Welcome to my presentation on equivalent fractions. So equivalent fractions are essentially what they sound like. They're 2 fractions and although they use different numbers, they actually represent the same thing. Let me show you an example.
Let's say I had the fraction ½. Why is it not writing? Make sure I got the right color here. Say I had a fraction 1 over 2. So graphically if you were to draw that, if I have a pie and I were to cut into two pieces. It says the dominator there is 2. And if I were to eat 1 of the 2 pieces, I would’ve eaten ½ of this pie. Makes sense. Nothing too complicated there.
Well, what if instead of dividing the pie into 2 pieces, let me just draw that same pie again. Instead of dividing it in 2 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 1 piece, this time I actually ate 2 of the 4 pieces. So I ate 2 out of 4 pieces. Or I ate 2/4 of the pie.
Well if we look at these two pictures we can see that that I've eaten the same amount of the pie. So these fractions are the same thing. If someone told you that they ate ½ of a pie, or if they told you that they ate 2/4 of the pie. It turns out that they ate the same amount of pie. So that’s why were saying those 2 fractions are equivalent.
Another way, if we actually had, let's do another one. Let's say, that pie is quite ugly, let's just 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 ½ 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 ½, 2/4, and 4/8. Well, to go from ½ to 2/4, we multiply the denominator. The denominator, just a 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 will hit the point home.
Erase this. Why is it not letting me erase? Okay, good. Sorry for that.
So let's say I had a fraction 3 over 5. Well, by the same principle, as long as we multiply the numerator and the denominator, 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 multiply 3/5 times 7 over 7 to get 21 over three and a half inch. And if you look at this, what we’re doing here isn’t magic. 7 over 7, well, what's 7 over 7? If I had 7 pieces in a pie and I were to eat 7 of them. I ate the whole pie, right? So 7 over 7, this is the same thing as 1. So all we essentially did is that is well, 3/5 and we multiply it times 1 which is the same thing as 7 over 7. And that’s how we got 21 over 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 we figure out a different way of writing 21 over 35.
So let's say if I were, let's start with a fraction 5 over 12. And 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 go in to 36, 3 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 over 36 is the same thing as 5 over 12.
I'm just going to our original example. All that saying is if I had a pie with 12 pieces and I ate 5 of them. Let's say I did that, and you had a pie, the same size of pie, you had a pie with 36 pieces and you ate 15 of them. Then we actually ate the same amount of pie.