Number lines are used to visually represent the relationships between numbers. Some number lines are shown with arrows pointing in opposite directions on either end of the line to show that the number line continues infinitely in positive and negative directions.

A number line is shown as a line with equally spaced tick marks along the whole line. Some ticks may purposely be left out or left blank so that you have to find solutions for the missing values.

Numbers to the left of zero are negative, with the (‐) sign always shown, and numbers to the right of zero are positive, but the (+) sign is usually not shown.

If you move to the right on the number line, the numbers always increase in size, and if you move to the left on the number line, the numbers always decrease in size.

Remember, this means that when it comes to negative numbers, -3 < -2 < -1. The closer a negative number is to zero, the greater it is. However, the closer a positive number is to zero, the smaller it is.

Unless specifically noted, number lines are generally drawn to scale, which will enable you to make accurate estimations of distances and positions of points on a number line. Not all numbers will always be explicitly shown.

Based on the numbers shown and the positions of the ticks on the number line, you can figure out that the missing numbers are -6 and 3.

Number lines are not only useful for representing and comparing values, but also for visualizing basic operations like addition and subtraction. Number lines can help simplify the process and show how adding to a number increases its value and subtracting from a number decreases its value.

To calculate 2+4: start at 2 on the number line, then count four tick marks to the right and you see that you arrive at 6. To calculate 7-3, you begin at 7 on the number line and then count backwards three tick marks to 4. This is a simple process, but it is nonetheless an important foundation. For instance, this can help you to visualize why subtracting from a negative number decreases the value (moves it further left on the number line).

**Answers to Practice Problems**

- 0, 1.5
- 5, 10, 20, 45
- -8, 4

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