To arrange the given fractions in ascending order, we will follow these steps:
### Part (i): Arrange `5/8` and `7/12`
1. **Find the LCM of the Denominators**:
- The denominators are 8 and 12.
- The LCM of 8 and 12 is 24.
2. **Convert the Fractions to Like Fractions**:
- For `5/8`:
- Multiply both the numerator and the denominator by 3 (since \( 24 \div 8 = 3 \)).
- \( 5 \times 3 = 15 \) and \( 8 \times 3 = 24 \).
- So, \( 5/8 = 15/24 \).
- For `7/12`:
- Multiply both the numerator and the denominator by 2 (since \( 24 \div 12 = 2 \)).
- \( 7 \times 2 = 14 \) and \( 12 \times 2 = 24 \).
- So, \( 7/12 = 14/24 \).
3. **Compare the Like Fractions**:
- Now we compare \( 15/24 \) and \( 14/24 \).
- Since \( 14 < 15 \), we have \( 14/24 < 15/24 \).
4. **Write in Ascending Order**:
- Therefore, \( 7/12 < 5/8 \).
- The ascending order is: \( 7/12, 5/8 \).
### Part (ii): Arrange `3/4`, `5/12`, and `9/16`
1. **Find the LCM of the Denominators**:
- The denominators are 4, 12, and 16.
- The LCM of 4, 12, and 16 is 48.
2. **Convert the Fractions to Like Fractions**:
- For `3/4`:
- Multiply both the numerator and the denominator by 12 (since \( 48 \div 4 = 12 \)).
- \( 3 \times 12 = 36 \) and \( 4 \times 12 = 48 \).
- So, \( 3/4 = 36/48 \).
- For `5/12`:
- Multiply both the numerator and the denominator by 4 (since \( 48 \div 12 = 4 \)).
- \( 5 \times 4 = 20 \) and \( 12 \times 4 = 48 \).
- So, \( 5/12 = 20/48 \).
- For `9/16`:
- Multiply both the numerator and the denominator by 3 (since \( 48 \div 16 = 3 \)).
- \( 9 \times 3 = 27 \) and \( 16 \times 3 = 48 \).
- So, \( 9/16 = 27/48 \).
3. **Compare the Like Fractions**:
- Now we compare \( 36/48 \), \( 20/48 \), and \( 27/48 \).
- The smallest numerator is 20, so \( 20/48 < 27/48 < 36/48 \).
4. **Write in Ascending Order**:
- Therefore, \( 5/12 < 9/16 < 3/4 \).
- The ascending order is: \( 5/12, 9/16, 3/4 \).
### Final Answer:
- For part (i): \( 7/12, 5/8 \)
- For part (ii): \( 5/12, 9/16, 3/4 \)
