Minuend
The minuend is the number from which another number (the subtrahend) is subtracted in a subtraction problem.
Formula
\text{minuend} - \text{subtrahend} = \text{difference}
Definition
The minuend is the starting number in a subtraction problem, the number you subtract from. In the expression $a - b = c$, $a$ is the minuend, $b$ is the subtrahend, and $c$ is the difference; unlike addition, subtraction is not commutative, so the minuend and subtrahend cannot be swapped without changing the result. In algebra, $a - b$ is often written as $a + (-b)$, and the minuend is just the first addend while the subtrahend is the additive inverse of the second: at the abstract level, only the distinction between $a$ and $(-b)$ matters, and both are simply addends in that sum.
Example
In $15 - 6 = 9$, the minuend is $15$: you start with $15$ and take away $6$. In $47 - 29 = 18$, minuend $= 47$, subtrahend $= 29$, difference $= 18$, while swapping gives $29 - 47 = -18$, a completely different result. In polynomial subtraction, $(3x^2 + 5x + 1) - (x^2 + 2x + 4) = 2x^2 + 3x - 3$: the first polynomial is the minuend, and each term of the subtrahend is negated and added to the corresponding term.
Key Insight
The minuend is always the bigger number when the answer is positive: it is the "whole" before something is taken away. The terms minuend and subtrahend clarify the non-commutativity of subtraction, which is pedagogically important, but once students understand that subtraction is defined via additive inverses, the asymmetric roles dissolve into the symmetric structure of addition.