How do we simplify $13 + ( - 12) - ( - 15)$ ?

Hint: To solve this question, first we will discuss the steps for the addition of positive and negative numbers and then solve the given expression on the basis of the steps that we followed. And lastly conclude the answer by both addition and subtraction needed.

Complete step-by-step solution:
First, we will discuss the steps for the simplification of the addition of bunch of positive and negative numbers:-
Step-1: If one or more numbers are negative, then we add the numbers together and keep the negative sign for our answer and also keep the positive number remains the same.
Step-2: If one number is positive and more than one number is negative then we have to first find the absolute value of each number such that followed in step-1.
Step-3: Once we know the absolute value we will subtract the smaller number from the larger number and keep the sign of greater side.
Step-4: Our answer will have the same sign of the larger number.
Now, we will simplify the given expression:-
Rewrite the given expression as well:
$\Rightarrow 13 + ( - 12) - ( - 15)$
First remove each term from parenthesis. Be sure to manage the signs of each individual term correctly according to the above steps:
$\Rightarrow 13 - 12 + 15$
Now, add and subtract as appropriate:
$\Rightarrow (13 - 12) + 15 \\
  \Rightarrow 1 + 15 \\
  \Rightarrow 16 \\
$

Hence, the simplified form of the given expression is 16.

Note: Addition of a positive and a negative integer give either a positive or negative sum depending on the value of the given numbers. The sum of an integer and its opposite is always zero. We should always work on the numbers of the same sign first.