Answer:
41/56
Explanation:
The LCD is 7×4 = 28. With that denominator, the two fractions are ...
5/7 = 20/28
3/4 = 21/28
The average of the two values will be ...
(5/7 +3/4)//2 = (20 +21)/28/2 = 41/56
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Additional comment
5/7 ≈ 0.714285... (6-digit repeat)
3/4 = 0.75
Then numbers like 0.72 = 18/25, or 0.73 = 73/100, or 0.74 = 37/50 will all be between the given fractions.
Of course, any terminating or repeating decimal in that range will also be a rational number. For example, 0.727272727272... = 8/11 will be a rational number in the required range.