Subtrahend
The subtrahend is the number being subtracted from the minuend in a subtraction problem.
Formula
\text{minuend} - \text{subtrahend} = \text{difference}
Definition
The subtrahend is the number being taken away in a subtraction problem. In $a - b = c$, $b$ is the subtrahend; increasing it decreases the difference while the minuend stays fixed, and it can be any real number, including negative values. Formally, the subtrahend $b$ in $a - b$ is replaced by its additive inverse, $a - b = a + (-b)$: in any abelian group, this construction identifies the "subtrahend role" as that of the element whose inverse is being added, clarifying that subtraction is not a primitive operation but addition of the inverse.
Example
In $20 - 8 = 12$, the subtrahend is $8$: it is the amount being removed from $20$. Subtracting a negative subtrahend, $10 - (-3) = 13$, is the same as adding $3$, the algebraic reason "two negatives make a positive" in subtraction: $a - (-b) = a + b$. In modular arithmetic, $2 - 5 \bmod 7 = 2 + (-5) \bmod 7 = 2 + 2 \bmod 7 = 4$, since $-5 \equiv 2 \pmod 7$, so the subtrahend $5$ is replaced by its additive inverse $2$ in $\mathbb{Z}/7\mathbb{Z}$.
Key Insight
The subtrahend is what you "subtract," the minuend is what you start with, and the difference is what remains. Recognizing the subtrahend as an additive inverse unifies subtraction with addition across all algebraic structures: groups, rings, fields, and vector spaces all handle subtraction this way.