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what is 775/1212?
 Sep 6, 2013
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775/1212 is as far reduced as it ever will be.

Reducing fractions is based on dividing the top and bottom of your fraction by the same number. This works because a fraction is a ratio, meaning it compares two numbers by relative size. Another example of a ratio is this: If I have four apples and you have two, I still have twice as many apples as you do, even if we divide both our numbers by two. You will still have one apple, and I will still have two - twice as many.

You can break 775 down into smaller numbers by trying to divide it by other numbers. If you start with 2 (because everything is divisible by 1, and it's not very helpful), and keep going up, you'll see that 5 is the smallest number that divides 775 evenly. Doing it, you see that 775=5x155. You can divide 155 by 5 as well, which gives you 775=5x5x31. 31 isn't divisible by anything other than 1 and itself, so it's a prime number. 5 is as well, so we call 5x5x31 the prime factors of 775. If you know the prime numbers, you can skip all the numbers in between them when you're testing numbers because if the other ones are factors, you would have noticed their prime factors first.

1212 can also be broken down into 1212=2x2x3x101. 101 is a prime number, even though there are a lot of smaller numbers that might divide it. Because none of the prime factors of 775 and 1212 are the same, the fraction can't be reduced anymore.

If you want a decimal answer, you can just put it in a calculator. You'll get about 0.639494389... and no matter how big your calculator is, it will keep going forever.
 Sep 6, 2013

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