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Robert McKeown: Hello, and welcome to ALEKS

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walkthrough video number one. My name is Robert

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J. McKeown. And I'm very pleased to welcome you

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here today. These walkthrough videos are meant

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to help you get started, most of the learning

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you're going to do is going to be on your own.

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That said, I'm here to help you. And this video

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in particular is going to give you some tools to

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be successful on your path to mastering algebra.

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If you can master algebra, your undergraduate

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career is going to be a lot smoother and a lot

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better, I promise you. Now, that said, the real

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number line is the beginning of university

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mathematics. And so that's where we're going to

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start today. Now, what do I expect from you?

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Well, I expect you to have your paper scrap

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paper is fine. If you want to have a notebook,

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that's fine, too. If you want to print off the

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slides. If you have a printer and you want to

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print up the slides, by all means, complete the

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slides as we go and do your writing there. And

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then I highly recommend you use a pencil I like

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a mechanical pencil that I can put the lead

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into. If you don't have a pencil a pen is fine.

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But at university, you really want to get used

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to working with a pencil because on a test, you

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can erase your answer. So without any further

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ado, let's get started. Here's our first

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question. So we're on ALEKS. We've got a

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question under the real numbers topic. And it's

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a proportionate form the equations and in

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proportionate form. The most important thing

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here is that we're being asked to solve for V,

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the unknown variable is V, and we need to solve

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for its value. So how are we going to do that?

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I've reproduced the question here on my slides.

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And I'm going to take it very slow. And I want

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to illustrate to you an important property of a

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double sided equation, which is that as long as

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we perform the same operation on both sides of

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the equation, we do not change the quality. So

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what I'm going to do, maybe, maybe I'll start

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off by multiplying both sides of the expression

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by V. So let's see what happens when we do that.

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got eight over five, times v. And I'm going to

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multiply V by both sides of the equation. So

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I've got 12 over V, here, multiplied by v. What

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happens next? Well, you can probably see that

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the divided by V is just equal to one. And now

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I'm left with I could rewrite this as eight V

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over five is equal to 12. Now if I want to get

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rid of that five, eight V over five, I'm going

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to multiply both sides of the expression by

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five. So I'm following the algebra rules, you

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can see that these fives are just going to

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cancel each other out. And I'm going to have

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eight v is equal to 12 times five, well, that's

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like 12 plus 12, plus 12, plus 12, plus 12. And

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so I've got eight v is equal to 60. And V is

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going to be equal to 60 divided by eight, I

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divided eight by both sides of the expression.

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And I know that 64 divided by eight is equal to

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eight. So this looks like the answer is going to

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be 7.5. If I go back to ALEKS, I've got a little

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box here. And I'm going to put seven decimal

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five. And I'll click the check button down here

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and see if I get the right answer. And I did so

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that was the right answer. The important thing

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for you to remember is those rules of algebra,

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perform the same operations on both sides of the

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equation and solve for any unknown variables.

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Let's take a look at this question. We're being

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asked to subtract one fraction from another. And

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the problem we have is that since the

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denominators of both these terms are different,

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We can't subtract one from the other directly.

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So what we're going to do is we're going to use

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the lowest common denominator technique. And

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similar to in the previous question, we're going

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to, we're going to multiply the numerator and

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the denominator by the same value, which means

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we're not actually changing the value of that

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fraction. So if I take a closer look here, I see

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that the simplest way for me to get a common

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denominator here is to take this two and

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multiply it by the numerator and denominator on

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the left hand term. And I'm going to do the same

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thing with this five to the right hand side, so

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let me clear that off. It's getting kind of

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messy. And so I've got nine over negative five.

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And I'm going to multiply the numerator and the

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denominator by two. I've got nine over two. And

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I'm going to multiply the numerator and

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denominator by five. Notice that I'm not worried

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about the negative sign. Now if I do a little

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bit of work, I'm going to get 18 over negative

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10 minus 45, over 10.

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Now, there's nothing wrong with me rewriting

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this equation as negative 18 over 10, or if you

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prefer, I could factor out which we'll learn

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about in a later topic, I could rewrite this as

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negative 18 over 10. And I'm going to subtract

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45 over 10. Another way to write this is to say

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I've got well I've got negative 18 minus 45. And

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since the denominator is the same for both the

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fractions, I can just write them together like

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that. And I have negative 63. Over 10. shifting

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back to ALEKS, here's the question and ALEKS.

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It's the exact same question we saw before. And

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I'm going to keep it as a fraction. So I like to

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have it as negative 63. And then I'll click on

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this little character there, over 10. And I'll

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click on the check button. And we'll see if I've

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got the right answer. I got the right answer. So

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negative 63 over 10. Now let's take a look at

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dividing fractions. So we have 15 over 14

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divided by seven over eight. So how are we going

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to get started? Well, it turns out that this

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thing is going to be equal to five over 14

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multiplied by eight, over seven. Yes, that's

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right. If we're dividing, we're essentially

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going to flip the numerator and denominator and

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multiply them together. How can I show you that

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this is true. And this is what we should do?

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Well, suppose I asked you what the answer was

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one half divided by one over four. So you should

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be able to see, you know, how many quarters fit

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in a half, while there should be two, right? And

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if I follow that rule,

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I end up with the correct answer that there are

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two quarters in one half. So now let's go back

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to our problem from ALEKS. How can I do this

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without a calculator? Well, you can sort of

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grind it through in your head. One little trick

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might be to do this. So five times eight, that's

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on the multiplication table. If it's on the

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multiplication table, I generally know what it

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is. So I know that that's going to be 40. Now,

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the denominator is a little tricky because it's

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off the multiplication tables. So I find it a

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little more challenging. Well, one thing I could

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do is I could rewrite this as two times seven,

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which is 14 times seven, and that's going to be

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equal to 40. Over Two times seven times seven

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that's on the multiplication table that's 49.

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And that's gonna give me 40 over two times 49.

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Well, 49 plus 49. I know that that's 98. And now

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I've got 40 over 98. Well, if I divide both the

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numerator and denominator by two, I'm going to

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get 20 over 49. So let me check my answer on

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ALEKS. So here we are on ALEKS. And we have the

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exact same question that I showed you on my

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slides. I'm going to type in the answer. So I'm

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going to leave it as 20. I'm going to press this

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little button over here, divided by 49. And if I

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check the answer, I see that I have the right

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answer. And that's how you divide fractions.