A fraction is a value in two parts; each part, the numerator or denominator, is an integer. The numerator is the fraction's top number, while the denominator is its bottom number. Lower-order fractional math like addition and subtraction requires that the denominators of the involved fractions be the same value. When finding a fraction that comes between two others, you ignore normal fractional math in favor of a simpler method.
Obtain two fractions for example purposes. For this example, let the fractions be 1/2 and 3/4.
Sum the fractions' numerators. In this example, 1 + 3 = 4.
Sum the fraction's denominators. In this example, 2 + 4 = 6.
Write a new fraction with the numerators' sum as the new numerator and the denominators' sum as the new denominator. In this example, the new fraction is 4/6.
Simplify the fraction by eliminating the greatest common factor shared by the numerator and denominator. To do this, list the factors of each number and factor out the largest shared number.
In this case, the factors of 4 are 1, 2 and 4, and the factors of 6 are 1, 2, 3 and 6. Both numbers have 1 and 2 as factors, with 2 being the greatest factor.
Eliminating 2 from both the numerator and denominator results in (4 ÷ 2) / (6 ÷ 2), which becomes 2/3.
To check your answer, write the fractions with common denominators and compare the numerators. The example fractions of 1/2, 2/3 and 3/4 with common denominators become 6/12, 8/12 and 9/12. The numerator 8 is between 6 and 9, so the fraction you created – 8/12, or 2/3 when simplified – is between the two fractions you started with.
