Absolutely! Ordering integers using a number line is a very visual and clear way to understand the concept of comparing and sorting numbers. Let's take the integers \(-3\), \(+1\), and \(-10\) and explore two ways to order them.
### Method 1: Using a Horizontal Number Line
1. Draw the Number Line:
- Draw a horizontal line and mark a point in the middle as zero (\(0\)).
- Going to the right, mark positive integers (\(+1\), \(+2\), \(+3\), and so on).
- Going to the left, mark negative integers (\(-1\), \(-2\), \(-3\), and so on).
2. Plot the Integers on the Number Line:
- Locate and mark \(-3\) on the number line: This will be three steps to the left of zero.
- Locate and mark \(+1\) on the number line: This will be one step to the right of zero.
- Locate and mark \(-10\) on the number line: This will be ten steps to the left of zero.
3. Order the Integers:
- On the number line, the further left a number is, the smaller it is.
- \(-10\) is to the left of \(-3\).
- \(-3\) is to the left of \(+1\).
Therefore, in ascending order, the integers are: \(-10, -3, +1\).
### Method 2: Using Distance from Zero
Another method involves comparing their distances from zero:
1. Understand Negative and Positive Distances:
- The further a number is to the left of zero, the smaller it is.
- The further a number is to the right of zero, the larger it is.
2. Compare Integer Distances from Zero:
- \(-10\) is 10 units to the left of zero.
- \(-3\) is 3 units to the left of zero.
- \(+1\) is 1 unit to the right of zero.
3. Order Based on Position Relative to Zero:
- Since \(-10\) is the furthest to the left, it is the smallest.
- Followed by \(-3\), which is closer to zero but still on the left side, making it larger than \(-10\) but smaller than \(+1\).
- \(+1\) is to the right of zero, making it the largest among the three integers.
Thus, the order from smallest to largest is: \(-10, -3, +1\).
Using these two methods, we confirm that the integers [tex]\(-3, +1\)[/tex], and [tex]\(-10\)[/tex] are ordered as [tex]\(-10, -3, +1\)[/tex]. Both approaches visually and conceptually help to understand the ordering of integers.
