In order to make a fraction as large as possible, you want the numerator to be large, and the denominator to be small.
Using the counting numbers, the smallest denominator (x - y) you can make is ' 1 '. Now you just have to make the numerator large. You do that simply by using the largest two numbers you have available . . . 49 and 50 .
Now the fraction is (49 + 50) / 1 = 99 .
The largest value will be for x=50 and y=49.
50 − 49 50 + 49 = 1 99 = 99
The largest value of x − y x + y when selecting two different numbers from 1 to 50 is 99, achieved by choosing x = 50 and y = 49 .
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