Find 3 rational numbers between `-3 and -4.`

Options

A. `(-13)/(4), (-14)/(4), (-15)/(4)`
B. `(-13)/(3), (-14)/(3), (-15)/(3)`
C. `(-10)/(2), (-11)/(2) , (-12)/(2)`
D. `(10)/(2), (11)/(2), (12)/(2)`

Answer

To find 3 rational numbers between -3 and -4, we can follow these steps:

### Step 1: Express -3 and -4 with a common denominator
We can convert -3 and -4 into fractions with the same denominator. Let's choose 4 as the common denominator.

- For -3:
\[ -3 = \frac{-3 \times 4}{4} = \frac{-12}{4} \]

- For -4:
\[ -4 = \frac{-4 \times 4}{4} = \frac{-16}{4} \]

### Step 2: Identify the range between the two fractions
Now we have:
\[ -12/4 \quad \text{and} \quad -16/4 \]
We need to find rational numbers between \(-12/4\) and \(-16/4\).

### Step 3: Find rational numbers
To find rational numbers between \(-12/4\) and \(-16/4\), we can take the average of these two fractions and find numbers in between.

1. The first rational number can be:
\[ \frac{-13}{4} \]

2. The second rational number can be:
\[ \frac{-14}{4} \]

3. The third rational number can be:
\[ \frac{-15}{4} \]

### Conclusion
Thus, the three rational numbers between -3 and -4 are:
\[ \frac{-13}{4}, \frac{-14}{4}, \frac{-15}{4} \]