To determine which of the given numbers are integers, we need to understand the definition of an integer. An integer is a whole number that can be positive, negative, or zero. Fractions, decimals, and non-whole roots are not considered integers.
Let's classify each of the given numbers:
1. [tex]\( 1 \)[/tex]
2. [tex]\( \frac{18}{73} \)[/tex]
3. [tex]\( \frac{62}{57} \)[/tex]
4. [tex]\( -61 \)[/tex]
5. [tex]\( \sqrt{92} \)[/tex]
### Checking each number individually:
1. Number 1:
- It is a whole number.
- Conclusion: 1 is an integer.
2. Number [tex]\( \frac{18}{73} \)[/tex]:
- This is a fraction where 18 and 73 are both positive integers.
- Since 18 is not a multiple of 73, the fraction cannot be simplified to a whole number.
- Conclusion: [tex]\( \frac{18}{73} \)[/tex] is not an integer.
3. Number [tex]\( \frac{62}{57} \)[/tex]:
- This is a fraction where 62 and 57 are both positive integers.
- Since 62 is not a multiple of 57, this fraction does not simplify to a whole number.
- Conclusion: [tex]\( \frac{62}{57} \)[/tex] is not an integer.
4. Number [tex]\( -61 \)[/tex]:
- It is a whole number, though it's negative.
- Conclusion: [tex]\( -61 \)[/tex] is an integer.
5. Number [tex]\( \sqrt{92} \)[/tex]:
- The square root of 92 is not a whole number as it doesn’t yield an integer value.
- Conclusion: [tex]\( \sqrt{92} \)[/tex] is not an integer.
### Final Classification:
Based on the given numbers:
- [tex]\(1\)[/tex]
- [tex]\( \frac{18}{73} \)[/tex]
- [tex]\( \frac{62}{57} \)[/tex]
- [tex]\( -61 \)[/tex]
- [tex]\( \sqrt{92} \)[/tex]
The integers among these are:
- [tex]\( 1 \)[/tex]
- [tex]\( -61 \)[/tex]
So, the integers are [tex]\( 1 \)[/tex] and [tex]\( -61 \)[/tex].
