How to Add Multiple Fractions

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You can add multiple fractions together by following a few quick steps. Learn how to add multiple fractions together with help from a mathematics educator in this free video clip.

Part of the Video Series: Mathematics Lessons
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Hi, I'm Jimmy Chang and we're here to talk about how to add multiple fractions. Now, typically you're, you're practicing how to add two fractions at a time which is the most common, but when it comes to adding more than two fractions, multiple fractions like three fractions or more, it does become a little bit more involved, but actually the idea is still the same as if you're adding two fractions. It's all about the least common denominator, LCD, and so we're going to do an illustration on seeing how this works. So, suppose you have 1/3 and you want to add it to, let's just say 2/5ths, and then let's just say you want to add it, to, 5/6ths. Now, what you want to think about is, examine the denominators 3, 5, and 6, and think about, OK, what's the first number that 3, 5, and 6, will go into? Now, in this particular problem, it's kind of easy to look at, if you think about 3 and 6, the least common denominator between 3 and 6 is going to be 6. So, 6 will take care of the 3. But if you think about 5 and the 6, the least common denominator 5, 5 and 6, because they're kind of prime to each other, is actually going to be the number 30. So basically, in this particular scenario, the least common denominator is going to be 30. Now, what you want to think about is, you want to convert all three fractions with the denominator 30. So it's just like finding the LCD of two fractions, except that you're finding that of three. Now, what you want to think about is, for each of these denominators, what do you need to multiply by to get to 30. So, 3 times what gives you 30? Well, that's going to be 10. But, like with the rules, if you're going to multiply the denominator by 10, you have to multiply the top by 10 as well. So 1/3 is really going to be 10/30ths. 5 times what is going to give you 30? That's gonna, you have to multiply 6. But again, you have to multiply both the denominator and the numerator, so 5 times 6 is 30. 2 times that same 6 is going to give you 12. And then, same thing with the 6. 6 times what is 30? 6 times 5 of course. And then you do the same thing by multiplying, the top by 5. 5 times 25, excuse me, 5 times 5 is going to give you 25. And when it comes to adding the fractions, you know you keep the denominator the same, you just have to add all the numerators. 10 plus 12 is 22. 22 plus 25 is going to be 47. Now you could leave it as an improper fraction or it can reduce as a mixed number, that's completely up to you. In this case it'll be 1 and 17 over 30th, but it all depends on what the preference is. So, I'm Jimmy Chang and this is an illustration on adding multiple fractions.

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