Find 9 rational numbers between `(1)/(2)and(3)/(5)`.

Explanation

To find 9 rational numbers between \( \frac{1}{2} \) and \( \frac{3}{5} \), we can follow these steps:

### Step 1: Convert the fractions to have a common denominator
We start with the two fractions:
- \( \frac{1}{2} \)
- \( \frac{3}{5} \)

To find a common denominator, we can multiply the first fraction by \( \frac{5}{5} \) and the second fraction by \( \frac{2}{2} \).

Calculating:
\[ \frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10} \]
\[ \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} \]

### Step 2: Identify the range between the two fractions
Now we have:
- \( \frac{5}{10} \) and \( \frac{6}{10} \)

We need to find rational numbers between \( \frac{5}{10} \) and \( \frac{6}{10} \).

### Step 3: Increase the denominator to find more rational numbers
To find more rational numbers, we can multiply both fractions by \( 10 \) to get a larger denominator:
\[ \frac{5}{10} = \frac{5 \times 10}{10 \times 10} = \frac{50}{100} \]
\[ \frac{6}{10} = \frac{6 \times 10}{10 \times 10} = \frac{60}{100} \]

### Step 4: List the rational numbers between \( \frac{50}{100} \) and \( \frac{60}{100} \)
Now we can find rational numbers between \( \frac{50}{100} \) and \( \frac{60}{100} \). The rational numbers can be:
- \( \frac{51}{100} \)
- \( \frac{52}{100} \)
- \( \frac{53}{100} \)
- \( \frac{54}{100} \)
- \( \frac{55}{100} \)
- \( \frac{56}{100} \)
- \( \frac{57}{100} \)
- \( \frac{58}{100} \)
- \( \frac{59}{100} \)

### Final Answer:
The 9 rational numbers between \( \frac{1}{2} \) and \( \frac{3}{5} \) are:
- \( \frac{51}{100}, \frac{52}{100}, \frac{53}{100}, \frac{54}{100}, \frac{55}{100}, \frac{56}{100}, \frac{57}{100}, \frac{58}{100}, \frac{59}{100} \)