To determine which of the given number lines show the fractions [tex]\( \frac{1}{2} \)[/tex], [tex]\( -1 \)[/tex], and [tex]\( -2 \)[/tex] correctly placed, we need to order these fractions in ascending order and then check their positions on each number line.
Step-by-step Solution:
1. Identify the fractions to be placed:
- [tex]\( \frac{1}{2} \)[/tex]
- [tex]\( -1 \)[/tex]
- [tex]\( -2 \)[/tex]
2. Order the fractions in ascending order:
- The smallest number is [tex]\( -2 \)[/tex].
- The next smallest number is [tex]\( -1 \)[/tex].
- The largest number is [tex]\( \frac{1}{2} \)[/tex].
So, the correct ascending order should be:
[tex]\[
-2 \quad < \quad -1 \quad < \quad \frac{1}{2}
\][/tex]
3. Evaluate the given number lines to check their correctness:
- Number Line 1: [tex]\([-2, -1, \frac{1}{2}]\)[/tex]
- This follows the correct order [tex]\(-2 < -1 < \frac{1}{2}\)[/tex].
- Number Line 2: [tex]\([\frac{1}{2}, -1, -2]\)[/tex]
- This does not follow the correct order.
- Number Line 3: [tex]\([-1, \frac{1}{2}, -2]\)[/tex]
- This does not follow the correct order.
- Number Line 4: [tex]\([-2, \frac{1}{2}, -1]\)[/tex]
- This does not follow the correct order.
4. Conclusion:
- Only Number Line 1 correctly places the fractions [tex]\( \frac{1}{2} \)[/tex], [tex]\( -1 \)[/tex], and [tex]\( -2 \)[/tex] in ascending order.
Therefore, the correct placement of [tex]\( \frac{1}{2} \)[/tex], [tex]\( -1 \)[/tex], and [tex]\( -2 \)[/tex] occurs on Number Line 1. This number line is:
[tex]\[
\boxed{-2, -1, \frac{1}{2}}
\][/tex]
