Sure! Let's analyze each number one by one and match them to the appropriate descriptions.
### Analyzing the Numbers
1. [tex]\( 3 \frac{1}{2} \)[/tex]:
- This number is written as a mixed number, which can be converted to an improper fraction: [tex]\( 3 \frac{1}{2} = \frac{7}{2} \)[/tex].
- A rational number is any number that can be expressed as the quotient of two integers (where the denominator is not zero).
- [tex]\( \frac{7}{2} \)[/tex] is such a quotient, so it is a rational number.
- Since [tex]\( \frac{7}{2} \)[/tex] is not a whole number (it's not an integer), we describe it as: "This is a rational number, but not an integer."
2. 0.56:
- This number is a decimal which can be expressed as a fraction: [tex]\( 0.56 = \frac{56}{100} \)[/tex].
- Simplifying, [tex]\( 0.56 = \frac{14}{25} \)[/tex].
- Since it can be written as the quotient of two integers, it is a rational number.
- However, because it is not a whole number (it's not an integer), we describe it as: "This is a rational number, but not an integer."
3. 5:
- This number is a whole number.
- It directly falls into the category of integers.
- As an integer itself, we simply describe it as: "This is an integer."
4. [tex]\( \sqrt{11} \)[/tex]:
- The square root of 11 is not a perfect square, meaning it cannot be expressed as the quotient of two integers.
- Numbers like these, which cannot be written as simple fractions, are called irrational numbers.
- We describe it as: "This is an irrational number."
5. [tex]\( -3 \frac{1}{2} \)[/tex]:
- This number is also a mixed number, which can be converted to an improper fraction: [tex]\( -3 \frac{1}{2} = -\frac{7}{2} \)[/tex].
- Since [tex]\( -\frac{7}{2} \)[/tex] can be expressed as a quotient of two integers, it is a rational number.
- However, it is not a whole number (not an integer), so we describe it as: "This is a rational number, but not an integer."
### Matching to Descriptions
- [tex]\( 3 \frac{1}{2} \)[/tex]: This is a rational number, but not an integer.
- 0.56: This is a rational number, but not an integer.
- 5: This is an integer.
- [tex]\( \sqrt{11} \)[/tex]: This is an irrational number.
- [tex]\( -3 \frac{1}{2} \)[/tex]: This is a rational number, but not an integer.
Let’s summarize our answers:
1. [tex]\( 3 \frac{1}{2} \)[/tex] — This is a rational number, but not an integer.
2. 0.56 — This is a rational number, but not an integer.
3. 5 — This is an integer.
4. [tex]\( \sqrt{11} \)[/tex] — This is an irrational number.
5. [tex]\( -3 \frac{1}{2} \)[/tex] — This is a rational number, but not an integer.
These descriptions correctly match each number with its respective classification.
