Answer :
The fraction that lies exactly halfway between 4/5 and 14/15 is 13/15 when expressed in its simplest form. By finding the average of the two fractions, we determine the fraction that represents the midpoint.
To find the fraction that is halfway between 4/5 and 14/15, we need to calculate their average.
The average of two fractions can be found by adding the two fractions and then dividing the sum by 2.
Adding 4/5 and 14/15:
(4/5) + (14/15)
To add these fractions, we need to find a common denominator. In this case, the least common multiple of 5 and 15 is 15.
(4/5) + (14/15) = (12/15) + (14/15) = (26/15)
Now, we divide the sum by 2:
(26/15) ÷ 2 = (26/15) × (1/2) = (26/30)
To simplify the fraction, we divide the numerator and denominator by their greatest common divisor, which is 2:
(26/30) ÷ 2/2 = (13/15)
Therefore, the fraction that is halfway between 4/5 and 14/15 is 13/15 in its simplest form.
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