Arrange the following fractions in descending order
(i)`3/4, 7/8, 7/12, 17/24`
(ii)`2/3, 3/5, 7/10, 8/15`

Answer

To arrange the given fractions in descending order, we will follow these steps for both parts of the question.

### Part (i): Arrange `3/4, 7/8, 7/12, 17/24` in descending order

**Step 1: Find the Least Common Multiple (LCM) of the denominators.**

The denominators are 4, 8, 12, and 24.

- The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...
- The multiples of 8 are: 8, 16, 24, ...
- The multiples of 12 are: 12, 24, ...
- The multiples of 24 are: 24, ...

The LCM of 4, 8, 12, and 24 is **24**.

**Step 2: Convert each fraction to have the same denominator (24).**

- For `3/4`:
\[ 3/4 = (3 \times 6)/(4 \times 6) = 18/24 \]

- For `7/8`:
\[ 7/8 = (7 \times 3)/(8 \times 3) = 21/24 \]

- For `7/12`:
\[ 7/12 = (7 \times 2)/(12 \times 2) = 14/24 \]

- For `17/24`:
\[ 17/24 = 17/24 \]

**Step 3: List the converted fractions.**

Now we have:
- `3/4 = 18/24`
- `7/8 = 21/24`
- `7/12 = 14/24`
- `17/24 = 17/24`

**Step 4: Arrange the fractions in descending order.**

Comparing the numerators:
- `21/24` (7/8)
- `18/24` (3/4)
- `17/24` (17/24)
- `14/24` (7/12)

So, the fractions in descending order are:
\[ \frac{7}{8}, \frac{3}{4}, \frac{17}{24}, \frac{7}{12} \]

### Part (ii): Arrange `2/3, 3/5, 7/10, 8/15` in descending order

**Step 1: Find the Least Common Multiple (LCM) of the denominators.**

The denominators are 3, 5, 10, and 15.

- The multiples of 3 are: 3, 6, 9, 12, 15, ...
- The multiples of 5 are: 5, 10, 15, ...
- The multiples of 10 are: 10, 20, ...
- The multiples of 15 are: 15, 30, ...

The LCM of 3, 5, 10, and 15 is **30**.

**Step 2: Convert each fraction to have the same denominator (30).**

- For `2/3`:
\[ 2/3 = (2 \times 10)/(3 \times 10) = 20/30 \]

- For `3/5`:
\[ 3/5 = (3 \times 6)/(5 \times 6) = 18/30 \]

- For `7/10`:
\[ 7/10 = (7 \times 3)/(10 \times 3) = 21/30 \]

- For `8/15`:
\[ 8/15 = (8 \times 2)/(15 \times 2) = 16/30 \]

**Step 3: List the converted fractions.**

Now we have:
- `2/3 = 20/30`
- `3/5 = 18/30`
- `7/10 = 21/30`
- `8/15 = 16/30`

**Step 4: Arrange the fractions in descending order.**

Comparing the numerators:
- `21/30` (7/10)
- `20/30` (2/3)
- `18/30` (3/5)
- `16/30` (8/15)

So, the fractions in descending order are:
\[ \frac{7}{10}, \frac{2}{3}, \frac{3}{5}, \frac{8}{15} \]

### Final Answers:
1. For part (i): `7/8, 3/4, 17/24, 7/12`
2. For part (ii): `7/10, 2/3, 3/5, 8/15`