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27 votes
27 votes
Find a rational number between 5/7 and 3/4​

User Egorlitvinenko
by
2.7k points

1 Answer

24 votes
24 votes

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.

User Daphney
by
3.1k points