yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Interpreting units in formulas: novel units | Mathematics I | High School Math | Khan Academy


2m read
·Nov 11, 2024

So, we're told to consider the formula ( Y ) is equal to ( \frac{2C}{P} ) where ( y ) represents the carrot yield.

So, ( y ) represents the carrot yield, ( c ) represents the number of expected carrots, and ( P ) represents the number of plants.

So, ( P ) represents a number of plants. Select an appropriate measurement unit for carrot yield.

So, the key here is to realize that we can treat units like we would treat algebraic variables.

And so, for example, over here, if we're saying our yield is going to be two times the number of expected carrots divided by the number of plants, well, our units are going to be—well, actually, we could put some numbers in here actually just to make something more interesting.

Let's just say that ( c ) is equal to 10 carrots, and I'm just making these numbers up, just hopefully it makes sense what I'm about to do.

And let's say that ( P ) is equal to, I don't know, 30 plants. ( P ) is equal to 30 plants.

And so, using this formula, ( y ) would be equal to ( \frac{2 \times 10 \text{ carrots}}{30 \text{ plants}} ).

So, ( 2 \times 10 ) carrots, that's going to be 20 carrots.

So, we can write the numerator as this is 20 carrots divided by 30 plants.

And so that is going to be equal to—you could divide the numbers, so it would be ( \frac{20}{30} ), which would be ( \frac{2}{3} ).

( \frac{2}{3} ) and then the units would be carrots per plant: ( \frac{2}{3} ) carrots per plant, carrots per plant, carrots per plant.

And once again, the whole point of what I just did is to see what the units would be for our carrot yield, and we can see the units would be carrots per plant.

And I put the numbers there just so hopefully it makes a little bit of intuitive sense of what we just did, that we're algebraically manipulating or mathematically manipulating the numbers; we do the same thing with the units.

And so when we try to find the appropriate measurement unit for carrot yield, which I had never heard of before this video, we see it's carrots per plant, not carrots per plant squared.

That would have been the case if we were squaring this ( P ) over here, or plants times the square root of carrots—well, that would be more so if we were taking the square root up here and we weren't dividing by ( P ), but we were multiplying by ( P ).

But the general theme that you could see is this constant, this two, didn't affect what happens to the units, but what did matter is how these variables relate to each other.

We're taking the variable ( C ), dividing it by ( P ), so whatever the units were for ( C ), we divide those units by the units for ( P ), and we get the units for yield: carrots per plant.

More Articles

View All
Continuity and change in the postwar era | Period 8: 1945-1980 | AP US History | Khan Academy
The era from 1945 to 1980 was action-packed, to say the least. During this period, the United States experienced the baby boom, the civil rights movement, the tumultuous 1960s, and the quagmire of Vietnam. This era was also riddled with contradictions; a …
15 APPS RICH PEOPLE USE
Did you know there is an entirely different universe of apps that rich people use? Let’s get you plugged in. Here are 15 apps rich people use. Welcome to alux.com, the place where future billionaires come to get inspired. Number one: Twitter. You might b…
Law Without Government. Robert P. Murphy.
So what’s interesting, I think, is that actually the case for private defense is a piece of cake. That’s really not what trips people up. Really, when people give you all these zingers about “well, what if this happens? What if that happens? You know, wha…
I Failed - How Much Money I Lost
What’s up here, guys? It’s Grams. You know what’s easier than making money? Losing money. And unfortunately, this video is a prime example of doing exactly that because I messed up. See, two years ago, during the pandemic, where every redditor on Wall St…
Endocrine system introduction
What you see in these pictures is a forward view of a transparent man or a semi-transparent man, and this is a posterior back view of a semi-transparent woman. But what are these organs that are depicted? These organs secrete molecules into the bloodstre…
Biden's Student Loan Forgiveness Is A MISTAKE! | Sen. Lummis Crypto Policy Interview
[Applause] [Music] The Biden administration is leaning towards ten thousand dollars in student loan forgiveness. For more on this issue and a look at the best path forward, let’s bring in O’Leary Ventures chairman Kevin O’Leary. He’s also a CNBC contribut…