Algebra Symbols (Basic Algebraic Symbols in Maths) with Example
Algebra is a subdomain of mathematics that helps us to transfer data in mathematical form. Using different operators and algebra symbols we can convert information into the form of equations. It helps to solve daily life problems using mathematics. With the help of variables and the interrelation between them, we can find the values of different quantities. Variables are often represented as alphabets. They take the value as per the constraints on them. Constants are generally numbers that do not change values over time. Algebra is further classified as Pre-algebra, elementary algebra, abstract algebra, and universal algebra.
This Story also Contains
- Algebra Symbols
- List Of Algebra Symbols
- Order Of Operation
- Examples
Algebra Symbols
Algebra symbols denote the operations they perform. They are applied to the data to perform certain operations. Every symbol has its meaning and function. The priority of operation can be checked using an algebra signs rules chart.
List Of Algebra Symbols
Arithmetic symbols
Arithmetic symbols are '+', '-', '/', and '*'. Each of them performs different applications. They are the expression symbols and help us to write the expression.
'+' is used to add one or more quantities
'-' is used for the subtraction of quantities
'*' is used to multiply the quantity
'/' is used to divide the quantities
x
An unknown variable is denoted using the variable "x".
Symbols used for comparing quantities
Symbol | Name | Use |
= | Equal to | This symbol is used to show that two quantities are equal to each other. |
≠ | Unequal | When two quantities are unequal we make use of this symbol to show their inequality |
~ | Approximation | When two quantities are almost equal to each other we make use of this symbol to denote them. |
∝ | Proportional to | When one quantity varies with the other, we make use of this symbol. |
>,< | Less than or greater than | When one quantity has greater value than another we make use of this symbol. |
Use of brackets
Bracket when used in the expression helps us to identify the priority of the operation. Other than that it serves many different purposes.
Symbol | Name | Meaning |
[] | A square bracket | This is used in an expression to give the order of the operation. We need to do operations inside the bracket first. |
() | Round brackets | Round brackets are also used to denote the priority of the operation. |
{} | Braces or curly brackets |
|
⌊x⌋ | Floor bracket | It carries the instruction to round the integer to its lower value. |
x!
A factorial is represented using an exclamation mark. Here, x takes the value of any number. The factorial of x means the multiplication of elements starting with x and decreasing by 1 till you are only remaining with the number 1. This symbol is used in permutations and combinations.
For example, 3!=3✕2✕1
|x|
This gives the absolute value of any number. It means no matter whether the number is negative or positive when you take the absolute value of it then you get a positive integer.
for example |-3|=|3|=3
∆
The symbol is called a delta. It gives the difference between two quantities. It is used to denote the change.
Intervals
Symbol | Name | Meaning |
(a, b) | Open interval | It means all the numbers from a to b are included except for a and b. |
[a, b] | Closed interval | It means all the numbers from a and b are included without excluding a and b. |
Functions
Symbol | Name | Meaning |
F(x) | Function | Here, x acts as input and the function gives the output. It is used to map two sets. |
(fog) | Composite function | This used write composite function. |
Matrix
Name | Symbol | Meaning |
[], () | Matrix | Both symbols are used to denote the matrix. |
|A| | Determinant | It gives the determinant of any matrix A. |
A^{T} | Transpose | It gives the transpose of a matrix. |
A^{-1} | Inverse | It is used to denote the inverse of a matrix. |
A^{H} | Hermitian | It is used to denote the Hermitian matrix. |
Order Of Operation
To find the order of operation you can make use of the rule PEDMAS.
P is for parenthesis. Any operation inside the parenthesis has the first preference.
E is for exponents. Any exponential operation gets second preference.
D is for division and M is for multiplication. After exponents performing division or multiplication is necessary.
A is for addition and S is for subtraction. This operation gets the last preference.
Examples
Write all elements of the given interval [3, 9)
This interval includes all the elements from 3 to 9. As 3 has a square bracket it is included in the interval. As 9 has an open bracket, it is excluded from the interval.
So the elements are 3,4,5,6,7,8
Find the value of {(34 + 73) - 9*8}
To solve the question we will follow PEDMAS
{(34 + 73) - 9*8} = {107 – 72}
= 35
If y = 3x + 7. Find the first 3 elements in the domain and range if x and y are positive integers. And x is not equal to zero.
The values of x from the domain. And the output forms the range.
As x is a positive integer its value starts from 1.
For x = 1
y = 3(1)+7
= 10
For x = 2
y = 3(2) + 7
= 13
For x = 3
y = 3(3) + 7
= 16
Domain = {1, 2, 3}
Range = {10, 13, 16}
Find the value is 5!
The value of a given factorial is
5! = 5 × 4 × 3 × 2 × 1
= 120
Check if 62 and (12 × 3) are equal or not.
62 = 36
12 × 3 = 36
So, we can write
62 =12 × 3
Frequently Asked Questions (FAQs)
The symbol π denotes a constant whose value is 3.1415…
The Hermitian matrix can be represented as A^{H} 
or A^{†} 
.
Rank(A) denotes the rank of matrix A.
The symbol is a Greek letter known as sigma. It is used for summation. It means you can add the quantities in series with its help of it.
The addition follows two rules of algebra Association and Commutative rule.
