# 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:

• 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?

## 2 Answers

• 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".

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

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

• Can you add more details? Once you have earned reputation, you can post this as a comment. – Aditya Dev Apr 11 '16 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. – Tuupertunut Apr 12 '16 at 16:11