Arrange the following fractions in ascending order and descending order.
(i) `7/9, 13/15,23/27, 20/21`
(ii) `4/5 , 11/20, 11/15, 22/25`

Explanation

To arrange the given fractions in ascending and descending order, we will follow these steps:

### Step 1: Find the LCM of the Denominators
For both sets of fractions, we need to find the Least Common Multiple (LCM) of the denominators.

**(i)** For the fractions `7/9, 13/15, 23/27, 20/21`:
- Denominators: 9, 15, 27, 21
- Prime factorization:
- 9 = 3²
- 15 = 3 × 5
- 27 = 3³
- 21 = 3 × 7
- LCM = 3³ × 5 × 7 = 945

**(ii)** For the fractions `4/5, 11/20, 11/15, 22/25`:
- Denominators: 5, 20, 15, 25
- Prime factorization:
- 5 = 5
- 20 = 2² × 5
- 15 = 3 × 5
- 25 = 5²
- LCM = 2² × 3 × 5² = 300

### Step 2: Convert Each Fraction to Have the Same Denominator
Now we will convert each fraction to have the common denominator found in Step 1.

**(i)** Convert to 945:
1. `7/9 = (7 × 105)/(9 × 105) = 735/945`
2. `13/15 = (13 × 63)/(15 × 63) = 819/945`
3. `23/27 = (23 × 35)/(27 × 35) = 805/945`
4. `20/21 = (20 × 45)/(21 × 45) = 900/945`

**(ii)** Convert to 300:
1. `4/5 = (4 × 60)/(5 × 60) = 240/300`
2. `11/20 = (11 × 15)/(20 × 15) = 165/300`
3. `11/15 = (11 × 20)/(15 × 20) = 220/300`
4. `22/25 = (22 × 12)/(25 × 12) = 264/300`

### Step 3: Arrange the Fractions in Ascending Order
Now we will arrange the converted fractions in ascending order.

**(i)** Ascending order:
- `735/945` (7/9)
- `805/945` (23/27)
- `819/945` (13/15)
- `900/945` (20/21)

So, in ascending order: **7/9, 23/27, 13/15, 20/21**

**(ii)** Ascending order:
- `165/300` (11/20)
- `220/300` (11/15)
- `240/300` (4/5)
- `264/300` (22/25)

So, in ascending order: **11/20, 11/15, 4/5, 22/25**

### Step 4: Arrange the Fractions in Descending Order
Now we will arrange the fractions in descending order.

**(i)** Descending order:
- `900/945` (20/21)
- `819/945` (13/15)
- `805/945` (23/27)
- `735/945` (7/9)

So, in descending order: **20/21, 13/15, 23/27, 7/9**

**(ii)** Descending order:
- `264/300` (22/25)
- `240/300` (4/5)
- `220/300` (11/15)
- `165/300` (11/20)

So, in descending order: **22/25, 4/5, 11/15, 11/20**

### Summary of Results
- **(i)** Ascending: 7/9, 23/27, 13/15, 20/21
- **(i)** Descending: 20/21, 13/15, 23/27, 7/9
- **(ii)** Ascending: 11/20, 11/15, 4/5, 22/25
- **(ii)** Descending: 22/25, 4/5, 11/15, 11/20