How do you reduce 51 over 68 in a fraction?

Answer 1

51/68 is equal to 3/4. In general, to reduce a fraction, you have to find the largest number which divides both the top and the bottom, called the Greatest Common Factor (GCF) or Greatest Common Divisor (GCD). In many cases, you can do this by simple observation, but sometimes, as here, the GCD is not obvious -- most people don't know the multiples of 17 off the top of their head. If the GCD isn't readily apparent, the straightforward thing to do is to try to find all the factors of both numbers. By trial division, you'll find that 3 divides 51, so 51 is 3*17, where 17 is prime and can't be broken up further. 68 is even so we write it as 2*34; 34 is also even, and is 2*17, so 68 is 2*2*17. The only prime factor in common is 17, so this is the GCF. A far easier way (for large numbers you wouldn't want to factor) is Euclid's Algorithm, which relies on the observation that if a number divides A and B, it will also divide their difference A-B. So we can make the problem simpler by subtracting the smaller number from the larger. Observe how this works in our case: we start off with 51 and 68. 68 is the larger, so we replace it by 68-51, which is 17. Now our problem is to find the GCD of 17 and 51. Subtract 17 from 51 to get 34, and then 17 from 34 to get 17. Now the answer is obvious: the largest number that divides both 17 and 17 is 17 itself. Whichever way you found the GCD, the thing to do is to cancel it from the top and the bottom. 51 becomes 51/17 or 3, and 68 becomes 68/17 or 4, so 51/68=3/4.