Find 3 rational numbers between `(3)/(4) and (1)/(2).`

Answer

To find three rational numbers between \( \frac{3}{4} \) and \( \frac{1}{2} \), we can follow these steps:

### Step 1: Write the given fractions
We have:
- \( \frac{3}{4} \)
- \( \frac{1}{2} \)

### Step 2: Make the denominators the same
To compare these fractions easily, we need to convert them to have a common denominator. The denominator of \( \frac{3}{4} \) is 4, and we can convert \( \frac{1}{2} \) to a fraction with a denominator of 4.

To do this, we multiply both the numerator and denominator of \( \frac{1}{2} \) by 2:
\[ \frac{1}{2} = \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \]

Now we have:
- \( \frac{3}{4} \)
- \( \frac{2}{4} \)

### Step 3: Identify the range
Now we can see that \( \frac{2}{4} \) is less than \( \frac{3}{4} \). We need to find rational numbers between \( \frac{2}{4} \) and \( \frac{3}{4} \).

### Step 4: Multiply to find more rational numbers
To find more rational numbers, we can multiply both fractions by a number to increase the numerators while keeping the denominators the same. Let's multiply both fractions by 10:
- For \( \frac{2}{4} \):
\[ \frac{2 \times 10}{4 \times 10} = \frac{20}{40} \]
- For \( \frac{3}{4} \):
\[ \frac{3 \times 10}{4 \times 10} = \frac{30}{40} \]

Now we have:
- \( \frac{20}{40} \)
- \( \frac{30}{40} \)

### Step 5: Find three rational numbers between
Now, we can easily find three rational numbers between \( \frac{20}{40} \) and \( \frac{30}{40} \). We can select:
- \( \frac{21}{40} \)
- \( \frac{22}{40} \)
- \( \frac{23}{40} \)

### Conclusion
Thus, three rational numbers between \( \frac{3}{4} \) and \( \frac{1}{2} \) are:
- \( \frac{21}{40} \)
- \( \frac{22}{40} \)
- \( \frac{23}{40} \)

---