Three rational numbers between 3/5 and 7/8 can be found by finding the average of these two numbers and then finding the average of each of the resulting numbers with the original numbers.

Here are the steps to find these rational numbers:

1. Finding the average of 3/5 and 7/8:
- To find the average, add the two numbers and divide the sum by 2.
- (3/5 + 7/8) / 2 = (24/40 + 35/40) / 2 = 59/80

2. Finding the average of 3/5 and 59/80:
- Add the two numbers and divide the sum by 2.
- (3/5 + 59/80) / 2 = (48/80 + 59/80) / 2 = 107/160

3. Finding the average of 59/80 and 7/8:
- Add the two numbers and divide the sum by 2.
- (59/80 + 7/8) / 2 = (59/80 + 70/80) / 2 = 129/160

So, the three rational numbers between 3/5 and 7/8 are 59/80, 107/160, and 129/160.

Now let's represent these rational numbers on a number line:

- Start by drawing a number line with appropriate intervals.
- Mark the endpoints 3/5 and 7/8 on the number line.
- Divide the space between these two points into four equal intervals.
- Mark the three rational numbers 59/80, 107/160, and 129/160 on the number line within these intervals.

Visually, it would look like this:

0 1/2 1 3/5 59/80 107/160 129/160 7/8 1

By following these steps, we have found three rational numbers between 3/5 and 7/8 and represented them on a number line.

50 by 80 ,107 by 160 and 129 by 160