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Comparing rates example

A conservationist thinks that squirrels exhibit higher aggression rates when crowded together. To test this, they compare three parks with different squirrel populations and areas. By calculating squirrels per hectare, they find Park C to be the most crowded, followed by Park B and Park A. The conservationist expects the highest aggression rate in Park C due to its crowdedness.

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Video transcript

- [Instructor] We're told that a conservationist has the hypothesis that when squirrels are more crowded together, they have higher rates of aggression. The table below shows the area of three parks and the number of squirrels in each, that's given right over here. Order the parks from least crowded to most crowded. Based on the crowdedness, in which park would the conservationist expect to see the highest rate of aggression? So pause this video and see if you can figure this out. All right, now let's work through this together. So we wanna order the parks from least crowded to most crowded. So how can we think about crowded? Well, we could think about it in terms of the number of squirrels. Squirrels per area, per hectare. And so something with a lot of squirrels per hectare would be more crowded, and something with fewer squirrels per hectare would be less crowded. You could also, if you wanted to, think about it in terms of hectares per squirrel, this would also be a legitimate way of tackling it. And of course, if you have more hectares per squirrel, that would be less crowded. It would be the other way around. While if you had fewer hectares per squirrel, it would be more crowded. But here, when we look at this, the numbers of squirrels are larger than the number of hectares in every scenario. So it might be a little bit easier to divide in this one. And this is also how my brain tends to think about it. So let's calculate the number of squirrels per hectare for each of these parks. So, first of all, let's think about park A, and I will do that over here. Park A, you have 54 squirrels. I'll write squ for short, per every eight hectares. And so this is going to be the same thing as 54 over eight squirrels per hectare. And we could try to estimate it, but it looks like they're all actually a little bit around seven if we divide the number of squirrels by the number of hectares, so we might have to get a little bit more precise. So let's see, eight goes into 54. I will do it over here. Eight goes into 54, it goes six times, six times eight is 48. And I subtract, I get a remainder of six. And then let me put a little decimal here. And then if I bring down that zero, eight goes into 60 seven times, seven times eight is 56. And I can keep going, but let me see if this is enough precision for me to compare. So park A is approximately, I'll make this little squiggle here for approximately, 6.7 squirrels per hectare. Now let me do park B right over here. So for park B, we have 20 squirrels, squ for short, for every 2.7 hectares. Now, one thing we can do to help simplify this so we don't have to deal with decimals is let's multiply both the numerator and the denominator by 10. Notice that's just equivalent to multiplying by one. So this is equivalent to saying you have 200 squirrels for every 27 hectares, or you could view it as 200 over 27 squirrels per hectare. So let's take 27 into 200, and if I were to estimate it, let's see, 27 is close to 30. 30 would go into 200 six times. Let me try that out. So it goes into 200 six times, six times seven is 42, six times two is 12, plus four is 16. And then if I subtract, I am going to actually get, it looks like 38. So maybe I can fit in one more 27 there. So let me do that seven. So seven times seven is 49. 49, seven times two is 14 plus four is 18. Yep, that worked out nicely. If you subtract 189 from 200, you're going to get 11. And now let me bring down a zero. So how many times does 27 go into 110? Well, it looks like it goes three times, I think. Three times seven is 21, three times two is six, plus two is eight. And it looks like actually I could fit in one more. So let's see, it might go four times. So 110. So if they go four times, four times seven is 28, and then four times two is eight, plus two is 10. Yeah, it went four times, so get a remainder of two. So we could keep going, but this is approximately 7.4. So approximately 7.4 squirrels per hectare. So we already see that park B is more crowded than park A, but now let's check out park C. And so for park C, we have 51 squirrels for every 6.8 hectares, 6.8 hectares. So we could do the same idea. Let's multiply the numerator and the denominator by 10, which means that we have 510 squirrels for every 68 hectares. And so 68 will go into 510. I'm guessing I'm gonna have to have some decimals here. So it's close to 70. 70 would go into 510 about seven times. Let me see how that works out. Seven times eight is 56, seven times six is 42, plus five is 47. And I think I did well there. So if I subtract here, I could do some regrouping, or I could try to do it in my head. To go from 476 to 500, I would have to add 24 plus another 10. So I'm gonna have 34 right over here, bring down a zero. And so if I'm thinking roughly 70 goes into 340, let's see, will it go? It might go five times actually. Let me try that out. If I say 7.5, five times eight is 40, and then five times six is 30 plus four, it went exactly five times. So that means in park C, we're at 7.5 squirrels per hectare. So what's the most crowded if I wanted to order it? Well, the most crowded is park C, the second crowded is park B, and the third most crowded is park A. And so based on crowdedness, in which park would I expect the highest rate of aggression? Well, park C, those squirrels are all, they're much closer to each other. They might be fighting over things, who knows? But there we go. We answered the question.