write 11 as a fraction that has a denominator of 8, okay. So write 11 as a fraction with a denominator of 8, okay. Hopefully you did that, so you want a denominator of 8. What would go in the numerator? 8 times 11 is 88. Does it make sense? Is 88 divided by 8, 11? Yes. And the other way some of you may have done this is you may have written 11 as 11 over one, and so I want to have a fraction with a denominator of 8. So I would multiply top and bottom by 8 getting 88 over 8 that way. All right, just for fun, let’s do a problem where it might be useful to change a whole number to a fraction. All right, let’s do 7 minus 3/8. Okay, now there’s a couple of ways to do this problem, okay, but one way is, you’re just going to get a common denominator. So let’s do that. So if I want to get a common denominator, I want to write 7 for the same denominator, as a fraction that has the same denominator as this other one, which is 8. So I want to write 7 with a denominator of 8, okay. So how would I do that? That’s what we just went over. That would be 7 times 8, 56 over 8, that would equal 7, right. Now if you prefer to write it like this, remember, you could write 7 over 1 minus 3/8. You can say, well, I’m going to multiply by 8 over 8, which is the same thing as 56/8, and then go minus 3/8. If you like to do it vertically and show what you’re multiplying numerator and denominator by, we’re still going to get 56 minus 3/8, okay. Okay, so then what is 56 minus 3/8? That’s 53/8. Remember you subtract the numerators and you just keep the same denominator. All right, so there’s one problem doing it this way. You could also change this back to a mixed number by dividing 8 into 53, and so what would that be. 8 goes into 53 six times, that’s 48, and then you would have 5/8 left. So remember, both of these are correct along as it’s reduced. So the answer to be written is 53/8 or 6-5/8. This problem could be done a little bit differently. Let’s say I wrote this as 7 minus 3/8. It could also be done using a borrowing technique. You could thing of 7 as the same as 6 plus 1. So I could think of this problem, watch. I’m going to borrow 1 from the 7, then this becomes the number 1. So I’ve got 6, the whole number, and I’m going to subtract down. 6 minus — there’s nothing here, that’ll give me 6, and I have to have to do 1 minus 3/8, and here we go again. How would I do 1 minus 3/8. I could change that 1 to a fraction with the same denominator. So one is really the same thing as 8/8. And now I can go ahead and subtract 8/8 minus 3/8 is 5/8. And notice I get the same answer as when I did it this other way, 56/8 minus 3/8, and I got 53/8. And then I changed it to the mixed number, okay. All right, let’s do another one where we’re going to have a whole number minus a mixed number. Let’s see what that looks like. All right, let’s take 5 minus 2-1/3. Well, one way of doing this is we could change both of these to fractions, to improper fractions, and then get a common denominator. So let’s do the 2-1/3. That would be 3 times 2 plus 1. The numerator would be 7/3, okay. So I know I want the denominator to be 3, and so 15, using the technique we’ve been going over, would be what over 3. That’ll be 15 over 3. Remember you just multiply the 5 times 3. And so then, we have 15 minus 7 in the numerator, that would be 8/3, okay. Written as a mixed number, that’ll be 2-2/3. Okay, second way with borrowing. So we have 5 minus 2-1/3, okay. So you could do the borrowing technique. See, the problem is I can’t take 1/3 away from nothing, so, if I borrow, right, I know that 5 is the same as 4 plus 1, okay. Instead of me writing 1, how about if I write 1 as a fraction with a denominator of 3. What would that be? Well, it would be the same thing, just 3 over 3. All right, so now I could do 4 minus 2 which is 2, and 3/3 minus 1/3 which is 2/3, and look it, I got the same answer again, 2-2/3. So this is, you know, an example of where you might want to be able to change a whole number to a fraction so that you could do subtraction with mixed numbers and whole numbers, et cetera. Now this isn’t the only way to do this kind of a subtraction problem. I could think of two other ways, but I’m just going to leave it for now at this, because this video is really over about how to write a whole number as a fraction. [ Pause ] Please visit my website at yourmathgal.com where can view all of my videos, which are organized by topic.