To measure distance on a number line, you find the difference between the values of two points and take the absolute value of that difference.
Understanding Measurement on a Number Line
A number line is a visual tool representing numbers in a straight line. Measuring on a number line typically refers to finding the distance or length between two specific points on that line. This distance represents the numerical separation between the two numbers the points correspond to.
Step-by-Step Guide: Finding Distance
Finding the distance between any two points on a number line is a straightforward process:
- Identify the Points: Locate the two numbers (points) on the number line whose distance you want to find. Let's call them Point A and Point B.
- Find the Difference: Subtract the value of one point from the value of the other point. It doesn't matter which number you subtract from which, but the result is called the difference.
- Calculate the Absolute Value: Take the absolute value of the difference you found in step 2. The absolute value of a number is its distance from zero, always resulting in a positive number.
This final positive number is the distance between the two points on the number line.
Why Absolute Value is Key
As highlighted in the reference ([Measurement with Number Lines (Simplifying Math) - YouTube, 1:38-6:48]), when you find the difference between two numbers, the result can be positive or negative depending on the order of subtraction (e.g., 7 - 2 = 5, but 2 - 7 = -5).
However, distance is always a positive value – you can't have a negative distance. Taking the absolute value ensures that your result is positive, accurately representing the length or separation between the points regardless of which number you subtracted first. The absolute value operation removes any negative sign, giving you the magnitude of the difference, which is the distance.
Example: Measuring Distance Between 2 and 7
Let's find the distance between the points corresponding to the numbers 2 and 7 on a number line using the steps above:
| Step | Calculation | Result | Explanation |
|---|---|---|---|
| Identify Points | Point A = 2 | The two numbers are 2 and 7. | |
| Point B = 7 | |||
| Find Difference 1 | 7 - 2 | 5 | Subtracting 2 from 7. |
| Find Difference 2 | 2 - 7 | -5 | Subtracting 7 from 2 (results in negative). |
| Absolute Value | |5| or |-5| | 5 | The absolute value of both differences is 5. |
| Distance | 5 | The distance between 2 and 7 is 5 units. |
As shown, whether you calculate 7 - 2 or 2 - 7, taking the absolute value gives you the correct positive distance of 5.
