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

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

• 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?
• Not a full answer, but with regard to the 2nd question: I've heard "nominator" has been used before to describe a generic operand of division, but its usage is rare. Apr 2, 2023 at 18:32

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

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

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

## 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

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

• Can you add more details? Once you have earned reputation, you can post this as a comment. Apr 11, 2016 at 4:06
• I agree. I tried, but copying an HTML table while retaining markup (like those big multiline braces) is hard. I also tried to attach a picture, but I don't have enough reputation for that. Apr 12, 2016 at 16:11
• Isn't "quotient" only for euclidean division (when there's also a remainder)? Or does it refer to real division (or whatever it's called) as well? If I'm talking specifically about real/rational division should I avoid using "quotient" to avoid confusion and use "ratio" instead? Apr 1, 2021 at 23:27
• 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".

• "Nothing comes immediately to mind regarding extracting roots", that's degree and radicand (radic = root, e.g. in radix or in eradicate). I'm curious about the use of term and factor respectively for a sum and a product when the position is not important. Are they less common? In French they are the only words we use and addend form is only found in addendum, the words added after the fact to a document.
– mins
Feb 6, 2023 at 11:10
• I know I'm like 10 years late but I've heard "radication" used as a way (source: en.wikipedia.org/wiki/Nth_root#History) Dec 30, 2023 at 16:30