Find five rational numbers between `3//5` and `4//5` .

Answer

To find five rational numbers between \( \frac{3}{5} \) and \( \frac{4}{5} \), we can follow these steps:

### Step 1: Identify the given rational numbers
The two rational numbers we have are:
- \( \frac{3}{5} \)
- \( \frac{4}{5} \)

### Step 2: Find a common denominator
Since both fractions have the same denominator (5), we can find numbers in between by manipulating the numerators. To make it easier, we can multiply both the numerator and denominator of each fraction by 10 to work with whole numbers:
- \( \frac{3 \times 10}{5 \times 10} = \frac{30}{50} \)
- \( \frac{4 \times 10}{5 \times 10} = \frac{40}{50} \)

### Step 3: List the numerators between 30 and 40
Now, we need to find rational numbers between \( \frac{30}{50} \) and \( \frac{40}{50} \). The numerators between 30 and 40 are 31, 32, 33, 34, 35, 36, 37, 38, and 39.

### Step 4: Select five rational numbers
We can choose any five of these numerators to form our rational numbers. Let's select:
- \( \frac{31}{50} \)
- \( \frac{32}{50} \)
- \( \frac{33}{50} \)
- \( \frac{34}{50} \)
- \( \frac{35}{50} \)

### Step 5: Write the final answer
The five rational numbers between \( \frac{3}{5} \) and \( \frac{4}{5} \) are:
- \( \frac{31}{50} \)
- \( \frac{32}{50} \)
- \( \frac{33}{50} \)
- \( \frac{34}{50} \)
- \( \frac{35}{50} \)