The ascending arrangement of `2/3, 6/7, 13/21` is

Options

A. `6/7, 2/3, 13/21`
B. `13/21, 2/3, 6/7`
C. `6/7, 13/21, 2/3`
D. `2/3, 6/7, 13/21`

Answer

To arrange the fractions \( \frac{2}{3}, \frac{6}{7}, \frac{13}{21} \) in ascending order, we will follow these steps:

### Step 1: Find a common denominator
To compare the fractions, we need to convert them to have a common denominator. The denominators are 3, 7, and 21. The least common multiple (LCM) of these numbers is 21.

### Step 2: Convert each fraction to have the common denominator of 21
- For \( \frac{2}{3} \):
\[ \frac{2}{3} = \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \]

- For \( \frac{6}{7} \):
\[ \frac{6}{7} = \frac{6 \times 3}{7 \times 3} = \frac{18}{21} \]

- For \( \frac{13}{21} \):
\[ \frac{13}{21} = \frac{13}{21} \quad (\text{already has the common denominator}) \]

### Step 3: Compare the numerators
Now we have the fractions:
- \( \frac{14}{21} \)
- \( \frac{18}{21} \)
- \( \frac{13}{21} \)

We can compare the numerators:
- 14
- 18
- 13

### Step 4: Arrange the fractions in ascending order
From the numerators, we can see:
- The smallest is 13, which corresponds to \( \frac{13}{21} \).
- The next is 14, which corresponds to \( \frac{14}{21} \).
- The largest is 18, which corresponds to \( \frac{18}{21} \).

Thus, the fractions in ascending order are:
\[ \frac{13}{21}, \frac{2}{3}, \frac{6}{7} \]

### Final Answer
The ascending arrangement of \( \frac{2}{3}, \frac{6}{7}, \frac{13}{21} \) is:
\[ \frac{13}{21}, \frac{2}{3}, \frac{6}{7} \]

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