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An easy method for finding a fraction between two fractions would be to take the average of two fractions. You find the average by adding the two fractions together and then dividing the final sum by 2.
The two fractions are 1/6 and 3/8
That their sum is always equal to the denominator.
30/70
The sum of two fractions will only be a whole number if the fractions have a common denominator. When the denominators are different, the sum will be a fraction with a different denominator, making it impossible to be a whole number. Thus, estimating the sum of two fractions will generally result in a fraction, not a whole number.