Addition & subtraction word problems with negatives
One of the coldest temperatures ever recorded outside was negative 128 degrees Fahrenheit in Antarctica. One of the warmest temperatures ever recorded outside was 134 degrees Fahrenheit in Death Valley, California. How many degrees difference are there between the coldest and warmest recorded outside temperatures? So let's think about this a little bit. Now, what I'll do is I'll plot them on a number line. But I'm going to plot it on a vertical number line that has a resemblance to a thermometer, since we're talking about temperature. So I'm going to make my number line vertical right over here. So there's my little vertical number line. And this right over here is 0 degrees Fahrenheit, which really is of no significance. If it was Celsius, we'd be talking about the freezing point. But for Fahrenheit, that happens at 32 degrees. But let's say this is 0 degrees Fahrenheit. And let's plot these two points. So one of the coldest ever recorded temperatures was negative 128 degrees Fahrenheit. So let's say that's right over here. This is negative 128 degrees Fahrenheit. And one of the warmest temperatures ever recorded was 134 degrees. This is a positive 134. So it's about that far and a little bit further. So it's a positive 134 degrees Fahrenheit. So when they're asking us how many degrees difference are there between the coldest and the warmest, they're essentially saying, well, what is this distance between the coldest and the warmest right over here? What is this distance? And there's a couple of ways you could think about it. You could say, hey, if I started at the coldest temperature and I wanted to go all the way up to the warmest, how much would I have to add? Or you could say, well, what's the difference between the coldest and the warmest? So you could take the larger number. So it's, say, 134. And from that, you could subtract the smaller number, which is negative 128. So this essentially saying what's the difference between these two numbers? It's going to be positive, because we're subtracting the smaller one from the larger one. This is going to give you the exact same thing as this. Now, there's several ways to think about it. One is we know that if you subtract a negative number, that's the same thing as adding the positive of that number, or adding the absolute value. So this is the same thing. This is going to be equal to 134 plus positive 128 degrees. And what's the intuition behind that? Why does this happen? Well, look at this right over here. We're trying to figure out this distance. This distance is 134 minus negative 128. And if you look at that, it's going to be the absolute value of 134. It's going to be this distance right over here, which is just 134-- which is just that right over there-- plus this distance right over here. Now, what is this distance? Well, it's the absolute value of negative 128. It's just 128. So it's going to be that distance, 134, plus 128. And that's why it made sense. This way, you're thinking of what's the difference between a larger number and a smaller number. But since it's a smaller number and you're subtracting a negative, it's the same thing as adding a positive. And hopefully this gives you a little bit of that intuition. But needless to say, we can now figure out what's going to be. And this is going to be equal to-- let me figure this out separately over here. So if I were to add 134 plus 128, I get 4 plus 8 is 12, 1 plus 3 plus 2 is 6. It's 262. This right over here is equal to 262. How many degrees difference are there between the coldest and warmest recorded outside temperature? 262 degrees Fahrenheit difference.