Comparing fractions with unlike denominators
- [Voiceover] What I want to do in this video is get some practice comparing fractions with different denominators. So, let's say I wanted to compare two over four, or 2/4, and I want to compare that to five over 12, or 5/12. And I encourage you to pause the video if you could figure out which one is greater, 2/4 or 5/12, or maybe they are equal. So, let's think about this a little bit. When I just look at it, it's not obvious which one is larger and there's several ways that we can look at this. One way is we can try to have the same denominator. We can rewrite these so that we can have the same denominator. So one way to think about it, can I write two over four as something over 12? Well, let's think about it. If instead of having fourths, if you have twelfths, you now have three times as many sections that you've divided something into. So, two pieces would then turn into three times as many pieces. So, you multiply the numerator by three, as well. If you multiply the denominator by three, you multiply the numerator by three, as well. So, 2/4 is the same thing as 6/12. Another way to think about it is two is half of four, six is half of 12. Now, can we compare 6/12 to 5/12? Well, I have more twelfths here. I have six of them versus 5/12. Now, I can make the comparison. And I can say, look if I have six of something, in this case, this thing I have six of is twelfths, that's going to be more than having five of the twelfths. So, 6/12 is greater than 5/12, and I always think of the greater than sign, you're always going to be opening to whichever one is larger. So, this is the greater than sign. So if 6/12 is greater than 5/12, then 2/4 is greater than 5/12, because 2/4 and 6/12 are the exact same thing. Now, let's tackle another one. This one might be a little bit more interesting. Let's say we want to compare three over five and we want to compare that to 2/3, two over three. And like always, pause the video and see if you can figure this out. And I'll give you a hint, try to rewrite both of these so that they have the same denominator. So, let's try to do that. So, five isn't a multiple of three, three isn't a multiple of five, so we need to find a common denominator. Well, a common denominator would be something that is divisible by both five and three. So the easiest thing I can think of is 15, which is five times three. So, let's write 3/5 as something over 15, and let's write 2/3 as something over 15. So, 2/3 I'm going to write as something over 15. Well, to go from five to 15, I multiply it by three. So, I multiplied by three. So, if I multiply the denominator by three, I need to multiply the numerator by three. So, multiply by three. So, 3/5 is going to be the same thing as 9/15. I multiplied the numerator and the denominator both by the same number, which doesn't change its value. I'm just rewriting it, so 3/5 is the same thing as 9/15. And now, let's look at 2/3. To go from three to 15, you multiply by five. So, you do the same thing with the numerator. We need to multiply the numerator by five. Two times five is 10, so 2/3 is the same thing as 10/15. And now, we can make a comparsion because we have a certain number of fifteenths compared to another number of fifteenths. So what's larger, 9/15 or 10/15? Well 10, if you have 10 of something, it's going to be more. So, 10/15 is larger than 9/15. So, I've put the symbol that opens to the larger one. And so this one is the less than symbol. 9/15 is less than 10/15, but since 9/15 is the same thing as 3/5 and 10/15 is just another way of rewriting 2/3, we can also put the less than symbol there. 3/5 is less than 2/3.