Write all the proper fractions whose numerator and denominator are prime numbers between 65 and 80.

Answer

To solve the problem of writing all the proper fractions whose numerator and denominator are prime numbers between 65 and 80, we can follow these steps:

### Step 1: Identify the prime numbers between 65 and 80.
- Prime numbers are numbers that have only two factors: 1 and the number itself.
- The prime numbers between 65 and 80 are: **67, 71, 73, and 79**.

### Step 2: Understand what a proper fraction is.
- A proper fraction is a fraction where the numerator (the top number) is less than the denominator (the bottom number).

### Step 3: Create proper fractions using the identified prime numbers.
- We will use each prime number as a numerator and pair it with the larger prime numbers as denominators.

1. **Using 67 as the numerator:**
- 67/71
- 67/73
- 67/79

2. **Using 71 as the numerator:**
- 71/73
- 71/79

3. **Using 73 as the numerator:**
- 73/79

4. **Using 79 as the numerator:**
- 79 cannot be used as a numerator since it is the largest prime number.

### Step 4: List all the proper fractions.
- The proper fractions formed from the prime numbers between 65 and 80 are:
- 67/71
- 67/73
- 67/79
- 71/73
- 71/79
- 73/79

### Final Answer:
The proper fractions whose numerator and denominator are prime numbers between 65 and 80 are:
- 67/71
- 67/73
- 67/79
- 71/73
- 71/79
- 73/79

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