#Quick course on units

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flat tinsel
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I'll introduce you to working with units

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For this kind of problems, it's probably overkill, but even now I still use that method a lot, so I think it's worth knowing
Treat units such as "litres", "days" or "bottles" just like you would treat numbers
That means that you can use operations on them

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Examples, with growing complexity :
2 apples + 5 apples = (2+5) apples = 7 apples
2 apples / 8 days = 0.25 apples / day
(⬆️ see how the "apples/day" in our formula merely translates to "apples by day" in casual language. That's quite convenient and understandable !)
3 meter * 2 meter = 2 * 3 (meter * meter) = 6 meter²
15 apples/child * 5 children = (15/5) (children/child) * apples = 5 apples
(⬆️ since we treat units just like numbers, they can also be cancelled via division)
But sometimes, some numbers just don't have units. The best visual example I can think of is when counting from 1 to 10.

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I think that's enough examples for you to understand how this works in general

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But note that you can never add or substract two units that aren't the same. You can't even write it.
Example : 3 people + 2 trains makes absolutely no mathematical sense. It is just wrong and there's no way around it

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----- Transition -----

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Now, regarding your question, you've got the following data :
Goats produce milk at an average rate of : 21.7 litres/day
Milk has been produced for : 280 days
The bottles used ot store the milk have a capacity of : 0.5 litre/bottle
You're looking for an answer whose units are "bottles" (because you're looking for the total number of bottles needed to store all the produced milk)

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That means that you want the unit "bottles" to end up at the "top" of the formula (fraction-wise, just like in 1/3, the 1 is considered at the "top" and the 3 at the "botttom" of the fraction). Currently it is at the bottom (because of 0.5 litres/bottle). Thus, you can observe you'll have to divide something by "0.5 litre/bottle" so that the "bottle" can go back up (-- Reminder : 1/(a/b) = b/a --)

Also, you want every unit that isn't "bottle" to get cancelled from the final result
Knowing all of that, here's what you can do to solve your problem :

  • Compute the total quantity of milk produced : 21.7 (litres/day) * 280 days = 6076 litres
    See how we managed to get a value that doesn't contain any "day" unit. That's a step towards our final result :)

  • Compute the total number of bottles needed to store the milk : 6076 litres / (0.5 litre/bottle) = (6076/0.5) * (litres/(litre/bottle)) = 12152 bottles
    If you're wondering why I chose to multiply in the first calculation, and why I divided in the second one, here's the answer : the units.
    That's the reason of why I took 40 minutes (omg it's been 40 minutes 😳) to explain that way of using units inside calculations to you.
    It is just easier. I knew I wanted the "bottle" to be on "top" and the "litre" units to cancel each other out, so I just picked the only operation among the four main ones (+ - * /) that allowed me to do both
    You don't even have to interpret what all the values you compute mean, just having their units is enough to understand what role they must play in the final result, if you'll need to use it in a multiplication or division, ...

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I really hope I was able to help you (or anyone out there) understand the fundamentals of using units inside calculations. It is very important and useful, and especially in higher levels of mathematics and physics, where constants and values become more and more abstract and difficult to interpret using casual words.

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If you really want to push yourself and make sure you've understood everything, then you should be able to know how many apples I eat every 3 weeks knowing that

  • I work 7 hours a day during weekdays
  • I work 5 hours on Saturdays and don't work during Sundays
  • I eat on average one apple every 4 hours of work
    One piece of data is missing (because it is implicit), but if you use units correctly I'm sure you'll still get to the answer ☺️
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Quick course on units

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If you manage to find the answer to that question, then I'm sure you'll be feeling way more confident with the kind of questions that you sent