What is the exact terminology for the four basic mathematical operations?

In my native language we have clearly defined and official terms for the operands involved in mathematical calculations. I am talking about the basic four arithmetic operations addition, subtraction, multiplication and division.

I know some of the terms but am unable to find equivalent translations into English for them all. For example, when performing addition, the stuff being added is called "addend" and the result "sum" in Danish:

addend + addend = sum

In English I realize that we have the word "sum" but I can't in my dictionary nor on Wikipedia find the English equivalent of "addend". Same goes for the other three operations.

In Danish:

addend + addend = sum

minuend - subtrahend = forskel

faktor or multiplikand × faktor or multiplikator = produkt

dividend / divisor = kvotient

In English:

_____ + _____ = sum

_____ - _____ = difference

factor × factor = product

_____ / divisor = fraction or quotient

I would appreciate help with filling out these empty spots of my English knowledge with the formal and correct terminology.

• Augend and addend; minuend and subtrahend; multiplier and multiplicand; dividend and divisor.
– user3395
Feb 26, 2018 at 20:12
• And if you have anything left over after division it is remainder. Feb 26, 2018 at 20:37
• Note that the terms "minuend", "subtrahend", "addend", "dividend" are extremely formal, and barely ever used. "Summand", "divisor", "multiplier" are in common enough usage that they are not formal. "Multiplicand" is in the middle ground; it's not often used, but is not overly formal. The general term for an argument to a mathematical operator is "operand", which is weirdly more often used in computer science. Feb 26, 2018 at 21:24

3 Answers

And what exactly seems to be the problem? It's absolutely the same thing across many European languages:

addend + addend = sum (or summand + summand = sum)

minuend - subtrahend = difference

factor × factor = product (or multiplicand × multiplier = product)

dividend / divisor = quotient

The only thing that I would disagree with you about is that you would not call the result of a division problem a fraction. A fraction is really an incomplete division problem (the numbers are all there, but you're not dividing) where the thing that's on top is called the numerator and the thing that's on the bottom is called the denominator. But that's just me nitpicking. Don't pay attention. For further reference, see this Wikipedia page. The sidebar on the right there has got all the information you're looking for.

• Oh, well... That was easy. Feb 26, 2018 at 20:11

Addend + addend = sum or total

Minuend - subtrahend = difference

Facto X factor = product

Dividend / divisor = quotient

See also Basic Mathematical Terminology

Augend + Addend = Sum (aka Total)
Augend is what is augmented and Addend is what is added in order to augment

Minuend - Subtrahend = Difference
Minuend is what is diminished and Subtrahend is what is subtracted in order to diminish

Multiplicand (aka Factor) * Multiplcator (aka Factor) = Product
Multiplicand is what is multiplied and Multiplicator is the multiplier

Dividend / Divisor = Quotient (aka Ratio, Fraction)
Dividend is what is divided and Divisor is the divider