To determine between which two numbers the given numbers [tex]\(-2\)[/tex], [tex]\(\frac{1}{2}\)[/tex], [tex]\(-0.5\)[/tex], and [tex]\(\frac{7}{3}\)[/tex] lie on the number line, we need to first arrange these numbers in ascending order.
1. Start by examining each number:
- [tex]\(-2\)[/tex]
- [tex]\(\frac{1}{2}\)[/tex] which is equivalent to [tex]\(0.5\)[/tex]
- [tex]\(-0.5\)[/tex]
- [tex]\(\frac{7}{3}\)[/tex] which is approximately [tex]\(2.333...\)[/tex]
2. Now, let's sort these numbers from smallest to largest:
- The smallest number is [tex]\(-2\)[/tex]
- The next smallest number is [tex]\(-0.5\)[/tex]
- Following this is [tex]\(0.5\)[/tex] (or [tex]\(\frac{1}{2}\)[/tex])
- The largest number is [tex]\(2.333...\)[/tex] (or [tex]\(\frac{7}{3}\)[/tex])
So, arranging these numbers, we get:
[tex]\[ -2, -0.5, 0.5, 2.333... \][/tex]
3. To find the two numbers between which all these numbers lie, identify the minimum and maximum from the sorted list:
- The minimum number is [tex]\(-2\)[/tex]
- The maximum number is [tex]\(2.333...\)[/tex] (or [tex]\(\frac{7}{3}\)[/tex])
Therefore, the given numbers [tex]\(-2\)[/tex], [tex]\(\frac{1}{2}\)[/tex], [tex]\(-0.5\)[/tex], and [tex]\(\frac{7}{3}\)[/tex] lie between [tex]\(-2\)[/tex] and [tex]\(\frac{7}{3}\)[/tex] on the number line.
