Find five rational numbers between -3 and -2.

Answer

To find five rational numbers between -3 and -2, we can follow these steps:

### Step 1: Understand the Range
We need to find rational numbers that lie between -3 and -2.

### Step 2: Convert the Numbers to a Common Denominator
To find rational numbers, we can express -3 and -2 as fractions with a common denominator. We can choose a denominator of 6 for simplicity.

- Convert -3 to a fraction:
\[ -3 = \frac{-3}{1} = \frac{-18}{6} \]

- Convert -2 to a fraction:
\[ -2 = \frac{-2}{1} = \frac{-12}{6} \]

### Step 3: Identify the Range in Terms of the Common Denominator
Now we have:
- The lower limit: \(-18/6\)
- The upper limit: \(-12/6\)

### Step 4: Find Rational Numbers Between -18/6 and -12/6
We can find rational numbers by taking fractions with the same denominator (6) that lie between -18 and -12.

The integers between -18 and -12 are -17, -16, -15, -14, and -13. We can express these as:
- \(-17/6\)
- \(-16/6\)
- \(-15/6\)
- \(-14/6\)
- \(-13/6\)

### Step 5: List the Rational Numbers
Thus, the five rational numbers between -3 and -2 are:
1. \(-17/6\)
2. \(-16/6\)
3. \(-15/6\)
4. \(-14/6\)
5. \(-13/6\)

### Final Answer
The five rational numbers between -3 and -2 are:
- \(-17/6\)
- \(-16/6\)
- \(-15/6\)
- \(-14/6\)
- \(-13/6\)

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