TenMarks teaches you how to add fraction with unlike denominators.
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Learn about Addition of Unlike Fractions This video lesson covers the addition of unlike fractions and we’re asked to solve the expression, -1/8, -5/16. It looks like a subtraction operation, -1/8-5/16 and we are to write the answer in simplest form. The key thing to remember is if the signs are the same, you got a negative sign and a negative sign then it’s an addition operation. Here’s why. Because I can write this expression, I can pull the negative sign out and I’ll be left with 1/8+5/16 because I can’t pull the negative sign out. Once we do that, it’s left with an addition operation inside. Let’s try this addition operation. As we can see the denominators are not equal. Denominators are different. If the denominators are different, the fractions are called unlike fractions. In order to add unlike fractions, we must use the lowest common multiple of the denominator. We need to find the lowest common multiple of 8 and 16. Let’s do that. In order to find the LCM of 8 and 16, we need to find the prime factors of 8. The prime factors of 8 are 2×2×2 which is 8. The prime factors of 16 are 2×2×2×2. Well, 2 appear four times here and three times here, so the common multiple of 3 is 2×3. So, the lowest common multiple is 2×2×2×2 which is 16. So, the multiples here are 16. So, if the LCM is 16, next I need to convert both of these fractions so they have the denominator of 16. So 1/8, I can write as something over 16. Well, if 8 is multiplied by 2 to get to 16, I need to multiply the numerator 1 with 2 as well. So, 1/8 is the same as 2/16. Instead of 1/8, I can write 2/16 + 5/16 already has the denominator of 16 so, I don’t need to change anything and the negative sign is right above. This is what we need to add. Let’s look at how do we do this. So, negative sign outside, 2/16+5/16. Denominators are the same. So 2+5 is 7. So, the final result of this is -7/16. You don’t have to do anything more because it’s already in its lowest forms. The key thing to remember what we learned in this track is if we are adding unlike fractions, the denominators are different. The key is two things; one, if the denominators are different, we need to first compute the LCM of the denominators. I’ve done that using the prime factorization method to get the LCM of 16. Once I know the LCM is 16, we convert both fractions to fractions so that the denominator is 16. Here, 1/8 is the same as 2/16. So, now I’m trying to add instead of 1/8 + 5/16, we’re adding 2/16 + 5/16 because these two are equivalent. If that’s the case then 2+5=7, 16 comes down below and the negative sign remains. So, the final result is -7/16.