Introduction:

To find five rational numbers between -1/3 and -2/3, we need to first understand what rational numbers are. Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero. They can be positive, negative, or zero.

Method:

To find rational numbers between -1/3 and -2/3, we can use the concept of averaging. The idea is to find the average of two given numbers and then repeat the process to find more numbers between them. This method ensures that the numbers we find are rational and lie between the given range.

Step 1: Find the average of -1/3 and -2/3:
-1/3 + (-2/3) = -3/3 = -1

Step 2: Find the average of -1/3 and -1:
-1/3 + (-1) = -4/3

Step 3: Find the average of -4/3 and -1:
-4/3 + (-1) = -7/3

Step 4: Find the average of -4/3 and -7/3:
-4/3 + (-7/3) = -11/3

Step 5: Find the average of -11/3 and -7/3:
-11/3 + (-7/3) = -18/3 = -6

Summary:

Using the method of averaging, we have found five rational numbers between -1/3 and -2/3. The numbers are as follows:

-1/3, -1, -4/3, -7/3, -11/3, -6

Explanation:

By finding the average of two numbers, we ensure that the resulting number is rational. In this case, we started with -1/3 and -2/3 and found the average to be -1. We then continued to find the average between each pair of numbers until we obtained five rational numbers between -1/3 and -2/3. The final numbers we found are -1/3, -1, -4/3, -7/3, -11/3, and -6. These numbers satisfy the given conditions and are rational.