Sum of two consecutive numbers
To solve this problem, we need to find two consecutive numbers whose sum is 15. Let's call the smaller number "n" and the greater number "x".

Mathematical representation
We can represent the problem mathematically as:
n + x = 15

Expressing the greater number in terms of the smaller number
We are given that the greater number is "x". To express it in terms of the smaller number "n", we can use the fact that the numbers are consecutive. This means that the greater number is 1 more than the smaller number. So, we can write:
x = n + 1

Substituting the value of x in the equation
Now, we can substitute the value of "x" in the equation n + x = 15:
n + (n + 1) = 15

Simplifying the equation
Let's simplify the equation by combining like terms:
2n + 1 = 15

Isolating the variable
To solve for "n", we need to isolate the variable on one side of the equation. We can do this by subtracting 1 from both sides:
2n = 15 - 1
2n = 14

Then, we can divide both sides by 2 to solve for "n":
n = 14 / 2
n = 7

Finding the smaller number
So, the smaller number is 7. Since the greater number is 1 more than the smaller number, the greater number is:
x = n + 1
x = 7 + 1
x = 8

Conclusion
Therefore, the smaller number is 7 and the greater number is 8. We found these numbers by expressing the greater number in terms of the smaller number and solving the resulting equation.