Final answer:
The initial question had a typo by asking for numbers between an identical fraction. To find rational numbers between different fractions, one can use equivalent fractions with common denominators to identify the numbers between them. For example, between 3/5 and 4/5, we can find 7/10, 13/20, and 15/20.
Step-by-step explanation:
The question asks for finding rational numbers between 3/5 and 3/5. It seems there has been a typo because 3/5 is identical to itself, and there are no numbers between two identical numbers. However, if we consider the intention was to find rational numbers between two different rational numbers, then let's take an example between 3/5 and 4/5.
To find rational numbers between two fractions, one straightforward method is to look for common denominators or to increment the numerator of the lower fraction or decrement the numerator of the higher fraction.
Example:
- 3/5 is equivalent to 6/10 (by multiplying both numerator and denominator by 2).
- Similarly, 4/5 is equivalent to 8/10 (also by multiplying by 2).
Now, we can easily see that 7/10 is between 6/10 and 8/10. Two more examples within this range could be 6.5/10 and 7.5/10, which in reduced form are 13/20 and 15/20 respectively. Note that we can generate as many rational numbers as needed between any two rational numbers by following similar steps, as rational numbers are dense within the real numbers.