Equivalent fractions 2
Welcome to my presentation on equivalent fractions. So equivalent fractions are, essentially what they sound like. They're two fractions that although they use different numbers, they actually represent the same thing. Let me show you an example. Let's say I had the fraction 1/2. Why isn't it writing. Let me make sure I get the right color here. Let's say I had the fraction 1/2. So graphically, if we to draw that, if I had a pie and I would have cut it into two pieces. That's the denominator there, 2. And then if I were to eat 1 of the 2 pieces I would have eaten 1/2 of this pie. Makes sense. Nothing too complicated there. Well, what if instead of dividing the pie into two pieces, let me just draw that same pie again. Instead of dividing it in two pieces, what if I divided that pie into 4 pieces? So here in the denominator I have a possibility of-- total of 4 pieces in the pie. And instead of eating one piece, this time I actually ate 2 of the 4 pieces. Or I ate 2/4 of the pie. Well if we look at these two pictures, we can see that I've eaten the same amount of the pie. So these fractions are the same thing. If someone told you that they ate 1/2 of a pie or if they told you that they ate 2/4 of a pie, it turns out of that they ate the same amount of pie. So that's why we're saying those two fractions are equivalent. Another way, if we actually had-- let's do another one. Let's say-- and that pie is quite ugly, but let's assume it's the same type of pie. Let's say we divided that pie into 8 pieces. And now, instead of eating 2 we ate 4 of those 8 pieces. So we ate 4 out of 8 pieces. Well, we still ended up eating the same amount of the pie. We ate half of the pie. So we see that 1/2 will equal 2/4, and that equals 4/8. Now do you see a pattern here if we just look at the numerical relationships between 1/2, 2/4, and 4/8? Well, to go from 1/2 to 2/4 we multiply the denominator-- the denominator just as review is the number on the bottom of the fraction. We multiply the denominator by 2. And when you multiply the denominator by 2, we also multiply the numerator by 2. We did the same thing here. And that makes sense because well, if I double the number of pieces in the pie, then I have to eat twice as many pieces to eat the same amount of pie. Let's do some more examples of equivalent fractions and hopefully it'll hit the point home. Let me erase this. Why isn't it letting me erase? Let me use the regular mouse. OK, good. Sorry for that. So let's say I had the fraction 3/5. Well, by the same principle, as long as we multiply the numerator and the denominator by the same numbers, we'll get an equivalent fraction. So if we multiply the numerator times 7 and the denominator times 7, we'll get 21-- because 3 times 7 is 21-- over 35. And so 3/5 and 21/35 are equivalent fractions. And we essentially, and I don't know if you already know how to multiply fractions, but all we did is we multiplied 3/5 times 7/7 to get 21/35. And if you look at this, what we're doing here isn't magic. 7/7, well what's 7/7? If I had 7 pieces in a pie and I were to eat 7 of them; I ate the whole pie. So 7/7, this is the same thing as 1. So all we've essentially said is well, 3/5 and we multiplied it times 1. Which is the same thing as 7/7. Oh boy, this thing is messing up. And that's how we got 21/35. So it's interesting. All we did is multiply the number by 1 and we know that any number times 1 is still that number. And all we did is we figured out a different way of writing 21/35. Let's start with a fraction 5/12. And I wanted to write that with the denominator-- let's say I wanted to write that with the denominator 36. Well, to go from 12 to 36, what do we have to multiply by? Well 12 goes into 36 three times. So if we multiply the denominator by 3, we also have to multiply the numerator by 3. Times 3. We get 15. So we get 15/36 is the same thing as 5/12. And just going to our original example, all that's saying is, if I had a pie with 12 pieces and I ate 5 of them. Let's say I did that. And then you had a pie, the same size pie, you had a pie with 36 pieces and you ate 15 of them. Then we actually ate the same amount of pie.