Introduction:
To find a number whose sixth part exceeds its 13th part by -5/7, we need to first understand the terms involved. The "sixth part" of a number refers to dividing the number by 6, while the "13th part" refers to dividing the number by 13. We are given that the sixth part exceeds the 13th part by -5/7.

Let the number be x:
Let's assume the number we are trying to find is represented by the variable "x".

Equation:
We can now set up an equation based on the given information. The sixth part of the number exceeds the 13th part by -5/7. Mathematically, this can be represented as:

x/6 - x/13 = -5/7

Solving the equation:
To solve the equation, we need to eliminate the denominators. We can do this by finding a common denominator, which in this case is 78 (the product of 6 and 13).

Multiplying both sides of the equation by 78:
By multiplying both sides of the equation by 78, we can eliminate the denominators and simplify the equation.

78(x/6) - 78(x/13) = 78(-5/7)

Simplifying the equation:
Simplifying the equation further, we get:

13x - 6x = -60

7x = -60

Solving for x:
To solve for x, we divide both sides of the equation by 7:

7x/7 = -60/7

x = -60/7

Final Answer:
Therefore, the number we are looking for is -60/7.