Final answer:
There is no subunit fraction with consecutive numerator and denominator natural numbers whose sum is 51.
Step-by-step explanation:
To find a subunit fraction that has consecutive numerator and denominator natural numbers, and their sum is 51, we can set up the equation:
x/(x+1) = 51
Where x is the numerator and x+1 is the denominator. We can solve this equation by cross multiplying and then solving for x:
x = 51(x+1)
Simplifying further, we get:
x = 51x + 51
Subtracting 51x from both sides, we get:
x - 51x = 51
-50x = 51
Dividing both sides by -50, we get:
x = -51/50
Since we are looking for consecutive natural numbers, x must be a positive integer. Therefore, there is no subunit fraction with consecutive numerator and denominator natural numbers whose sum is 51.