Adding Fractions with Unlike Denominators | Step-by-Step Guide (Examples + Practice)

Welcome to Math with Mr. J. In this video, I'm going to cover how to add fractions with unlike denominators. We will go through a couple of examples together, and then I'll give you a couple of practice problems that you can try on your own. Let's jump into number one, where we have 2 5ths plus 1 10th. Now, when adding fractions, the first thing that we need to do is check the denominators. If they are the same, we can add the fractions as is. If the denominators are different, we can't add as is. We have some steps before we can add. So for number one, we have unlike denominators, different denominators. We have a 5 and a 10. That means we need to find a common denominator. That's our first step. Then we rename the fractions with that common denominator. After we rename, we can add the fractions. That's going to give us our answer. And then lastly, we can simplify that answer if needed. So our first step here is to find a common denominator between 5 and 10. Basically, this is just a common multiple between 5 and 10. A number 5 and 10 both go into, so to speak. And to show you what I mean here, I'll write out the first five multiples of 5 and 10 to see if we have any multiples in common. The first five multiples of 5 are 5, 10, 15, 20, 25, and these continue on. The first five multiples of 10 are 10, 20, 30, 40, 50, and these continue on. So looking at our lists of multiples, do we have any in common? Yes, 10 and 20. And really, these will have an infinite number of common multiples. So what we want is the least common multiple. Now we can use any common multiple, but the least common multiple makes things simpler. That's going to be 10 here. So that's the common denominator that we are going to use. And more specifically, that's the least common denominator. So now we need to rename these fractions with that least common denominator of 10. Let's start by renaming 2 5ths. So we put our denominator of 10, and now we need to think, how do we get that denominator of 5 to equal 10? Well, 5 times 2 gives us 10. Whatever we do to the denominator, we must do to the numerator in order to keep this equivalent. So we need to do 2 times 2, and that gives us our numerator of 4. So 4 10ths is our renamed fraction, and this is an equivalent fraction. So we're not changing the value of anything here. Plus, and now we need to rename our other fraction, 1 10th. Well, 1 10th already has that denominator of 10. So we actually don't need to rename here. 1 10th is fine as is. Again, because we already have that denominator of 10. And now that we have a common denominator, we are able to add. So we add our numerators. 4 plus 1 gives us 5. And then we keep that denominator of 10 the same. So we end up with 5 10ths, and that's our answer. Now once we have our answer, we can look to see if it can be simplified. Can 5 10ths be simplified? Yes, we have a common factor other than 1 that we can divide both 5 and 10 by. We can divide by 5. So let's divide 5 by 5, and 10 by 5. 5 divided by 5 gives us 1, and 10 divided by 5 gives us 2. So we end up with 1 half. The only common factor between 1 and 2 is 1, so this is now in simplest form. Our simplified answer is 1 half. Let's move on to number two, where we have 7 12ths plus 3 8ths. Do we have a common denominator here? No, so we can't add these fractions as is. We need a common denominator. So we need a common multiple of 12 and 8, specifically the least common multiple. Let's try to do this one without writing out the multiples. So what's the least common multiple here? We can think, what number does both 12 and 8 go into? Now I like to always start with the larger denominator and see if it will be our least common denominator, like how 10 was for number one. 12 is our larger denominator here. So is 12 a common multiple of 12 and 8? No, 12 works for 12, but 12 doesn't work for 8. 12 is not a multiple of 8. So let's try the second multiple of 12 and see if that works. That's 24. Will 24 work? Yes, 24 works for 12, 12, 24, 36, and so on. So 24 is a multiple of 12. And yes, 24 works for 8 as well. 8, 16, 24, and so on. So 24 is a multiple of 8. 24 is our least common multiple between 12 and 8, therefore our least common denominator. So let's rename these fractions with that denominator of 24. We'll start with 7 12ths. So how do we get 12 to equal 24? 12 times two gives us 24. Whatever we do to the denominator, we must do to the numerator in order to keep this equivalent. Seven times two gives us a numerator of 14. So we get 14 24ths. Plus, and now let's rename 3 8ths. How do we get eight to equal 24? Eight times three gives us 24. So we need to do that to the numerator as well. Multiply by three. Three times three gives us a numerator of nine. So 9 24ths. And now we have both fractions renamed with that common denominator, that least common denominator of 24. And now we can add. So let's add the numerators. 14 plus nine gives us 23. And then we keep that denominator of 24 the same. So we end up with 23 24ths. Now can we simplify this fraction? No, the only common factor between 23 and 24 is one. So this is already in simplest form. We are done. Our answer, 23 24ths. So now that we've gone through a couple of examples together, it's time for you to try some practice problems on your own. So have paper and a pencil ready. Here are your practice problems. I'll give you three minutes and then we will go over the answers. Feel free to pause if you need more time or jump ahead to the answers whenever you are ready. Go ahead and start. Okay, so that was three minutes. Let's go over the answers. Here are our answers. For number one, our least common denominator was nine. Once we renamed and added, we got eight ninths. Now, if you used a different common denominator other than nine, for example, 18, that still works. You would get 16 over 18 in that case, 16 eighteenths. And that simplifies to eight ninths. So we get the same thing. Moving on to number two, our least common denominator was 30. Once we renamed and added, we got 21 over 30, 21 thirtieths, which we were able to simplify. Our simplified answer, seven tenths. So there you have it. There's how to add fractions with unlike denominators. I hope that helped. Thanks so much for watching. Until next time, peace.