Verified answer

Step-by-step explanation:

To find six, sixty, and six hundred rational numbers between -5/8 and 3/8, we can use the concept of linear interpolation.

First, let's find the difference between the two given rational numbers: 3/8 - (-5/8) = 8/8 = 1.

To find six rational numbers, we divide the difference by 7 (6 + 1) and add it successively to the starting point (-5/8).

For example:

-5/8 + (1/7) = -37/56

-5/8 + (2/7) = -29/56

-5/8 + (3/7) = -21/56

-5/8 + (4/7) = -13/56

-5/8 + (5/7) = -5/56

-5/8 + (6/7) = 3/56

To find sixty and six hundred rational numbers, we follow the same process, dividing the difference by 61 and 601 respectively.

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