What is 31/12 + 1/9?
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Here's how we add
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Step 1We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator. Now we multiply 31 by 9, and get 279, then we multiply 12 by 9 and get 108. Now for the second term. You multiply 1 by 12, and get 12, then multiply 12 by 9 and get 108. This gives us a new problem that looks like so:
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Step 2Since our denominators match, we can add the numerators. 279 + 12 = 291 So what's the answer so far?
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Step 3Can this fraction be reduced? First, we attempt to divide it by 2... No good. So next you try the next prime number, which is 3... Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:
So far so good... let's try to divide by that number again. No good. So next you try the next prime number, which is 5... No good. So next you try the next prime number, which is 7... No good. So next you try the next prime number, which is 11... No good. So next you try the next prime number, which is 13... No good. So next you try the next prime number, which is 17... No good. So next you try the next prime number, which is 19... No good. So next you try the next prime number, which is 23... No good. So next you try the next prime number, which is 29... No good. So next you try the next prime number, which is 31... No good. So next you try the next prime number, which is 37... No good. 37 is larger than 36. So we're done reducing. And we're done! Here's the final answer to 31/12 + 1/9
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