Minuend
ArithmeticThe 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. It is the number you subtract from.
Example
In $15 - 6 = 9$, the minuend is $15$. You start with $15$ and take away $6$.
Key Insight
The minuend is always the bigger number when the answer is positive. It is the "whole" before something is taken away.
Definition
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: the minuend and subtrahend cannot be swapped without changing the result.
Example
In $47 - 29 = 18$, minuend $= 47$, subtrahend $= 29$, difference $= 18$. Swapping: $29 - 47 = -18$, a completely different result.
Key Insight
In algebra, we often write $a - b$ as $a + (-b)$, making the "minuend" just the first addend and the "subtrahend" the additive inverse of the second. This unified view makes the role of the minuend less special.
Definition
In formal algebra, the minuend is the element from which the subtrahend is subtracted, defined via $a - b = a + (-b)$ in any abelian group. The terminology minuend/subtrahend is largely pedagogical; at the abstract level only the distinction between $a$ and $(-b)$ matters, and both are simply addends in the sum $a + (-b)$.
Example
In polynomial subtraction: $(3x^2 + 5x + 1) - (x^2 + 2x + 4) = 2x^2 + 3x - 3$. The first polynomial is the minuend. Each term of the subtrahend is negated and added to the corresponding term of the minuend.
Key Insight
The terms minuend and subtrahend clarify the non-commutativity of subtraction, which is pedagogically important. Once students understand that subtraction is defined via additive inverses, the asymmetric roles dissolve into the symmetric structure of addition.