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Interpreting absolute value

In this weight change scenario, three individuals track their monthly progress. Jenna experiences a 3-pound weight loss, while Sarah gains 2.5 pounds and Bill gains 4 pounds. By plotting these changes on a number line, we can determine that Jenna lost the most weight, Bill had the largest change, and Sarah had the smallest change.

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Video transcript

- [Voiceover] So we have three folks: Jenna,Sarah and Bill and they're keeping track of their weight. And in particular they're keeping track of their weight over a month. And right over here we have their weight change over the month. So if you take their ending weight and from that you subtract their starting weight. So, let me just write that, that's your end weight minus your starting weight. That's going to be your change in weight over that month. And so we have the change in weights here. So, Jenna's change in weight is negative three pounds which means that she lost weight. Sarah's change in weight is positive 2 1/2 pounds which means she gained 2 1/2 pounds. And then Bill's change in weight is positive four pounds which means he gained four pounds over the month. So, given that, let's answer some questions. Who lost the most weight? Who had the largest change in weight? And who had the smallest change in weight? And I encourage you to pause the video and try to work through it on your own. Well let's just plot all of these on a number line here to help us think through it, although some of you might already have an answer here. So Jenna's weight change is negative three pounds. So that's Jenna right over there. I'll say J for Jenna. Sarah's weight change, and she had a weight gain is 2 1/2 pounds so that's right over there. Positive 2 1/2 pounds for Sarah. And then finally Bill gained four pounds so that is Bill right over there. Now let's answer the question, who lost the most? So when we talk about lost, where we care about directions, we said hey, who moved most to the left of zero? Well Sarah and Bill didn't move to the left of zero at all. They gained weight. That's why they're to the right of zero. Jenna's the only person who lost anything. So the person who lost the most is Jenna. Now who had the largest change? And if we think about the largest change, one way to think about it is, who is the furthest away from zero? So one way to think about it is, which of these is the largest absolute value? Well the absolute value here, the absolute value of negative three is, and we can just call this the absolute change, is just going to be the absolute value. The absolute value of negative three is positive three. Absolute value of 2.5 is 2.5. Let me make this a little bit clearer. Absolutue value of four is just equal to four. So who had the largest absolute change? Well Bill had the largest absolute change and then second place was actually Jenna. She lost weight, but she had a pretty big change. She had a three pound change although it was a three pound loss. Bill's was a four pound gain. But the largest change is definitely Bill. Now who had the least change? Well another way to think about it, this is the least absolute change. Who changed the least from zero? Well if you look at here, Sarah had the smallest absolute change. Jenna lost weight so the weight change of Jenna, she has negative three vs. Sarah's positive 2.5. But if we talk about who had the least change from zero. If your weight change was zero, that means you didn't gain or lose weight from the beginning of the month to the end of the month. So who had the least change? Well that's the least absolute change? Well, we see that right over here. 2.5 is less than three or four. So the least change is Sarah. And we're done.