Hi and welcome to this section of the tutor where we are going to talk about a very, very, very important section in math and that is called fractions, okay. Fractions can sometime seem difficult because they do not look exactly like real numbers and they can seem to be a little bit challenging at first but I promise you if you stick with me I will teach you what a fraction is. And in this section we are going to learn what a fraction is and we are also going to learn how to what we call simplify fraction and that will all make sense at the end of this section.
And then we will go in later on and we will learn how to add them and subtract them and all that good stuff, okay. But first let us talk about what is a fraction, it is a very important topic. So let us go in and talk about that right away. I am going to use pie as an example all the time in this class, okay. So I hope you guys like pie because we are going to talk about a lot about pies right now. I think everybody knows what three pies would look like, right. You would have one pie, two pie, three pie these are circles and each one of these is a pie. So I think you can visualize in your head what three pies would look like, so just hold that in your head for a second. I think you could also visualize what two pies looks like in your head, that would be two giant pies, right.
I love pie myself and having two pies is even better than having one pie. I think you also would know what one pie looks like which would just be one circle. But the question is three pies, two pies and one pie what happens when you start cutting a pie up. What do you call those pieces of the pie because if the pie is one whole giant circle we call that a pie and you start cutting into that pie. Well if you start eating some of the pie then what you have left over is not going to be a whole pie it is going to be something less that a pie. It is going to be a part of the pie but it is not going to be a whole pie and what we are going to say is that you are going to have something left over when you cut out there and you will have some pieces left over. And what we are going to do is we are going to talk about fractions. You have a fraction of the pie left, you have something less than one.
So basically, anytime you have something less than one you can talk about it in terms of a fraction because that is what it is. A fraction is used to talk about things when you are talking about less than one of them. So three pies, two pies, one pie we are going to start cutting the pies up and then we are going to have less than one pie, we are going to have a fraction. So let us say we have this is our whole pie here, actually let me go ahead and raise this real quick, I want to make it clearer. Here is our whole pie right here, we said that this is one pie. Now let us say for some reason I cut this pie down the middle like this, I take this half over here, and I give it to my dog, so my dog eats it he love pie. Well I have some pie left, how much pie do I have? I think you can probably realize or most of you heard the term half, half of something, if I take this pencil and I break it in half then I cut it right in the middle right?
Well I have taken this pie and I have cut it in the middle and so we have taken away half of the pie and what we have left, we have half of the pie left. Now how do you write that down? Well you can say that this is half of a pie, and that is absolutely true. But in math you want to write this stuff down in terms of a number right, so you can also write it down like this. Once I first cut the pie I had two piece right, so I am going to say I had two piece here but when I take one pie and I throw it to my dog how many pieces do I have left? I only have one piece. So this is called one half, I just take a one which is how many pieces I am talking about or in this case how many pieces I am talking about here out of two possible pieces and this is what I have. You just a draw this a line in the middle and this just does not mean it is a fraction, it is just telling you that you have less than one.
So I do not have a whole pie I have half of the pie. The top number tells you how many pieces that you have and the bottom number tells you how many total pieces you have. So this is how you can talk about things less than one. I take this I throw it away, so how many do I have left? Well I have I piece out of a possible two pieces so I do not have both pieces that would be a whole pie, I do not have both pieces that would be a whole pie, I threw one piece away. I have one piece left out of a possible two pieces so I have half a pie so this is called one half. Now what would happen if I took the pie and what if I cut it up like this? What if I cut it down like this and then across like this? And let us say I am going to eat some of this pie I like pie, so let us take this piece here and I just take this piece out, out of the pie tray and I eat it and that is the only piece that I eat. How much pie have I eaten? That is my question.
Well this is called a quarter of a pie, so this is a quarter of a pie. And you might even heard of that before, you may have heard that word a quarter of this, a quarter of that but in math how would you write it? I have got one piece in my mouth out of a possible total of four pieces. So there is four pieces available because I cut it to make four pieces but I am only eating one piece. So the piece that I took is one fourth or one quarter, it is the same thing. So this is how you write it. you are talking about fractions here, this is exactly what this is, these are both a fraction, this is a fraction, this is a fraction.
Now obviously this is more pie than this, right, so this fraction one half if more than one quarter. Now it is not so easy to see that here by looking at the numbers but by looking at the pictures this is a whole lot more pie than this. All right, now what I want to show you next is what if I look at this half of pie in a little bit different way. We just talked about what a half is and we just talked about what a quarter is. What if I took this pie, here is my pie and I cut it right down the middle in half and I am going to use blue here because I like blue and I take this half away. How much have I taken away?
This is one half of a pie because I have taken one piece away out of a possible two pieces, that is one half of a pie. Now hold that in your brain and we are going to talk about this for a second. What if I have another pie and I cut it again just like in the previous board like this but I do not just take one piece of this pie away I take two pieces away. So I am going to take all of this, I am going to take two pieces of pie and I have cut it into four pieces. So how much have I taken away here? Here there was four pieces and I took two of them so I took pieces out of one, two, three, four total pieces. That is a fraction. So anytime you write a fraction down the top number is how many pieces do you have and the bottom number is how many total pieces are there.
So you have two fourths here. Now what I want to show you and this is very, very, very important is that this looks different than this. these two fractions look different because I have written it down, this is a two, this is a one, this is a four, this is a two. They look different but look at the pictures for a second. Even though I have taken two pieces out of four over here and even though I have taken one piece out of two over here the total amount of pie that I eat in each case is the same. So in other words these two fractions even though they look different are the same thing. They are no different from one anther they are exactly the same thing. I cut the pie in two pieces I eat half the pie. If I cut this pie into four pieces and then take two away I have eaten the same amount of pie. It is exactly the same thing, they only look to be different.
So these two things must be equal, they must be equal and they are equal, they are exactly equal. One half is equal to two fourths. Two over four it must be this way. Why is it his way? Well I am going to go ahead and show you that one half is equal
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