Question
Explain two ways you can use a number line to order the integers –3, +1, and –10.
Answers
GPT-4o mini
A number line is a visual representation of numbers that helps in understanding their relative positions and order. Here are two ways you can use a number line to order the integers –3, +1, and –10:
### Method 1: Plotting Points on the Number Line
1. **Draw the Number Line**: Start by drawing a horizontal line. Mark the center point as 0, because zero is the point of reference for positive and negative integers.
2. **Mark Negative and Positive Values**: To the left of 0, mark the negative integers (e.g., -1, -2, -3, -4, etc.) and to the right, mark the positive integers (e.g., +1, +2, +3, etc.).
3. **Plot the Given Numbers**: Now locate and plot the three integers:
- For –10, move 10 units to the left of 0 and place a point.
- For –3, move 3 units to the left of 0 and place a point.
- For +1, move 1 unit to the right of 0 and place a point.
4. **Identify Their Order**: Once plotted, you can see that –10 is farthest left, then –3, and +1 is farthest right. Therefore, in order from least to greatest, the integers are: –10, –3, +1.
### Method 2: Comparing Distances from Zero
1. **Reference Zero**: Use 0 as the reference point on the number line.
2. **Evaluate Distances**: Determine the distance of each integer from zero:
- For –10, the distance from 0 is 10 units (to the left).
- For –3, the distance from 0 is 3 units (to the left).
- For +1, the distance from 0 is 1 unit (to the right).
3. **Order by Distance**: Since integers further to the left are smaller, you can order the integers based on how far they are from 0.
- The integer with the greatest distance on the left is the smallest: –10.
- The second smallest is –3, and the largest is +1.
4. **Conclusion**: Thus, the order from least to greatest remains: –10, –3, +1.
By using these methods, you can effectively visualize and order the integers on a number line!
### Method 1: Plotting Points on the Number Line
1. **Draw the Number Line**: Start by drawing a horizontal line. Mark the center point as 0, because zero is the point of reference for positive and negative integers.
2. **Mark Negative and Positive Values**: To the left of 0, mark the negative integers (e.g., -1, -2, -3, -4, etc.) and to the right, mark the positive integers (e.g., +1, +2, +3, etc.).
3. **Plot the Given Numbers**: Now locate and plot the three integers:
- For –10, move 10 units to the left of 0 and place a point.
- For –3, move 3 units to the left of 0 and place a point.
- For +1, move 1 unit to the right of 0 and place a point.
4. **Identify Their Order**: Once plotted, you can see that –10 is farthest left, then –3, and +1 is farthest right. Therefore, in order from least to greatest, the integers are: –10, –3, +1.
### Method 2: Comparing Distances from Zero
1. **Reference Zero**: Use 0 as the reference point on the number line.
2. **Evaluate Distances**: Determine the distance of each integer from zero:
- For –10, the distance from 0 is 10 units (to the left).
- For –3, the distance from 0 is 3 units (to the left).
- For +1, the distance from 0 is 1 unit (to the right).
3. **Order by Distance**: Since integers further to the left are smaller, you can order the integers based on how far they are from 0.
- The integer with the greatest distance on the left is the smallest: –10.
- The second smallest is –3, and the largest is +1.
4. **Conclusion**: Thus, the order from least to greatest remains: –10, –3, +1.
By using these methods, you can effectively visualize and order the integers on a number line!