Explanation of Terminology Used in Algebra - Succeed in Understanding Algebra. Also refer to variable, operation, expression, equation, addition, subtraction, multiplication, division, mathematics, math, maths, Ron Kurtus, School for Champions. Copyright © Restrictions
Terminology Used in Algebra
by Ron Kurtus (revised 13 September 2008)
You should know and understand the major terms used in algebra, which are variable, constant, operation, expression and equation.
A variable is also called an unknown and can be represented by letters from the alphabet. Operations in algebra are the same as in arithmetic: addition, subtraction, multiplication and division. An expression is a group of numbers and variables, along with operations. An equation is the equality of two expressions.
Questions you may have include:
- What are variables and constants?
- What are algebraic operations?
- What is an expression and equation?
This lesson will answer those questions. There is a mini-quiz near the end of the lesson.
Variables and constants
Algebra started off as the addition and subtraction of similar objects. For example, you could add three apples plus two apples to equal five apples. If you substituted the letter "a" for apples, you would have 3 a + 2 a = 5 a in place of 3 apples plus 2 apples equals 5 apples.
Thus, a letter such as "a" could be used for any object. In fact, it could even represent another number or even group of numbers and objects.
Variables
The basis of algebra is that the various mathematical operations can be applied for no matter what you have for "a", "b", or "x".
These letters are called variables, because they can vary and be almost anything. They are also often called unknowns.
Constants
In some situations a quantity may be known, but it is convenient to designate it as a letter. In such a case, the letter represents a constant.
In Einstein's famous equation E = mc2, the letter c represents the speed of light and is thus a constant. It is easier to use c than to write out the speed of light as 186,000 miles per second (or 300,000 km per second).
In some cases, a constant can be an unknown, but it does not necessarily vary.
Common convention
Although any alphabetical letter can be a variable, a common convention used is to designate letters toward the end of the alphabet to be variables and letters to the front as constants.
Thus, variables are usually represented by the letters x, y or z and constants are a, b or c.
In Einstein's equation, c is a constant, but m is a variable because it represent the unknown mass of an object (thus the reason to use m instead of some other letter).
Operations
Mathematical operations are addition, subtraction, multiplication and division. Their common symbols are:
- Addition +
- Subtraction −
- Multiplication ×
- Division ÷
Multiplication and division have some variations.
Multiplication sign
Since the letter "x" is often use as a variable or unknown in algebra, and x looks like the multiplication sign ×, an asterisk (*) or a dot (·) is often used instead. This is done to avoid confusion. Thus, instead of x × y, you would use x*y or x·y.
But another problem then pops up. If you use the dot when dealing with numbers, it may be confused with a decimal point. For example, writing 2 times 5 as 2·5 might be confused with 2½ or 2.5. With numbers, it is better to use *, as in 2*5, or even the × sign.
Using no multiplication sign
When multiplying with variables and constants, mathematicians decided to completely drop the multiplication sign altogether. Instead of writing x times y times z as x*y*z, it is usually written as xyz in algebra.
When including numbers in the multiplication, the number is written first and no multiplication sign is used. Thus, x times 3 is written as 3x, and x times 2 times a is written as 2ax.
But if you are multiplying two or more numbers together, you must include a multiplication sign. 2 times 5 times 3 is not written as 253 but as 2*5*3. If there is a letter involved, try to make it as clear as possible. 2*5x or 2*5*x are both acceptable.
Division sign
The slash (/) is also used to denote division. a÷b and a/b are both a divided by b.
a
—
b also can denote the division of a by b or a fraction. Since it is difficult to write on a
web page, it is seldom used in websites.
Other algebraic operations
Other algebraic operations, such as square root and exponent will be explained in other lessons.
Expressions and equations
Expressions lead into equations.
Expressions
An expression is any group or collection of algebraic numbers and variables, including mathematical operations such as addition, division, etc. Examples of expressions include:
3 + 5
2a + 3x − 6/7
5abc
Some expressions may be long and complex, even including parentheses:
3x + (2z − y)/x + 125y − (x + y)/(z +2)
Equations
An equation consists of expressions separated by an equal sign. The assumption is that the expressions on the left side of the equal sign are equal to those on the right side.
3 + 5 = 8
5x − 3y = 4z
27 + x = 17/3x
Since some these equations contain unknowns or variables, they require a solution to verify the equation is valid.
3x − 7 = 2 is valid with when x = 3.
Some equations are equalities when the values are known or the solution is trivial. 3 + 5 = 8 and x = 3 are considered equalities.
Summary
Major terms used in algebra include: variable, constant, operations, expression and equation. A variable can be represented by letters from the alphabet. Operations in are the same as in arithmetic. There are some different designation of those operations in algebra. An expression is a group of numbers and variables, along with operations. An equation is the equality of two expressions.
See side menu for more Algebra topics
Understand what the words mean
Resources
The following resources provide information on this subject:
Websites
Books
Mini-quiz to check your understanding
If you got all three correct, you are on your way to becoming a Champion in Algebra. If you had problems, you had better look over the material again.
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Terminology Used in Algebra