Arrange the following fraction in ascending order:
`(1)/(2), (3)/(4), (5)/(6) and (7)/(8)`

Answer

To arrange the fractions \( \frac{1}{2}, \frac{3}{4}, \frac{5}{6}, \frac{7}{8} \) in ascending order, we can follow these steps:

### Step 1: Identify the denominators
The denominators of the given fractions are 2, 4, 6, and 8.

### Step 2: Find the Least Common Multiple (LCM)
To compare the fractions easily, we need a common denominator. We find the LCM of the denominators 2, 4, 6, and 8.

- The multiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24...
- The multiples of 4 are: 4, 8, 12, 16, 20, 24...
- The multiples of 6 are: 6, 12, 18, 24...
- The multiples of 8 are: 8, 16, 24...

The smallest common multiple is 24. Thus, the LCM of 2, 4, 6, and 8 is 24.

### Step 3: Convert each fraction to have the common denominator
Now, we will convert each fraction to have the denominator of 24.

1. For \( \frac{1}{2} \):
\[ \frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24} \]

2. For \( \frac{3}{4} \):
\[ \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} \]

3. For \( \frac{5}{6} \):
\[ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \]

4. For \( \frac{7}{8} \):
\[ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \]

### Step 4: Compare the converted fractions
Now we have the fractions:
- \( \frac{12}{24} \)
- \( \frac{18}{24} \)
- \( \frac{20}{24} \)
- \( \frac{21}{24} \)

### Step 5: Arrange in ascending order
From smallest to largest, we have:
1. \( \frac{12}{24} \) (which is \( \frac{1}{2} \))
2. \( \frac{18}{24} \) (which is \( \frac{3}{4} \))
3. \( \frac{20}{24} \) (which is \( \frac{5}{6} \))
4. \( \frac{21}{24} \) (which is \( \frac{7}{8} \))

Thus, the fractions in ascending order are:
\[ \frac{1}{2}, \frac{3}{4}, \frac{5}{6}, \frac{7}{8} \]