Which of the following is a rational number between 5 and (5)/(14)?(1 point)
The rational number between 5 and (5)/(14) is (6)/(14), which simplifies to (3)/(7).
To find a rational number between 5 and (5)/(14), we can convert both numbers to a common denominator.
First, let's convert 5 to a fraction with a denominator of 14:
5 = (5 * 14) / 14 = 70 / 14
Now we have the given numbers as fractions:
5 = 70 / 14
(5)/(14) = 5 / 14
To find a rational number between these fractions, we can take the average (mean) of the two fractions:
Average = (70 / 14 + 5 / 14) / 2
Calculating the average:
Average = (75 / 14) / 2
Average = (75 / 14) * (1 / 2)
Multiplying the fractions:
Average = (75 * 1) / (14 * 2)
Average = 75 / 28
Therefore, 75 / 28 is a rational number between 5 and (5)/(14).