Adding fractions with unlike denominators (video) | Khan Academy

Video transcript

– [ Voiceover ] Let ‘s say that we have the fraction 9/10, and I want to add to that the divide 1/6. What is this, what is this going to equal ? so when you foremost look at this, you say, “ Oh, I have unlike denominators here. It ‘s not obvious how I add these. ” And you ‘d be right and the means to actually move forth is to find a coarse denominator, to convert both of these fractions into fractions that have a coarse denominator. So how do you think about a common denominator ? Well, a common denominator’s gon na have to be a common multiple of these two denominators of 10 and six. So what ‘s a common multiple of 10 and six ? And it ‘s normally simple to find the least common multiple, and a good room of doing that is start with the larger denominator here, 10, and say, okay is 10 divisible by six ? No. Okay, now, is 20 divisible by six ? No. Is 30 divisible by six ? Yes. 30 is divisible by six. So I ‘m merely going through the multiples of 10 and saying, “ Well what is the smallest multiple of 10 that is divisible by six ? ” And that ‘s going to be 30. So I could rewrite both of these fractions as something over 30. so nine over 10. How would I write that as something over 30 ? well I multiply the denominator, I ‘m multiplying the denominator by three. So I ‘ve precisely multiplied the denominator by three. So if I do n’t want to change the value of the fraction, I have to do the same thing to the numerator. I have to multiply that by three a well because now I ‘m equitable multiplying the numerator by three and the denominator by three, and that does n’t change the measure of the divide. thus nine times three is 27. so once again, 9/10 and 27/30 represent the lapp number. I ‘ve just written it now with a denominator of 30, and that ‘s utilitarian because I can besides write 1/6 with a denominator of 30. Let ‘s do that. so 1/6 is what over 30 ? I encourage you to pause the video and try to think about it. So what did we do go from six to 30 ? We had to multiply by five. so if we multiply the denominator by five, we have to multiply the numerator by five equally well, thus one times five, one times five is five. so 9/10 is the same thing as 27/30, and 1/6 is the lapp thing as 5/30. And now we can add, now we can add and it ‘s fairly aboveboard. We have a certain count of 30ths, added to another issue of 30ths, so 27/30 + 5/30, well that ‘s going to be 27, that ‘s going to be 27 plus five, plus five, plus 5/30, plus 5/30, which of class going to be equal to 32/30. 32 over 30, and if we want, we could try to reduce this fraction. We have a common agent of 32 and 30, they ‘re both divisible by two. so if we divide the numerator and the denominator by two, numerator divided by two is 16, denominator divided by two is 15. indeed, this is the lapp thing as 16/15, and if I wanted to write this as a interracial number, 15 goes into 16 one fourth dimension with a remainder one. So this is the same thing as 1 1/15. Let ‘s do another exercise. Let ‘s say that we wanted to add, we wanted to add 1/2 to to 11/12, to 11 over 12. And I encourage you to pause the video recording and see if you could work this out. well like we saw earlier, we wan na find a common denominator. If these had the lapp denominator, we could fair add them immediately, but we wan na find a common denominator because right immediately they ‘re not the lapp. well what we wan sodium witness is a multiple, a common multiple of two and 12, and ideally we ‘ll find the lowest coarse multiple of two and 12, and barely like we did earlier, let ‘s start with the larger of the two numbers, 12. now we could just say well 12 times one is 12, so that we could view that as the lowest multiple of 12. And is that divisible by two ? Yeah, certain. 12 is divisible by two. indeed 12 is actually the least coarse multiple of two and 12, so we could write both of these fractions as something over 12. indeed 1/2 is what over 12 ? Well to go from two to 12, you multiply by six, so we ‘ll besides multiply the numerator by six. nowadays we see 1/2, and 6/12, these are the same thing. One is half of two, six is half of 12. And how would we write 11/12 as something over 12 ? Well it ‘s already written as something over 12, 11/12 already has 12 in the denominator, so we do n’t have to change that. 11/12, and now we ‘re fix to add. So this is going to be peer to six, this is going to be peer to six plus 11, six plus 11 over 12. Over 12. We have 6/12 plus 11/12, it ‘s gon sodium be six plus 11 over 12, which is adequate to, six plus 11 is 17/12. If we wanted to write it as a shuffle numeral, that is what, 12 goes into 17 one time with a remainder of five, so 1 5/12. Let ‘s do one more of these. This is queerly fun. Alright. Let ‘s say that we wanted to add, We ‘re gon na add 3/4 to, we ‘re gon na add 3/4 to 1/5. To one over five. What is this going to be ? And once again, pause the video and see if you could work it out. well we have different denominators here, and we wan sodium recover, we wan na rewrite these so they have the same denominators, so we have to find a coarse multiple, ideally the least common multiple. So what ‘s the least common multiple of four and five ? Well permit ‘s startle with the larger number, and let ‘s look at its multiples and keep increasing them until we get one that ‘s divisible by four. so five is not divisible by four. 10 is not divisible by four, or perfectly divisible by four is what we care about. 15 is not perfectly divisible by four. 20 is divisible by four, in fact, that is five times four. That is 20. so what we could do is, we could write both of these fractions as having 20 in the denominator, or 20 as the denominator. So we could write 3/4 is something over 20. then to go from four to 20 in the denominator, we multiplied by five. So we besides do that to the numerator. We multiply by three times five to get 15. All I did to go from four to 20, multiplied by five. So I have to do the same thing to the numerator, three times five is 15. 3/4 is the lapp thing as 15/20, and over hera. 1/5. What is that over 20 ? Well to go from five to 20, you have to multiply by four. So we have to do the lapp thing to the numerator. I have to multiply this numerator times four to get 4/20. so now I ‘ve rewritten this alternatively of 3/4 plus 1/5, it ‘s nowadays written as 15/20 plus 4/20. And what is that going to be ? Well that ‘s going to be 15 plus four is 19/20. 19/20, and we ‘re done.

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