Adding & subtracting rational numbers
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79% minus 79.1 minus 58 and 1/10. And I encourage you to pause this video and try to compute this expression on your own. Well, the thing that jumps out at you is that these are in different formats. This is a percentage. These are different representations. There's a percentage. This is a decimal. This is a mixed number. And so to make sense of it, it's probably a good idea to get them all in the same format. And it seems like we could get all of these into a decimal format pretty easily. So let's go that way. So 79%, that literally means 79 per 100. If you wanted to write it as a fraction, it would be 79/100. But if you wanted to write it as a decimal, it's 0.79, which could be 0-- or we would write it down a 0.79. Now, 79.1 is already written as a decimal, so we'll just write it again. So minus 79.1. And then, 58 and 1/10. Well, 1/10 is the same thing as 0.1. So you could view this as 58-- well, and literally as 1/10. So it's minus 58 and 1/10. Or, you could view this as 58.1. So now they're all in the same format, let's actually do the computation. Now, the first thing that jumps out at you is you have a fairly small number here. Small positive number. It's less than 1. And you're subtracting fairly large numbers over here. So your whole answer is going to be negative. And to make sense of this a little bit, what I'm going to do is I'm going to factor out a negative sign. And that'll make the computation-- at least in my brain, it's going to make it a little bit easier. So if we factor out a negative sign, this becomes-- so we're going to factor it out. Actually, let me just do it this way. So if we factor out a negative sign, then this will become negative. This would be positive. And this would be positive. And just to verify this, imagine distributing this negative sign, or if this was a negative 1. Negative 1 times this is positive. Negative 1 times this is negative. Negative 1 times this is negative. So these two expressions are the exact same thing. And the reason why I did that is now we'll do the more natural thing of we will add these two numbers. We'll get a positive number, a larger positive number than what we're going to subtract from it right over here. So we can use our traditional method. Although, we can't forget about this negative out here. So let's first do that. Let's add 79.1 plus 58.1. So 79.1 plus 58.1. So 0.1 plus a 0.1 is 0.2. 9 plus 8 is 17. So that's seven 1's and one 10. So one 10 plus seven 10's is going to get us to 0.8. Plus 0.5 gets us to thirteen 10's, or 130. So we have 137.2 is this part right over here. So 100. Let me write this down. So we have 137.2. And then from that, adding a negative 0.79 is equivalent of subtracting 0.79. So let's do that. Let's subtract 0.79, making a point to align our decimal points so that we're subtracting the right place from the right place. And now let's do our subtraction. So right now we're subtracting 9 from nothing. We could write a 0 right over here, but we still face an issue in the hundredths place. We're also subtracting a 0.7 from 0.2. So we're going to have to regroup a little bit in the numerator in order to subtract. Or at least, in order to subtract using the most traditional technique. So let's take a tenth from the 2, so it's only one tenth now, and give it to the hundredths. So one tenth is ten hundredths. So we could subtract that ten hundredths minus nine hundredths is one hundredth. Now in the tenths place. We don't have enough up here, so let's take 1 from the one's place. So that becomes a 6. 1 is ten tenths. So now we have 11 tenths. 11 minus 7 is 4. Add our decimal place. 6 minus 0 is 6. And then we got our 13 just like that. So outside the parentheses, I still have the negative sign. When I computed all of this inside the parentheses, I got 136.41. And then we can't forget about the negative sign out here. So this whole thing computes to negative 136.41.