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
Food and energy in organisms | Middle school biology | Khan Academy
Hey, quick question for you. You ever look at a person’s baby pictures and wonder how people go from being small to, well, big? I mean, yes, I get it; people grow up, but here I’m thinking more on the level of the atoms and molecules that make up the body…
15 Mistakes You Make In Your 20s
Hello, Alux! Welcome back. Your 20s are a time of exploration, growth, and learning, right? And with that comes the expectation that you’ll make some mistakes along the way. You are expected to make some of these mistakes, and here are 15 of them that you…
TIL: We Have Lost 50% of Wildlife Since 1970 | Today I Learned
So one thing that really surprised me was from 1970 to 2010. You know, in 40 years, we’ve lost over half our wildlife population. In 2014, there was this study that was done, and basically what they do is look at elephants and tigers and fish and all the…
A Conversation with Ooshma Garg - Moderated by Adora Cheung
Thank you for coming today. My name is Dora; I’m one of the partners here at Y Combinator. Today we’re going to have a conversation with Oozma Magog, who is the CEO and founder of Gobble, which creates and delivers 15-minute pan dinners to you. I am perso…
The True Cost of the Royal Family Explained
Look at that! What a waste! That Queen living it off the government in her castles with her corgis and gin. Just how much does this cost to maintain? £40 million. That’s about 65p per person per year of tax money going to the royal family. Sure, it’s stil…
Charlie Munger: Be a Survivor, Not a Victim
Of course, feeling like it’s rather interesting to make change. Some people are victimized by other people, and if it weren’t for the indignation that that causes, we wouldn’t have the reforms that we need. But that truth is mixed with another. It’s very…