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# Negative number word problem: temperatures

CCSS.Math:

## Video transcript

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 gonna plot 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 zero degrees Fahrenheit which really is of no significance if it was Celsius and we'd be talking about the freezing point but for a Fahrenheit that happens at 32 degrees but let's say this is zero degrees Fahrenheit and let's plot these two points so that one of the coldest ever recorded temperatures was negative 128 degrees Fahrenheit so let's say that's right over here negative this is negative 1 to negative 128 degrees Fahrenheit and the one of the warmest temperatures ever recorded was 134 degrees 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 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 start 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 let's say 134 and from that you could subtract the smaller number you could subtract the smaller number which is negative negative one and write negative 128 so this is essentially saying what's the difference between these two numbers is 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 not the positive of that number or adding it the absolute value so this is the same thing this is equal to this is going to be equal to 134 plus plus positive 128 degrees and what's the intuition behind that why 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 it's going to be this distance right over here which is just 134 which is just that right over there plus 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 the smaller numbers you're subtracting a negative you're really it's the same thing as adding the positive and hopefully this gives you a little bit of that intuition but needless to say we can now figure out what it's going to be and this is going to be equal to let me let me figure this out separately over here so if I were to add 134 plus 128 plus 128 128 I get 4 plus 8 is 12 1 plus 3 plus 2 is 6 it's 262 so it's 200 this right over here is equal to 262 how many degrees difference are there between the coldest in the warmest recorded outside temperature 262 degrees Fahrenheit difference