Find four rational numbers between `(2)/(9)` and `(3)/(7)`.

Answer

To find four rational numbers between \(\frac{2}{9}\) and \(\frac{3}{7}\), we can follow these steps:

### Step 1: Find a common denominator
To compare \(\frac{2}{9}\) and \(\frac{3}{7}\), we need to find a common denominator. The least common multiple (LCM) of 9 and 7 is 63.

### Step 2: Convert the fractions
Now, we will convert both fractions to have the common denominator of 63.

1. Convert \(\frac{2}{9}\):
\[ \frac{2}{9} = \frac{2 \times 7}{9 \times 7} = \frac{14}{63} \]

2. Convert \(\frac{3}{7}\):
\[ \frac{3}{7} = \frac{3 \times 9}{7 \times 9} = \frac{27}{63} \]

### Step 3: Identify the range
Now we have:
\[ \frac{14}{63} < \frac{15}{63} < \frac{16}{63} < \frac{17}{63} < \frac{18}{63} < \frac{27}{63} \]
This shows that \(\frac{14}{63}\) (which is \(\frac{2}{9}\)) and \(\frac{27}{63}\) (which is \(\frac{3}{7}\)) are the bounds, and we can find rational numbers between them.

### Step 4: List the rational numbers
The four rational numbers between \(\frac{2}{9}\) and \(\frac{3}{7}\) are:
1. \(\frac{15}{63}\)
2. \(\frac{16}{63}\)
3. \(\frac{17}{63}\)
4. \(\frac{18}{63}\)

### Final Answer
The four rational numbers between \(\frac{2}{9}\) and \(\frac{3}{7}\) are \(\frac{15}{63}\), \(\frac{16}{63}\), \(\frac{17}{63}\), and \(\frac{18}{63}\).

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