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

Adding and subtracting fractions with negatives | 7th grade | Khan Academy


2m read
·Nov 10, 2024

Let's say we wanted to figure out what (3 \frac{7}{3}) minus (-\frac{7}{3}) minus (\frac{11}{3}) is. Pause this video and see if you can have a go at it before we do it together.

All right, now let's work on this together. You might be tempted to deal with the (-\frac{7}{3}) and the (\frac{11}{3}) first because they already have a common denominator. But you have to realize that with subtraction, you can't use the associative property. It's not this: ((a - b) - c) for example, which is what you would typically do first. It is not the same thing as this right over here. So you have to be very, very, very careful.

But what we could do is rewrite this. Instead of saying "subtracting something minus something else," we could rewrite it in terms of addition. What do I mean by that? Well, if I have (3 \frac{7}{3}), I'll start with that.

Subtracting something is the same thing as adding that something's opposite. So subtracting (-\frac{7}{3}) is the same thing as adding the opposite of (-\frac{7}{3}), which is just (\frac{7}{3}). And subtracting (\frac{11}{3}) is the same thing as adding the opposite of (\frac{11}{3}), which is (-\frac{11}{3}).

Now, with addition, you can use the associative property. You could add these two first or you could add these two first. I like adding these two first because they have the same denominator. So if I have (\frac{7}{3}) plus (-\frac{11}{3}), what is that going to get me?

Well, we have a common denominator. We could rewrite it like this: (3 \frac{7}{3}) plus a common denominator of three. We could write (7 + (-11)) in the numerator. So (7 + (-11)) is the same thing as (7 - 11) because subtracting something is the same thing as adding its opposite.

So, for adding (-11), the same thing as subtracting (11). So (7 + (-11))—you might want to get a number line out—but hopefully, you've gotten some practice. Now, that is going to be (-4). That is (-4).

And so now we have (3 \frac{7}{3}) plus (-\frac{4}{3}). Now we definitely need to find a common denominator. So let me rewrite this. This is equal to (3 \frac{7}{3}) plus (-\frac{4}{3}) or I could write this as even (-\frac{4}{3}). Either way.

But if we want to have a common denominator, it looks like (21) is going to be the least common multiple of (7) and (3). So let's rewrite each of these as something over (21).

From (7) to (21), we multiply by (3). So (3 \times 3 = 9). And then from (3) to (21), we multiply by (7). So if we have (-4) times (7), that is (-28).

And so this is going to be equal to (\frac{9 + (-28)}{21}), which is the same thing as (\frac{9 - 28}{21}) because subtracting a number is the same thing as adding its opposite.

And so this gets us—let's see—if (9 - 9 = 0) and then we're going to have (19) more to go below zero. So this is (-\frac{19}{21}) or we could write that as (-\frac{19}{21}) and we are done.

More Articles

View All
Marcus Aurelius and the Guiding Principles of Stoicism
In the year 165 CE, a black wave of death rose from the East and quickly spurred across the globe faster than anyone could have ever imagined. They called it the Antonine Plague after the reigning Roman Emperor at the time, Caesar Marcus Aurelius Antoninu…
How Secure is Your Password? And 21 Other DONGs
Hey, Vsauce. Michael here. And are you still doing things in the real world? C’mon, I mean, why flip a coin when you could just flipacoin.com? Every time you refresh the page, it flips again. Of course, there are plenty of other things you can Do Online N…
Khan Academy Ed Talks with Benjamin Riley - Wednesday, January 5, 2022
Hello and welcome to Ed Talks, where we at Khan Academy talk to folks who are influential in the field of education. I’m Kristen Deserver, the Chief Learning Officer here at Khan Academy, and I am happy today to welcome Ben Riley, who is with Deans for Im…
Warren Buffett: This investment will increase your net worth by 50%
If they just they increase their value at least 50 percent. So, I was recently watching an interview with Warren Buffett, and he said something so impactful I just had to make a video on it. Buffett recommended an investment anyone can make that will inst…
Enterprise Sales | Startup School
[Music] My name is Pete Kuman. I’m a group partner at YC and a YC Alum. I was co-founder and CTO of Optimizely in the winter 2010 batch. In this talk, I’m going to walk step by step through the process of closing your first Enterprise customers. I’m goin…
Citizenship in early America, 1789-1830s | Citizenship | High school civics | Khan Academy
In this video and the one that follows, I’m going to give you a brief overview of citizenship rights in early America. Who was considered a citizen? Did having citizenship mean that you had the right to vote? How did citizenship and voting rights change…