Number lines are linear representations of numeric values. Any negative integer left of zero is part of the negative number line. Any positive integer right of zero is part of the positive number line. When you move left to right, you are heading in a positive direction. Shifting right to left along the number line indicates a move in the negative direction.
Positive vs. Negative Number Line
Most of the time, the positive numbers you'll see on a number line are natural numbers. A natural number isn't a fraction or decimal. It's simply a whole number that's always on the side of the number line that's right of zero. As soon as you cross over to the negative number line, you’re no longer dealing with natural numbers.
See the number line below. We are subtracting 7 from 5. Since the answer is -2, we've now crossed over to the negative number line, where we do not have natural numbers.
Here is an example where we are only using the negative number line. We have started with -1, moved three spaces to the left, and ended at -4.
The equation for the line above must be written as:
In order to move in a negative direction from a smaller negative number to a larger negative number along the number line, you must use an addition sign. If you use a subtraction sign, the two negatives cancel out. You would then move into in a positive direction:
Why We Use the Number Line
Using the negative number line shows us going left on the line is a move in the negative direction and going right is a move in the positive direction. Writing out the equations of each move allows us to understand how to use a plus sign to indicate decreasing negative values.
Though the number line seems like a basic way of explaining subtraction and addition, it can actually be used in many other ways. You can apply it in real life to measure bank balances and sea levels. Number lines are a useful tool for demonstrating increases and decreases in value.