Let's evaluate each of the given statements one by one to determine which are true:
1. Statement: [tex]\(-2.5 = -2 \frac{1}{2}\)[/tex]
This statement is true. The mixed number [tex]\(-2 \frac{1}{2}\)[/tex] can be converted to the improper fraction [tex]\( -2.5 \)[/tex], which is equal to [tex]\(-2.5\)[/tex].
2. Statement: [tex]\(-1.5 > -0.5\)[/tex]
This statement is false. When comparing negative numbers, the number with a smaller absolute value is actually greater. Therefore, [tex]\(-1.5\)[/tex] is less than [tex]\(-0.5\)[/tex].
3. Statement: [tex]\(-0.5 < 0\)[/tex]
This statement is true. Negative numbers are always less than zero.
4. Statement: [tex]\(-2.5 < -2\)[/tex]
This statement is true. When comparing negative numbers, the number with the larger absolute value is less. Therefore, [tex]\(-2.5\)[/tex] is less than [tex]\(-2\)[/tex].
5. Statement: [tex]\(1 \frac{1}{2} > 1.5\)[/tex]
This statement is false. The mixed number [tex]\(1 \frac{1}{2}\)[/tex] is equal to the improper fraction [tex]\(1.5\)[/tex], so it is not greater than [tex]\(1.5\)[/tex]; they are equal.
Therefore, the statements that are true are:
- [tex]\(-2.5 = -2 \frac{1}{2}\)[/tex]
- [tex]\(-0.5 < 0\)[/tex]
- [tex]\(-2.5 < -2\)[/tex]
So, the correct statements are the first, third, and fourth ones.
