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Rewriting a fraction as a decimal: 6/12

Sal rewrites 6/12 as a decimal. Created by Sal Khan.

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Video transcript

Let's see if we can rewrite 6/12 as a decimal. And once again, I encourage you to pause this video and try this on your own. And I'll give you a little hint. See if you can rewrite this fraction, not in terms of 12ths, but in terms of 10ths. Well, let's just visualize this thing. So let's say that this right over here is a 12th. So that is a 12th. And so let me try to make 12 12ths. So copy and paste that, so that's two 12ths. And that is three 12ths. And that is-- actually let me just copy and paste the three 12ths. So copy and paste. So now we have six 12ths, which I'll color it in a second. And now we have 9/12, and now we have 12 12ths right over there. And we care about six of these 12ths, so this is representing six of these 12ths. So let me see if I can color in six of them. So let me go to-- let me see if I can pull this off. So this is going to be 1. Let me do a bigger paint brush. So 1, 2, 3, 4, 5, 6. That's right. That's 6/12. I'm just going to color all of this business in. So there you have. We have represented our fraction. Now, how do we represent this thing right over here in terms of 10ths? So the one thing that I might want to do is well look, 6 and 12 are both divisible by 6. So what if we divide this, not if we rewrite this whole, not in terms of 12ths, but we write it in terms of halves? Well, how would we do that? Well, we could say-- we could call all of this stuff-- this is 1/2, and this is another 1/2. Or another way of thinking about it is we're taking six of our 12ths together, and then we're putting them together, and we're turning them into a 1/2. So in terms of the number of sections we have, we're dividing the number of sections we have by 6. So let's do that. So let's divide the number of sections by 6. So now we're only going to have two sections. We're only going to have two halves. That right over there is 1/2, and that right over there is the other 1/2. Notice we had 12/12. Now we're taking 6 of those at a time putting them together, so now we only have two sections instead of 12 sections. But those 6/12, what are they going to be in halves? Well, once again, where we're taking six of the things and putting them together into one. So we're going to divide that by 6 as well. And so this is going to be the same thing as 1/2. And you see this 1/2 right over here. And notice, all we did in the past, we had multiplied and divided-- sorry, in the past we had multiplied the numerator and the denominator by the same quantity to get an equivalent fraction. Now, we're dividing the numerator and the denominator by the same quantity to get the same fraction. Hopefully, this makes sense, that 1/2 is equivalent to 6/12. Now, why did I do that? Didn't I say that I wanted to get this in terms of 10ths? And yes, I do want to get it in terms of 10ths, but 1/2 is fairly easy to rewrite in terms of 10ths. So let me re-express 1/2. So 1/2, let me write it like this. So 1/2, I could represent 1/2 again. I'm going to re-represent 1/2. So let's say this right over here is clearly 1/2, so I'm just representing it. So I'm taking a whole, dividing it into 2, and 1/2-- let me just color it in-- would be that right over there, which as we already seen, it's equivalent to the 6/12. Now, I want to write this as 10ths. So what if I take each of those halves, and I turn it into five times as many pieces? So let me do that. So I'm going to do it into 1, 1, 2, 2, 3, 4, and 5. So what did I just do? I multiplied. I now have five times as many pieces and the 1/2 is going to represent five times as many 10ths. So this is going to be equal to 5/10. Let me do it in a green color, 5/10. Notice, 6/12 is the same thing as 1/2, which is the same thing as 5/10. All I did here is I multiplied the numerator and the denominator by the same quantity 5, so I could get 10 in the denominator. And 5/10, well that's the same thing as 5 times 1/10. It's literally 5/10, and we can represent this as a decimal, or you could say in decimal notation. 5/10, we know that-- let's say that that is the ones place, and if we go one place to the right of the decimal, that is the tenths place. That right over there is the tenths place. And we have 5/10, so we would put a 5 right over there. So this could be rewritten as the decimal, 0.5. Now, there's other ways you could have thought about it. You could say hey, look. 6 is half of 12, and so what is half of 10? Well, 5 is half of 10, and so 5/10 is the same thing as 5/10, which is the same thing as 5/10 written as a decimal.