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
From Homeless To Owning A Bugatti | TheStradman
I decided to live in my Audi TT in Beverly Hills, California. I would just stand there on Rodeo Drive for eight to twelve hours a day, just hoping to see cool cars. Every evening, I would park outside McDonald’s, edit my videos, use their free Wi-Fi, post…
Electromagnetism | Forces at a distance | Middle school physics | Khan Academy
You know what a magnet is, but did you know that some magnets can be turned on and off? One type of temporary magnet is called an electromagnet. So what is electromagnetism? Well, the hint is in the name itself: Electro for electrical and magnet for, well…
Jim Crow part 2 | The Gilded Age (1865-1898) | US History | Khan Academy
So, in the last video, we started talking about the system of Jim Crow segregation, which was a legal form of segregation and denial of voting rights or disenfranchisement that characterized the American South from approximately 1877 to 1954. We finished …
Tracy Young Speaks at Female Founders Conference 2015
Hi everyone! It’s an honor to be here today. My name is Tracy Young. I’m one of the co-founders of PlanGrid. So, I need your help picturing 2010. I’m a construction engineer, new graduate with a construction management degree, and I’m on my first constru…
Intro to articles | The parts of speech | Grammar | Khan Academy
Garans, I would like to tell you a Tale of Two Elephants in order to get at the idea of this thing called the article, and we’ll explain what that is after I tell you about the elephant and an elephant. Now, articles are words like a, or an, or the. Arti…
How To Financally Plan Before Marriage | Jason Tartick & Kaitlyn Bristowe
It’s a crazy thought process to leave 10 years of NBA grinding all over the country in corporate America to go on reality TV, but it was that thought process that actually changed my life. Somebody in your family, either side, comes to you and says, “Loo…