Understanding Negative Integers

Whole numbers, 1, 2, 3, and so on are natural for counting and you are already familiar with them. Zero represents nothing (or nothing left), and can be the result of 2 − 2, or 8 − 8.

But what about 5 − 7? Reducing 5 by 5 is already zero. Here, we come up 2 short. We say the answer is negative 2. Thus, negative means "short by" or "not enough by". For example, negative 5 means "not enough by 5".

In bookkeeping, negative numbers are written in parenthesis, (7) for negative 7 for example; or in red, 9 for negative 9 for example. In mathematics, we use the negative sign −. For example, −4 means negative 4. The same − sign is also used to indicate the subtraction operation. Thus, − 13 means negative 13, but 4 − 2 means subtract 2 from 4.

DEFINITION: An integer is a positive, zero, or negative whole number.

By putting integers on the number line, we can demonstrate clearly the meaning of negative numbers and how they work in addition and subtration operations. Here is a model that we call walking the number line:

• Moving forwards models a positive integer.
• Moving backwards models a negative integer.
• Facing the positive direction models the addition operation.
• Facing the negative direction models the subtraction operation.

Let's see how this model works.

8 + (−3) means: Start at 8, face the positive direction, and move backwards 3.

5 − (−3) means: Start at 5, face the negative direction, and move backwards 3..

This tool helps you visualize what we mean.

Do 8 + (−3)

Next, do 5 − (−2)