Introduction:
Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. In this case, we are asked to find five rational numbers between -3 and -2. To accomplish this, we can use the concept of equivalent fractions and find rational numbers with different denominators between -3 and -2.

Step 1: Finding the common denominator:
To find rational numbers between -3 and -2, we need to find a common denominator that will allow us to divide the given range into equal intervals. In this case, we can choose the denominator as 10, as it will give us a good range to work with.

Step 2: Finding the equivalent fractions:
Once we have the common denominator, we can find the equivalent fractions for -3 and -2. To do this, we multiply both the numerator and denominator of the fraction by the same number.

For -3:
-3 = (-3 * 10) / (1 * 10) = -30/10

For -2:
-2 = (-2 * 10) / (1 * 10) = -20/10

Step 3: Finding the rational numbers:
Now that we have the equivalent fractions for -3 and -2, we can find five rational numbers between them by incrementing the numerator by 2 and keeping the denominator constant.

-3/10, -5/10, -7/10, -9/10, -11/10

Explanation:
We have found five rational numbers between -3 and -2 by incrementing the numerator by 2 and keeping the denominator constant at 10. This allows us to divide the range into equal intervals and find rational numbers within that range.

Summary:
In summary, we have found five rational numbers between -3 and -2 by using the concept of equivalent fractions. By choosing a common denominator of 10, we were able to find the rational numbers -3/10, -5/10, -7/10, -9/10, and -11/10. These numbers satisfy the condition of being rational, as they can be expressed as fractions with integer numerators and denominators.

There can be many possible numbers you can find between two integers