Alright, let's classify each number and match it with the appropriate description.
1. [tex]\( 3 \frac{1}{2} \)[/tex]
- Written as a decimal, [tex]\(3 \frac{1}{2}\)[/tex] is 3.5.
- This is a rational number because it can be expressed as a fraction (7/2), but it is not an integer because it includes a fractional part.
- Hence, the correct description is: This is a rational number, but not an integer.
2. 0.56
- 0.56 is already in decimal form.
- This is a rational number because it can be expressed as a fraction (56/100 or 14/25), but it is not an integer since it includes a fractional part.
- Hence, the correct description is: This is a rational number, but not an integer.
3. 5
- The number 5 is an integer.
- Since it has no fractional part and it is a whole number, it is classified as an integer.
- Hence, the correct description is: This is an integer.
4. [tex]\( \sqrt{11} \)[/tex]
- The square root of 11 is an irrational number.
- It cannot be expressed as a simple fraction or a repeating or terminating decimal.
- Hence, the correct description is: This is an irrational number.
5. [tex]\( -3 \frac{1}{2} \)[/tex]
- Written as a decimal, [tex]\(-3 \frac{1}{2}\)[/tex] is -3.5.
- This is a rational number because it can be expressed as a fraction (-7/2), but it is not an integer because it includes a fractional part.
- Hence, the correct description is: This is a rational number, but not an integer.
So, the final matches are:
- [tex]\(3 \frac{1}{2} \quad\)[/tex] This is a rational number, but not an integer.
- 0.56 \quad This is a rational number, but not an integer.
- 5 \quad This is an integer.
- [tex]\(\sqrt{11}\)[/tex] \quad This is an irrational number.
- [tex]\(-3 \frac{1}{2}\)[/tex] \quad This is a rational number, but not an integer.
