Arrange the fractions `2/(7), 5/(7), 6/(14), 12/(21)` in ascending order.

Answer

To arrange the fractions \( \frac{2}{7}, \frac{5}{7}, \frac{6}{14}, \frac{12}{21} \) in ascending order, we will follow these steps:

### Step 1: Write down the fractions
We start by listing all the fractions we need to arrange:
- \( \frac{2}{7} \)
- \( \frac{5}{7} \)
- \( \frac{6}{14} \)
- \( \frac{12}{21} \)

### Step 2: Convert fractions to have a common denominator
To compare the fractions easily, we need to convert them to have a common denominator. The denominators we have are 7, 14, and 21. The least common multiple (LCM) of these denominators is 21.

### Step 3: Convert each fraction
Now, we will convert each fraction to have a denominator of 21:
- \( \frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{6}{21} \)
- \( \frac{5}{7} = \frac{5 \times 3}{7 \times 3} = \frac{15}{21} \)
- \( \frac{6}{14} = \frac{6 \times 1.5}{14 \times 1.5} = \frac{9}{21} \)
- \( \frac{12}{21} \) remains \( \frac{12}{21} \)

### Step 4: List the converted fractions
Now we have:
- \( \frac{6}{21} \)
- \( \frac{15}{21} \)
- \( \frac{9}{21} \)
- \( \frac{12}{21} \)

### Step 5: Arrange the fractions based on their numerators
Now we can compare the numerators since the denominators are the same:
- \( 6 < 9 < 12 < 15 \)

### Step 6: Write the fractions in ascending order
Based on the comparison of numerators, we can write the fractions in ascending order:
- \( \frac{6}{21} \) (which is \( \frac{6}{14} \))
- \( \frac{9}{21} \) (which is \( \frac{6}{14} \))
- \( \frac{12}{21} \) (which is \( \frac{12}{21} \))
- \( \frac{15}{21} \) (which is \( \frac{5}{7} \))

Thus, the ascending order of the original fractions is:
- \( \frac{2}{7}, \frac{6}{14}, \frac{12}{21}, \frac{5}{7} \)

### Final Answer
The fractions in ascending order are:
- \( \frac{2}{7}, \frac{6}{14}, \frac{12}{21}, \frac{5}{7} \)

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