Numbers & Operations - The Real & Complex Number Systems 222-226
Let's think about the meaning of negative numbers in different situations.
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- Grandma Millie is shrinking. Her height decreases by a quarter centimeter each year. She want to predict the total change in her height over the next three years. Which of the following equations matches the situation above? Her height is decreasing. We can view that as either changing her height each year is a negative fourth of a centimeter. That's going to happen for three years. We multiply negative one-fourth times three. Which is exactly what's happening in this first choice right over here. Her height is decreasing by a quarter centimeter each year, that's this part right over here. She's doing this for three years. After three years, her change in height would be negative three-fourth of a centimeter. You just multiply this out, which means that she lost three-fourths of a centimeter. The second choice would evaluate, if you multiply positive one-fourth times negative three, you still get negative three-fourths, but this doesn't seem to follow as naturally from this statement up here. We're decreasing by a fourth. I like putting the negative in front of the fourth, and then we're going in forward in time by three years. It feels weird to put a negative on the three. We're not backwards in time here. Even though this expression evaluates to the same things as this first one, the first one seems to better match what this statement is describing. I wouldn't pick none of the above just because I found one that I like, that I think that describes the equation that matches the situation above. Let's do another one of these. A zombie lost three limbs each day for four days. He's going to lose 12 limbs, three times four. It's not a human zombie. It's an alien zombie that has at least 12 limbs to lose. The following equation describes this situation. The zombie lost three limbs each day. Lost three limbs. A negative three could represent, hey I'm losing three limbs. The negative is going ... my number of limbs is going down by three. This is negative three. It's dong that for four days. For four days. We have negative 12, which is the total number of limbs that our zombie loses. What does negative 12 tell us? Well, I just said it. The zombie lost a total of 12 limbs over this time period. That looks right. Now, let's see what are these other one. The zombie has negative 12 limbs. Well, no. To have negative 12 ... I don't even know a negative limb would be. We don't know how many limbs the zombie started with. The zombie, I don't know, it might be some type of centipede zombie or something. It might have had a hundred limbs, and if it lost 12 of them, it would now have 88 limbs. The zombie might have had 12 limbs, and now it has a zero limbs. In fact, I don't even know how you get to negative limbs. I don't think this makes sense. I'm not going to pick none of the above, because I agree with this first choice. Let's do one more of these. All right, a certain reality TV show lost, so we're losing, so a negative might be a nice way to represent the lost, lost a total of 9,000 viewers over the past three months. Over three months. It lost the same number of viewers each month. The following equation describes the situation. It lost a total of 9,000 viewers, and it did it over three months. What they're figuring out here is, what was the change in viewership. What was the change in viewership per month? It tells us ... the negative 3,000 tells us that they lost on average ... it actually tells us they lost the same number. This is actually ... it's the same number every month. They actually lost 3,000 viewers every month. Let's see which of these choices match up to that. There are 3,000 fewer people watching the show compared to three months ago. No, they lost 3,000 every month. That's what this is telling us. Every month for three months. There's a same number each month. They lost 3,000 every month for three months for a total of 9,000. This isn't right. The total change in the number of people watching the show is negative 3,000. Over a month that would be true, but the total change was 9,000, or a negative 9,00 I guess I could say. They lost 9,000. I would say none of the above. Well, the negative 3,000 tells us that there was a choice that said, each month they lost 3,000 viewers. That's the choice that I would pick. I would say none of the above.