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When dealing with integers, especially when performing operations like addition and subtraction, it’s important to understand the concept of opposites. Each positive integer has a negative counterpart, and vice versa.
Subtraction can often be thought of as adding the opposite. For instance, instead of saying "31 minus 44," you could say "31 plus negative 44." This is possible because subtracting a number is the same as adding its opposite. Thus, the expression \(31 - 44\) can be rewritten as \(31 + (-44)\).
Understanding this relationship between addition and subtraction helps simplify calculations and avoid mistakes. You simply need to:

• Change the subtraction sign to an addition sign.
• Change the sign of the second integer (the one being subtracted).

This approach makes it easier to manipulate numbers and solve problems with confidence.

Evaluating mathematical expressions involves performing operations according to specific rules. Once we've rewritten a subtraction problem as an addition problem, we need to calculate the sum or difference making use of the rules for integers.
To evaluate expressions like \(31 + (-44)\), we look at the signs of the numbers involved. In this case, one number is positive (31) and the other is negative (-44).
When adding a positive and a negative number, you subtract their absolute values and retain the sign of the larger number. Here are the steps:

• Find the absolute values: \(|31| = 31\) and \(|-44| = 44\).
• Subtract the smaller absolute value from the larger one: \(44 - 31 = 13\).
• Since -44 has the larger absolute value, the answer takes its sign: \(-13\).

Applying these steps ensures that you correctly evaluate expressions, even when negative numbers are involved.

Negative numbers are an essential part of mathematics, representing values less than zero. They are indicated by a minus sign (-) in front of a number. Understanding negative numbers is key in performing integer operations smoothly.
When working with negative numbers:

• Visualize them as positions on a number line, to the left of zero.
• Remember that adding a negative is the same as subtracting its positive counterpart.
• When subtracting negative numbers, you add their positive counterparts.

These principles help in manipulating expressions involving negatives.
In the context of our example, \(-44\) indicates moving 44 steps to the left on a number line, starting from zero. Combining such clear imagery with the straightforward rules of arithmetic makes working with negative numbers less intimidating and more intuitive.