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### Course: 8th grade foundations (Eureka Math/EngageNY) > Unit 4

Lesson 3: Topic C: Foundations# 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.

## Want to join the conversation?

- is 25% the same thing as 1/4(66 votes)
- yes! think about it like this, 25 cents is 1/4 of a dollar. because 25+25+25+25= 100, or 25x4= 100! <3(37 votes)

- I am dreadfully confused... Does anyone know a simpler way of doing this?(50 votes)
- Equivalent rates can be used to compare different sets of quantities that have the same value. A rate that compares a quantity to one is called a unit rate. The unit rate has a denominator equal to one when written as a fraction. Unit rates can be used to find larger equivalent rates.(30 votes)

- how is 8 larger than 8 1/3?(25 votes)
- I have to say... the problem is a little vague with it's wording. They seem to be ordering the tanks based on the number of fish in the tank, but doing it by looking at the rates: liters of water per fish. In this situation, the more water needed for 1 fish means the fewer fish you can put in that tank.

Thus: 8 1/3 liters / fish has more water than 8 liters / fish. Thus there are fewer fish in the tank with the 8 1/3 liters / fish.

Hope this helps.(22 votes)

- When Sal divided 100/12, how did he get 8 1/3?(9 votes)
- So 12 times 8 would be equal to a total of 96. It can’t be any larger, or it wouldn’t fit in the amount of 100. The remainder that you get after that would be 4. However, since the denominator is 12, you would get 4/12, which is equal to 1/3. That gives you 8 1/3.(16 votes)

- Does it matter which order you write it in?(11 votes)
- Yes it does because writing the rate backwards changes the value of the rate.(8 votes)

- IS 25% the same as 1/4?(9 votes)
- Yes, it is. For example, if you multiply the numerator by 25 and the denominator by 25, you get 25/100, or 0.25 which is 25%. Of course, you can also think of it as quarters which are $0.25 and you need 4 of them for $1, so one quarter would be 1/4. Hope you have a great day!(9 votes)

- How do you know when to divide(8 votes)
- huh?. ..HUh?How do u solve(7 votes)
- what is the ratio of area to the number of squirrels(5 votes)

## 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.