Learn the toughest concepts covered in your Macroeconomics class with step-by-step video tutorials and practice problems.

Introduction to Macroeconomics

1

Simplifying Fractions

9m

Play a video:

Was this helpful?

Alright, so now let's do a quick review on simplifying and comparing fractions. So for instance do some simplifying. I've got some steps here that make simplifying fractions a little easier. So the first thing we wanna do is we want to find a common factor. When I say common factor it's something that both the numerator and denominator can divide by this number and then we're gonna divide numerator denominator. What are these things again, numerator is the top part of the fraction, Denominators. The bottom part of the fraction. Um and so what we want to do is we're gonna want to keep finding a common factor and keep dividing until we can't do it anymore. Well either end up with a whole number like 236, right? We'll end up with a number or we'll just have a fraction that we can't simplify anymore. And a pro tip here that I've added is that most numbers are going to be divisible by two or three or five. But generally if you see two even numbers, it's a good sign that you just divide everything by two. Right? So even if they're kind of weird numbers, if they're both even you have the ability to just divide both of them by two. Alright. And another one if both of the numbers end in zero. So if you have let's say 10 divided by 50 you can take the zeros off of the end. So you can take like a 10 divided by 50 you can slash those zeros and be left with a 1/5 right? The idea there is that the common factor is 10 and you're dividing the top by 10 and the bottom by 10 to get to that, but that's just a quick and easy way to do it. Cool, so let's go ahead and practice some again. What I want you to do is just pause this video, try these out and then we'll solve them together and if you want we can do the first one together before you pause. So let's go ahead and do that. So the first one here we've got 8/6, so 86. How do we simplify this? Well when I see this, I see two even numbers, so I immediately think I can divide both of these by two. And that is what I'm gonna do, I'm gonna take eight divided by two and I'm gonna get four and six divided by two and I'm gonna get three. So we've got four and three. Now, generally when you've got a two or a three, something like that in the denominator, you're done. You can also tell four and three there's not a number that both can be divided by right? You're already pretty small, you can't divide three by two or you know four by three. This is it, this is your answer right here, 4/3 is the simplified fraction. Alright let's try the next one. We've got 1 20 divided by 1 40. So the first thing you should notice is that we've got two zeros here right, right at the end. So that's the first thing we can do, we can chop off those zeros and we will be left with 12/14. Now the question is are we done yet? So what I see is to even numbers 12 and 14 that immediately immediately signals to me that I can divide by two and simplify it. So if I divide by two, the top and divide by two on the bottom, we are going to be left with 6/7. So these two numbers six and seven again, there's not anything we can do to simplify this, that is going to be our final answer. Um There's not a common factor between those two. Let's try the next 1, 25/50. So this one too, you don't see too even numbers, that's not gonna work. You go to your calculator, you try 25 divided by three and you're still not getting anywhere. 25 divided by four. This is kind of the process I would try until you get to 25 divided by five, right, oh here we go. 25 divided by five works. 50 divided by five works. So we're gonna go ahead and divide by five on this one and we are going to get to 25 divided by five is 5 50 divided by five is 10. So we're gonna have 5/10. Now. This might look like a final answer but it's not yet. So let's see if there's anything else we can divide by and we've got five goes into 51 time and 10 goes into 51 time or two times here. So actually five is now a common factor of both of them. Right? So five divided by five and 10 divided by five and we're gonna get 1/2 so now we're at half, I don't think we can simplify from there. We've got a one in the numerator that's a good sign that we're done. Um So let's move on to the next one here. We've got 9/36. So in this case we try to and it doesn't work and then we try three we'll see that nine divided by three works, 36 divided by three works. So let's go ahead and do it nine divided by 3 36 divided by three and we're going to get 3/12. Now we can see if we're done. Two doesn't seem like it's gonna work but three does go into three and three goes into 12 as well. So let's go ahead and divide by three. Again we're gonna get 1 12 divided by three is four. You're gonna get 1/4 as the answer there, we can't simplify that anymore and if you were a little savvy, er you might have noticed that nine and 36 you could divide by nine with both of them. Hey if you noticed that go ahead and do it nine divided by nine is gonna give us 1 36 divided by nine is gonna give us four, it's just a shortcut to the final answer. There's not really um a wrong way to do it, I like to go with the easy numbers and just keep doing it until I can't anymore. Um But you just follow your method, so let's go ahead and do this. Next one here, 2100 divided by 1 40. And the first thing I noticed is I can cut the zeros off the back of it right and be left with 2 10/1 4/14, there's not another zero on the denominator so I can't do the zero slashing again. Um so now it's a matter of finding the correct uh common factor, so we've got to 10 and 14 I see two even numbers so I can just divide by two here. Um but what I'm also noticing is I see the 14 and the 21 there on the numerator I think that there's a seven that can work in this situation, so I'm gonna try seven and see what I get. So to 10 divided by seven sure enough it does work so this is a quicker way to get to a smaller number, I could have also used to at this point, but then it would have left me with some other numbers and I would have probably had to simplify again. Um So let's see what this gets us to. So I'm gonna divide by seven here divided by seven, so to 10 divided by seven is going to be 30 and 14 divided by seven is two. So notice this didn't even get us to the end answer actually because what I see is to even numbers here 30 divided by two, I can divide both of those by two And I'm gonna get 15/1 and when you have a one in the denominator, 15/1, that's the same as saying 15. So our answer there is 15, there's no fraction left at the end. Um A good trick for these as well as you can just go ahead and put the whole thing into your calculator. 2100 divided by 1 40 see what comes out. Apparently 1 40 is a common factor of 2100. So we could have just divided both uh by 1 40 right from the start. Cool, let's try this last 11 28 divided by 10 24. Um In this situation I see to even numbers again, write these numbers look a little funkier, so I'm just gonna go ahead and use my number two and divide both of those by two. It's gonna get me to 64 over 5 12 while I see to even numbers again. So I'm gonna do it again divided by two divided by two. So that's gonna get me 32 divided by 2 56. Alright, so this looks like it could keep going here, let's divide by two again, and I'm gonna get 16/1 28. Let me get out of the way here because it looks like we're gonna keep going. Uh Man at this point it looks like we can divide by two again and again. Let me see if 16 is a common factor at this point, I'm gonna do 16 1 28 divided by 16 and see if that'll get us an even number and it does it gets us eight. So I know that 16 is a common factor of both. I'm going to divide both by 16, so there's probably another one that I could have done even earlier, but this is where I finally drew the line and was like hey there's gotta be an easier way, so I'm gonna get 1/8, we can't simplify that anymore. Our final answer is gonna be 1/8 right? So the trick here, right, Use those common factors. Try and see when things are divisible by two, when things are divisible by three or five, right? And we are going to get to a simplified fraction. Cool, so let's move on to the next video

2

Comparing Fractions

2m

Play a video:

Was this helpful?

Alright guys, so let's continue with a video on comparing fractions. So when we have two fractions, how do we tell which one is larger than the other? Um The easiest way is you just literally do the division. You take the numerator, the top number divided by the bottom number. Get a decimal and then it's a lot easier to compare the decimals than just looking at fractions. So let's go ahead and start with this first one here and then why don't you guys pause the video and try these other ones? Cool. So the first fraction we've got here is 3/4 3/4. We put that on our calculator, three divided by four. And we're gonna get 40.750 point 75. Alright, how about 4/5 4 divided by five is going to give us 0.80 point 80. I'll put here and 0.8 is bigger than 0.75. So, I'm gonna put Our less than sign. Their 0.8 is bigger. 4/5 is the larger fraction. All right, so why don't you guys try these ones and then we will continue together. All right. So I'm assuming you tried it. Let's go on with 46/15. That comes out to be 3.0ops. 3.7. I'm going to round it off the 3.7 there And let's do 13 divided by four. And we get 3.25. Alright, so 13/4 looks bigger. 3.7. So 13/4 is the bigger fraction. Let's try this 1 to 17th and 3 29. So, too two divided by 17 Will give us 0.118. I will round it off to there. And how about 3/29 gives us 0.103. All right. So in this case we've got the .118 is bigger. So to 17th is the bigger fraction here. Let's go ahead and do this last 1 21. Excuse me, 25 divided by 40 gives us 0.625 and 60 divided by 96. It's also 0.625. So in this one they are equal. All right. So these are equal. There's no larger one. Cool. Alright, let's move on here.

© 1996–2023 Pearson All rights reserved.