TenMarks teaches you all about how to add unlike fractions.
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How to Add Fractions with Unlike Denominators Learn how to add fractions that do not have like denominators or have unlike denominators. We’re given two problems. Let’s do the first one. Five over 12, we need to add that to 1/6. We can see denominators are different which means these are unlike fractions. How do we add unlike fractions? Well first, we need to find the Lowest Common Multiple of the denominators. So, the denominators are six and 12. Well, to get the LCM of six and 12, what are the multiples of six? Well, multiples of six are 6×1 is six, 6×2 is 12, 6×3 is 18, 6×4 is 24, 6×5 is 30, 6×6 is 36 and so on. Multiples of 12 are, 12×1 is 12×2 is 24, 36, 48, 12×5 is 60 and so on. What we need to do is find the lowest common multiple. What are the common multiples? The common multiples are 12, it’s common to both, 24 is common to both, 36 is common to both, etcetera. Among this, the lowest common one is 12. So, the Lowest Common Multiple between six and 12 is 12. Now that we know this, let’s proceed. So we found out the LCM of the denominators. Next, we need to write equivalent fractions for both of these with denominator 12, 12 because that’s the LCM. So, let’s try and do that. If we have 5/12, we need to convert this to something that is equal or equivalent with denominator of 12. Well, there’s already has a denominator of 12, so I don’t need to do anything. The next one is 1/6, 1/6 I need to convert this to something that has a denominator of 12. In order to do that, six will have to be multiplied by two to get the 12. So, we have to multiply the numerator by two as well, 1×2 is two. So, the equivalent fraction of 1/6 is 2/12. So now that we have both these fractions, we can simply add them because that’s what we’re trying to do. So, 5/12 plus instead of 1/6, I’m going to write down 2/12 because that’s an equivalent fraction. Now, it becomes easy because the denominators are the same, so 5+2 is seven. So, the answer we were looking for is 7/12. Now, let’s look at the second problem we were given which is the Pacific Ocean covers a third of the earth’s surface. If the Atlantic Ocean covers 1/5 of the earth’s surface, what fraction of earth’s surface is covered by both the Atlantic and the Pacific? So, I just have to add 1/3+1/5. The Pacific Ocean covers 1/3 of earth’s surface. The Atlantic Ocean covers 1/5 of the earth’s surface. So that’s the case, this is over, 1/3. The total surface covered by both equals 1/3+1/5. Again, we’ve got two unlike fractions. So, let’s scroll down and let’s look at the LCM of three and five. Well three, multiples of three are three, six, nine, 12, 15, 18, etcetera. Multiples of five are five, 10, 15, 20, 25, 30. The lowest common one is 15. Before that none of them are common. So, the LCM is 15. If the LCM is 15, now what we have to do is write 1/3 as an equivalent fraction with the denominator 15, 3×5 is 15 so 1×5 is what we’re looking for which is five because 3×5=15. Similarly, the next one is 1/5 equals I know I need to make an equivalent so the denominator is 15. Well, to get from five to 15, I multiply it by three. So, let’s multiply the numerator by three as well, 1×3 is three. So now adding both, we get 5/15+3/15. Instead of adding 1/3 and 1/5, I can add the equivalent fractions which gives me fifteen at the denominator, they’re both like fractions, 5+3 is eight. So, what do we know? That the surface of the earth covered by both is 8/15. A quick recap, if we are converting also we are adding unlike fractions, unlike means the denominators are different, we first find the LCM of both the denominators. Once we have that, we write both fractions as equivalent fractions with the denominator which equals the LCM. They are 5/12 and 2/12. Now, addition becomes simple.
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