We're going to turn this into an equation and then use a little algebra to solve this problem. Your problem can be written like this:
x/12 + x/20 = 31
If you take a look at the equation, you'll see that x is equal to the number you're looking for. x/12 is the same as 1/12 times x or one twelfth of x. x/20 is the same way. Now we simply solve for x in this equation
x/12 + x/20 = 31
x + 12x/20 = 372 (i multiplied everything by 12)
20x + 12x = 7440 (now i multiplied everything by 20)
32x = 7440 (you can combine the two x values)
x = 232.5 (i divided by 32)
Now we check our answer:
232.5/12 = 19.375
232.5/20 = 11.625
19.375 + 11.625 = 31
It checks out.
So your answer is 232.5 or 465/2.
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1/20 = 5/100 = 5% actual sum: 0.05 * 750 = 37.5
The significance if the number minus 1/12 in Physics is that it helps us perform a number of Mathematical calculations. The reason it can do this is because according to some sophisticated analyses, minus one twelfth can represent the sum of all positive integers. This seems absurd, but it is true within the limits of its specialized use.
Integers have no fractional parts, so their sum will be zero.
Close. "The whole is more than the sum of its parts."
If I am twenty-five, does that mean I have twenty-five parts?