Mediant (mathematics)

Mediant (mathematics) Media

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  Determining the mediant of two rational numbers graphically. The slopes of the blue and red segments are two rational numbers; the slope of the green segment is their mediant.

In mathematics, the mediant of two fractions

[math]\displaystyle{ \frac{a}{c} \text{ and } \frac{b}{d} }[/math]

is

[math]\displaystyle{ \frac{a+b}{c+d} }[/math].

It is commonly referred to as the freshman sum, due to it being a common mistake when people learn about the addition of fractions. The operation is between two fractions, therefore the way these fractions are represented influence the mediant. For example, the mediant of 1/1 and 1/2 is 2/3, but the mediant of 2/2 and 1/2 is 3/4, even though the sum of both is 3/2.