To determine which of the two rational numbers is greater in each of the given pairs, we will analyze each pair step by step.
### Step-by-Step Solution:
**(i)** Compare `3/-7` and `1/7`:
- `3/-7` is negative, while `1/7` is positive.
- Therefore, `1/7` is greater than `3/-7`.
**(ii)** Compare `11/(-18)` and `-5/18`:
- Both numbers are negative.
- Convert `11/(-18)` to `-11/18`.
- Since `-11 < -5`, `-5/18` is greater than `-11/18`.
**(iii)** Compare `7/10` and `-9/10`:
- `7/10` is positive, while `-9/10` is negative.
- Thus, `7/10` is greater than `-9/10`.
**(iv)** Compare `0` and `-3/4`:
- `0` is greater than any negative number.
- Therefore, `0` is greater than `-3/4`.
**(v)** Compare `1/12` and `0`:
- `1/12` is positive, while `0` is neither positive nor negative.
- Thus, `1/12` is greater than `0`.
**(vi)** Compare `18/(-19)` and `0`:
- `18/(-19)` is negative.
- Hence, `0` is greater than `18/(-19)`.
**(vii)** Compare `7/8` and `11/16`:
- Convert `7/8` to have a common denominator with `11/16`:
- `7/8 = 14/16`.
- Now compare `14/16` and `11/16`.
- Since `14/16 > 11/16`, `7/8` is greater than `11/16`.
**(viii)** Compare `11/(-12)` and `-10/11`:
- Convert `11/(-12)` to `-11/12`.
- Since both are negative, we compare `-11/12` and `-10/11`.
- Convert `-10/11` to have a common denominator:
- `-10/11 = -120/132` and `-11/12 = -121/132`.
- Since `-120/132 > -121/132`, `-10/11` is greater than `-11/12`.
**(ix)** Compare `-13/5` and `-4`:
- Convert `-4` to have a common denominator:
- `-4 = -20/5`.
- Now compare `-13/5` and `-20/5`.
- Since `-13/5 > -20/5`, `-13/5` is greater than `-4`.
**(x)** Compare `17/(-6)` and `-13/4`:
- Convert `17/(-6)` to `-17/6`.
- Since both are negative, we compare `-17/6` and `-13/4`.
- Convert `-13/4` to have a common denominator:
- `-13/4 = -78/24` and `-17/6 = -68/24`.
- Since `-68/24 > -78/24`, `-17/6` is greater than `-13/4`.
**(xi)** Compare `7/(-9)` and `-5/8`:
- Convert `7/(-9)` to `-7/9`.
- Since both are negative, we compare `-7/9` and `-5/8`.
- Convert `-5/8` to have a common denominator:
- `-5/8 = -45/72` and `-7/9 = -56/72`.
- Since `-45/72 > -56/72`, `-5/8` is greater than `-7/9`.
**(xii)** Compare `-3/(-8)` and `5/9`:
- `-3/(-8)` simplifies to `3/8`, which is positive.
- Since `3/8` is positive and `5/9` is also positive, we compare them.
- Convert `3/8` to have a common denominator:
- `3/8 = 27/72` and `5/9 = 40/72`.
- Since `27/72 < 40/72`, `5/9` is greater than `3/8`.
### Summary of Results:
1. `1/7` > `3/-7`
2. `-5/18` > `11/(-18)`
3. `7/10` > `-9/10`
4. `0` > `-3/4`
5. `1/12` > `0`
6. `0` > `18/(-19)`
7. `7/8` > `11/16`
8. `-10/11` > `11/(-12)`
9. `-13/5` > `-4`
10. `17/(-6)` > `-13/4`
11. `-5/8` > `7/(-9)`
12. `5/9` > `-3/(-8)`
