Question
Explain two ways you can use a number line to order the integers –3, +1, and –10.
Answers
GPT-4o mini
To order the integers –3, +1, and –10 using a number line, you can follow these two methods:
### Method 1: Visual Placement
1. **Draw a Number Line**: Start by drawing a horizontal line and marking several key integers on it, such as -10, -5, 0, +1, and some integers in between.
2. **Locate Each Integer**: Place each integer on the number line:
- For –10, locate it on the far left since it's the smallest.
- For –3, place it to the right of –10 but to the left of 0.
- For +1, place it to the right of 0.
3. **Order Observation**: Once positioned, you can see that the integers are arranged from left to right as: –10, –3, +1. This visually shows their order from least to greatest.
### Method 2: Numerical Value Comparison
1. **Use Number Properties**: Recognize the absolute values of the integers to determine their order:
- Compare the values: |–10| = 10, |–3| = 3, and |+1| = 1.
- Notice that –10 has the greatest absolute value and is less than both –3 and +1.
2. **List in Order**: Based on this comparison:
- Identify that –10 is the smallest, followed by –3, and then +1, as they relate to each other numerically.
3. **Order Confirmation**: You can conclude that the order from smallest to largest is again: –10, –3, +1.
By using these two methods, you effectively order the integers on a number line!
### Method 1: Visual Placement
1. **Draw a Number Line**: Start by drawing a horizontal line and marking several key integers on it, such as -10, -5, 0, +1, and some integers in between.
2. **Locate Each Integer**: Place each integer on the number line:
- For –10, locate it on the far left since it's the smallest.
- For –3, place it to the right of –10 but to the left of 0.
- For +1, place it to the right of 0.
3. **Order Observation**: Once positioned, you can see that the integers are arranged from left to right as: –10, –3, +1. This visually shows their order from least to greatest.
### Method 2: Numerical Value Comparison
1. **Use Number Properties**: Recognize the absolute values of the integers to determine their order:
- Compare the values: |–10| = 10, |–3| = 3, and |+1| = 1.
- Notice that –10 has the greatest absolute value and is less than both –3 and +1.
2. **List in Order**: Based on this comparison:
- Identify that –10 is the smallest, followed by –3, and then +1, as they relate to each other numerically.
3. **Order Confirmation**: You can conclude that the order from smallest to largest is again: –10, –3, +1.
By using these two methods, you effectively order the integers on a number line!