Main content

## SAT

### Unit 10: Lesson 3

Problem solving and data analysis- Ratios, rates, and proportions — Basic example
- Ratios, rates, and proportions — Harder example
- Percents — Basic example
- Percents — Harder example
- Units — Basic example
- Units — Harder example
- Table data — Basic example
- Table data — Harder example
- Scatterplots — Basic example
- Scatterplots — Harder example
- Key features of graphs — Basic example
- Key features of graphs — Harder example
- Linear and exponential growth — Basic example
- Linear and exponential growth — Harder example
- Data inferences — Basic example
- Data inferences — Harder example
- Center, spread, and shape of distributions — Basic example
- Center, spread, and shape of distributions — Harder example
- Data collection and conclusions — Basic example
- Data collection and conclusions — Harder example

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# Units — Basic example

Watch Sal work through a basic Units problem.

## Want to join the conversation?

- this example was easy to understand and easy to learn(11 votes)
- Couldn't you just do 15*10 to get 150 and then choose the first one because if it is 3/4 then it will have to less than 150 and the only choice that is less than 150 is choice A(9 votes)
- There are more than one way to solve a problem. As long as the answer is right and you understand what you're doing, you should be fine.(4 votes)

- why do we keep the units when we know what our final units are(4 votes)
- Keeping the units is an easy way to see if you mix up the equation. For example, if you keep the units and end up with L/mg, you immediately know that you messed up, whereas without units, you might not catch that mistake.(2 votes)

- its easy just divide 10.3divided by 4 and multiply it by 15 you will get 112.5 you don't need to do complex math(2 votes)
- I multiplied 10 times 15 and then multiplied that by 0.75 and got the same answer. Is there any reason I shouldn't do it like that?(1 vote)
- No, there isn't. In these sort of converting-between-unit problems, all you're doing is multiplying, so the order doesn't matter. You can find a standard order of doing the problem that works best for you: Maybe it's in order of what's given in the problem, or maybe you start at what's being asked for and work backwards form there. Who knows. But as long as you have all of the conversion factors you need, any order works.(2 votes)

- Could I have used the calculator to do the calculation?(1 vote)
- So you convert the litters and milligrams?(0 votes)
- in a way yes i did it a different method so knowing that 1 liter = 10 mg , you'd just multiply 15 by 10 to get the amount in liter milligram or Lmg after that you multiply it by 3/4L causing you to just cancel the liters and making it milligrams :)(3 votes)

- So you convert the litters and milligrams?(0 votes)
- Pretty much, that is what is going on. But in this problem Sal isn't so much converting liters to milligrams as he is finding how many milligrams of nitrate per liter of water.(1 vote)

- so do you combine the litres and the miligrams?(0 votes)
- No, you don't combine the liters and milligrams; they are separate units. What Sal did was set up his equation so that liters were in the numerator and the denominator and so cancelled out. This was necessary because the question is asking for how many milligrams of nitrate the class would find in their water sample.(1 vote)

- i would reccomend putting the actual admin into the video(0 votes)

## Video transcript

- [Instructor] A high school
class is measuring the amount of nitrate in a local stream. To be considered safe to
drink, the maximum amount of nitrate that can be present in water is 10 milligrams per liter. The class takes a sample
of 15 liters of water. If the number of milligrams
per liter of nitrate in the stream water is 3/4 of the maximum that is safe to drink, how
many milligrams of nitrate should the class expect
to find in their sample? All right, this is interesting. So in this sample, in this
15-liter sample, they find that the number of milligrams
per liter of nitrate is 3/4 of the maximum. Well, what's the maximum? Well, they tell us up here. They tell us, let me underline this. The maximum amount of nitrate
that can be present in water is 10 milligrams per liter. So what the class finds is that
they find that their sample has 3/4 of this maximum value. So what's 3/4 of 10 milligrams per liter? Let's just write that down. So the maximum is 10 milligrams per liter. In their sample, they find 3/4 of this maximum concentration. So let's just multiply that. We can multiply that times 3/4, which is going to be equal to what? That is 7 1/2 milligrams per liter. So that is 7.5 milligrams per liter. The way I think about this, 3/4 of a hundred is 75. So 3/4 of 10 is going to be 7 1/2. You could have done it other ways. You could say 10 times three is 30. 30 divided by four is 7 1/2, and you keep your units. So this is the concentration that they find in their sample, 7.5 milligrams per liter. And they do this, they
find this concentration in 15 liters of water. So the total number of
milligrams they find, well, you take the liters
of water, 15 liters, and then multiply that
times the concentration. 7.5 milligrams per liter. Now, the units should work out, and they do indeed. You have a liter being divided by a liter, so those cancel out. Then you're left with
15 times 7.5 milligrams. So we just need to find
out what 15 times 7.5 is, so let's do that. So if you have 7.5 times 15, five times five is 25, five times seven is 35 plus two is 37, and then one times 75 is 75. So let's see, five plus zero is five, seven plus five is 12, and then four plus seven is 11, and you have one digit
behind the decimal point. They would expect to
find 112.5 milligrams, and there we go.