While explaining the ways in which we tackle the math here on this site it is sometimes easier to use the correct definition for the parts of the equation. The problem with this approach is not everyone is familiar with those definitions.
In this page I will cover the basic math definitions for terms that are used throughout this site and a few extra ones for good measure. I have grouped some of them by the basic operations they are used in:
General
Unit is a single quantity regarded as a whole in calculation.
Number is a word or symbol (such as “four” or “21”) that represents a specific amount or quantity.
Digit is any of the numerals from 0 to 9, especially when forming part of a number.
Odd number is any integer that cannot be divided exactly by 2.
Even number is any integer that can be divided exactly by 2.
Complement is the amount you must add to something to make it "whole". There are a number of different "whole" values that we use complements. For example: 9, 10, 100, 1000.
If we have a number less than ten then the complement of 10 would be the amount needed to add to this number so that the sum equals 10.
![\[ $2 + \textcolor{Red}{7} = 9$\qquad\qquad\quad\text{Complement of 9 for 2 is \textcolor{Red}{7}}\\ $4 + \textcolor{Red}{6} = 10$\qquad\qquad\quad\text{Complement of 10 for 4 is \textcolor{Red}{6}}\\ $25 + \textcolor{Red}{75} = 100$\qquad\quad\;\,\text{Complement of 100 for 25 is \textcolor{Red}{75}}\\ $160 + \textcolor{Red}{840} = 1000$\qquad\text{Complement of 1000 for 160 is \textcolor{Red}{840}} \]](https://trachtenbergspeedmath.com/wp-content/ql-cache/quicklatex.com-518110bd37ca749fa22d415c7fbc87e5_l3.png "Rendered by QuickLaTeX.com")
Addition
Addition is the act or process of adding numbers.
Addend is any of a set of numbers that is to be added.
Augend is a number to which another is added to form a sum.
Sum is the solution of the addition.
Addition is commutative, meaning that order you do the addition does not matter.
It is for this reason that the numbers being summed are simply referred to as addends.
The commutative property of addition is written like this:
where a and b are real numbers
Addition is associative, meaning that when one adds more than two numbers, it does not matter which order the addition is performed.
The associative property of addition is written like this:
where a , b and c are real numbers
Subtraction
Subtraction is the operation of deducting one number from another
Minuend is the number that is to be subtracted from.
Subtrahend is the number that is to be subtracted.
Difference is the result of subtracting one number from another.
Multiplication
Multiplicand is the number to be multiplied
Multiplier is the number by which another number is multiplied
Product is the number or expression resulting from the multiplication together of two or more numbers or expressions.
Factor is a number that evenly divides a larger number.
As Multiplication is commutative, meaning that order you do the multiplication does not matter. Both the multiplicand and the multiplier are often referred to as factors.
The commutative property of multiplication is written like this:
where a and b are real numbers
Multiplication is associative, meaning that when one multiplies more than two numbers, it does not matter which order the multiplication is performed.
The associative property of multiplication is written like this:
where a , b and c are real numbers
Division
Division can be written in two different ways:
Quotient is the number resulting from the division of one number by another. It is from a latin word meaning "how many times?"
Divisor is the number by which another number is being divided.
Dividend is a number that is being divided by another number.
Remainder is the number that is left over when one number does not divide evenly into another number.
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