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# In mathematics, algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics.

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##### Christina K.

Rutgers, The State University of New Jersey

##### Farnaz M.

Simon Fraser University

##### Aspen F.

University of Sheffield

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### Video Transcript

welcome to our algebra review in this video, we're going to cover dividing fractions. Now, again, this may seem like a trivial thing that you learned years and years ago. But it is one of the most common mistakes that I see when students are doing algebraic operations. So let's take a look. One of the things that really confuses students is the notation. Okay, how you write it down now? Normally, when we write a fraction, it's gonna look something like this, Of course. But when you're dividing fractions, Okay, generally speaking will write something like this instead. Okay, Um, now, before we attack this, let's remember how to multiply fractions. Okay, if I have a over B times C over D if I'm multiplying fractions, can I get a C over B D? Okay, it's pretty easy to handle. Okay, on the other hand, over here, what I want to the key is that I want a single numerator on. I want a single denominator. So in order to do that, I'm gonna actually use some of our algebraic properties from before. I'm gonna say is okay. If I have a over b, we're gonna leave that one alone. And down here we have C over D. I want to get rid of the C over D thing. So what I'm gonna do is I'm going to multiply it by de oversee notice. What I'm doing here is I'm using, um, the inverse off. What's in this denominator down here? This total denominator in order to say c over d times do you oversee? Well, that's gonna end up being one. But in order to do that, I also have to multiply the top by de oversee. Okay, So what, this is gonna end up being is a times D over B times C, all divided by C D over D. C, which thes canceled because of the community of property. And we're left with a times D divided by B times C. So, looking at that, it seems like you should be able to do that over and over again. No mistakes. But a lot of times people get thrown off because instead of you might get something like this. Where instead of having a nice it looks like a numerator. Looks like a denominator. Just with fractions inside. You haven't a over B oversee. And now again. The way you handle this is leave the top two terms alone. Okay, let's just get rid of the bottom one. So in order to do that, I'm actually gonna rewrite it like this over be divided by C, So I'm gonna multiply this by one oversee on that, I'm gonna multiply this by one oversee, which gives me the correct result of a divided by B times C. Okay, so, again, this is how you manipulate it just by hand. Where the problems really start to happen is when you start to try to type type things into your calculator. When you type things into your calculator, make sure that you use parentheses often the way things will appear on your calculator. For example, if I want what I had before a divided by B, divided by C okay, or even better yet, let's do a divided by B times C. So a divided by B times C. Okay, you write that into your calculator, I say, Okay, divide sign. BC. Okay, what your calculator may or may not see, depending on how it's coated is it might actually see a divided by B time. See, which is different. That's gonna look like this. A c over B. Okay, so make sure you use parentheses. Type it into your calculator like this. Use the parentheses there. So it knows that you are dividing a by the product of B times C not just by B and then multiplying the whole thing by sea. So make sure you do that, and you shouldn't ever have any problems with dividing fractions in physics class.

RC
University of North Carolina at Chapel Hill
##### Christina K.

Rutgers, The State University of New Jersey

##### Farnaz M.

Simon Fraser University

##### Aspen F.

University of Sheffield