What are the formal names of operands and results for basic operations?

Question

I'm trying to mentally summarize the names of the operands for basic operations. I've got this so far:

• Addition: Augend + Addend = Sum.
• Subtraction: Minuend - Subtrahend = Difference.
• Multiplication: Multiplicand × Multiplier = Product. Generally, operands are called factors.
• Division: Dividend ÷ Divisor = Quotient.
• Modulation: Dividend % Divisor = Remainder.
• Exponentiation: Base ^ Exponent = ___.
• Finding roots: Degree √ Radicand = Root.

My questions:

• I've heard addend used generally for addition operands. Is that correct formal usage?
• Do subtraction and division lack general names for their operands because they are not commutative? Or am I just ignorant of them?
• Is the base the same as a mantissa?
• Is there a formal name for the result of exponentiation?
• Is there a formal name for the operation of finding the nth root?
• Am I missing anything else?

Answer 1

• You will often see the terms in a general sum referred to as "addends" or "summands".

• Your suggestion regarding subtraction/division as compared to addition/mulipilication is as good as any. The roles of the operands are not interchangeable, so a single description isn't really appropriate.

• I've usually seen mantissa referring to the multiplier of a power in certain expressions. Specifically, in scientific notation. For example, in the expression $2.345\times10^8$, the mantissa would be $2.345$. It has other usage in connection with logarithms, but you can look that up.

• One sometimes refers to "powers". For example, a polynomial in one variable $x$ can be described as a sum of constant multiples of nonnegative powers of $x$. Technically, the "power" is the exponent, but it is also used on occasion to refer to the entire expression (base and exponent).

• Nothing comes immediately to mind regarding extracting roots.

I will comment that many of these names contain a wealth of Latin. If you happen to know Latin, you will understand their meaning more deeply. For example, "minuend" comes from a form meaning "about to be lessened" and "subtrahend" come from a form meaning "about to be taken away". In general, "-nd" will carry the meaning "about to be ---ed".

Answer 2

Found this table on Wikipedia. It has all the formal names for those operations plus logarithm.

https://en.wikipedia.org/wiki/Template:Calculation_results

Addition

${\left.{\begin{matrix}{\text{summand}}+{\text{summand}}\\{\text{addend (broad sense)}}+{\text{addend (broad sense)}}\\{\text{augend}}+{\text{addend (strict sense)}}\end{matrix}}\right\}}=sum$

Subtraction

${\text{minuend}}-{\text{subtrahend}}=difference$

Multiplication

$\left.{\begin{matrix}{\text{factor}}\times {\text{factor}}\\{\text{multiplier}}\times {\text{multiplicand}}\end{matrix}}\right\}=product$

Division

${\left.{\begin{matrix}{\frac {{\text{dividend}}}{{\text{divisor}}}}\\{\text{ }}\\{\frac {{\text{numerator}}}{{\text{denominator}}}}\end{matrix}}\right\}}={{\begin{matrix}fraction\\quotient\\ratio\end{matrix}}}$

Modulo

${\text{dividend}}{\bmod {\text{divisor}}}=remainder$

Exponentiation

${\text{base}}^{\text{exponent}}=power$

nth root

${\sqrt[{\text{degree}}]{{\text{radicand}}}}=root$

Logarithm

$\log _{\text{base}}({\text{antilogarithm}})=logarithm$