Mathematical symbols make it easier to write and solve problems without using long sentences. They are a universal language that lets mathematicians around the world communicate clearly and efficiently. By learning and understanding these symbols, you can solve problems more easily and understand mathematical concepts better.
Basic Mathematical Symbols – Name, Meaning, Examples
The below table shows the list of basic math symbols along with their meaning.
| Symbol | Symbol Name in Maths | Math Symbols Meaning | Example |
| ≠ | not equal sign | inequality | 10 ≠ 6 |
| = | equal sign | equality | 3 = 1 + 2 |
| < | strict inequality | less than | 7 < 10 |
| > | strict inequality | greater than | 6 > 2 |
| ≤ | inequality | less than or equal to | x ≤ y, means, y = x or y > x, but not vice-versa. |
| ≥ | inequality | greater than or equal to | a ≥ b, means, a = b or a > b, but vice-versa does not hold true. |
| [ ] | brackets | calculate expression inside first | [2 × 5] + 7 = 10 + 7 = 17 |
| ( ) | parentheses | calculate expression inside first | 3 × (3 + 7) = 3 × 10 = 30 |
| − | minus sign | subtraction | 5 − 2 = 3 |
| + | plus sign | addition | 4 + 5 = 9 |
| ∓ | minus – plus | both minus and plus operations | 1 ∓ 4 = -3 and 5 |
| ± | plus – minus | both plus and minus operations | 5 ± 3 = 8 and 2 |
| × | times sign | multiplication | 4 × 3 = 12 |
| * | asterisk | multiplication | 2 * 3 = 6 |
| ÷ | division sign / obelus | division | 15 ÷ 5 = 3 |
| ∙ | multiplication dot | multiplication | 2 ∙ 3 = 6 |
| – | horizontal line | division / fraction | 8/2 = 4 |
| / | division slash | division | 6 ⁄ 2 = 3 |
| mod | modulo | remainder calculation | 7 mod 3 = 1 |
| ab | power | exponent | 24 = 16 |
| . | period | decimal point, decimal separator | 4.36 = 4 +(36/100) |
| √a | square root | √a · √a = a | √9 = ±3 |
| a^b | caret | exponent | 2 ^ 3 = 8 |
| 4√a | fourth root | 4√a ·4√a · 4√a · 4√a = a | 4√16= ± 2 |
| 3√a | cube root | 3√a ·3√a · 3√a = a | 3√343 = 7 |
| % | percent | 1% = 1/100 | 10% × 30 = 3 |
| n√a | n-th root (radical) | n√a · n√a · · · n times = a | for n = 3, n√8 = 2 |
| ppm | per-million | 1 ppm = 1/1000000 | 10ppm × 30 = 0.0003 |
| ‰ | per-mille | 1‰ = 1/1000 = 0.1% | 10‰ × 30 = 0.3 |
| ppt | per-trillion | 1ppt = 10-12 | 10ppt × 30 = 3×10-10 |
| ppb | per-billion | 1 ppb = 1/1000000000 | 10 ppb × 30 = 3×10-7 |
Mathematics Symabols with Examples
Let’s explore some of the most important mathematical symbols you will come across from class 8 to class 12!
1. The Basics: Addition (+), Subtraction (−), Multiplication (×), and Division (÷)
These four symbols are the building blocks of arithmetic.
- Addition (+): This symbol is used when you want to add two or more numbers together. For example, 3 + 5 = 8.
- Subtraction (−): This symbol indicates that you want to subtract one number from another. For instance, 9 − 4 = 5.
- Multiplication (×): This is used to multiply numbers. An example would be 6 × 7 = 42. Sometimes, you might also see the dot symbol (·) or parentheses for multiplication, like 6⋅7 or 6(7).
- Division (÷): Division is splitting a number into equal parts. For example, 20 ÷ 4 = 5. You might also see the division represented by a slash (/), like 20/4 = 5.
2. Equals (=)
The equals sign === is used to show that two expressions are the same. For example, 2 +2 = 4. It’s like a mathematical way of saying “is the same as.”
3. Variables: x, y, and z
In algebra, we often use letters like x, y, and z to represent unknown values. For example, in the equation x + 3 =7, x represents a number that makes the equation true (in this case, x =4).
4. Exponents (^)
Exponents are used to show how many times a number is multiplied by itself. The symbol for exponents is a caret (^). For example, 2^3 means 2 × 2 × 2, which equals 8. In math class, you might also see this written as a superscript, like 23.
5. Square Roots (√)
The square root symbol √ is used to find a number that, when multiplied by itself, gives the original number. For example, √16 =4 because 4 ×4 =16.
6. Pi (π)
Pi (π) is a very special symbol in mathematics. It represents the ratio of the circumference of a circle to its diameter. No matter how big or small the circle is, this ratio is always about 3.14159. We often round it to 3.14 for simplicity.
7. Infinity (∞)
The infinity symbol ∞ represents a value that is limitless or without end. It’s used in various branches of mathematics to describe things that go on forever.
8. Inequality Symbols: >, <, ≥, ≤
Inequality symbols are used to compare two values.
- Greater than (>): 7 >5 means 7 is greater than 5.
- Less than (<): 3 <8 means 3 is less than 8.
- Greater than or equal to (≥): x ≥4 means x is 4 or larger.
- Less than or equal to (≤): y ≤ 10 means y is 10 or smaller.
9. Absolute Value (| |)
The absolute value symbol ∣∣| |∣∣ shows the distance of a number from zero on the number line, without considering direction. For instance, ∣−5∣ =5 and ∣5∣ =5.
10. Summation (Σ)
The summation symbol Σ is used to add up a sequence of numbers. For example, [latex]\Sigma_{i=1}^5[/latex] means 1 + 2 + 3 + 4 + 5.
11. Integral (∫)
The integral symbol ∫ is used in calculus to find the area under a curve. It’s a way to sum up infinitely many tiny pieces to get a total. For example, ∫f(x) dx represents the integral of the function f(x) with respect to x.
12. Parentheses ( )
Parentheses are used to group parts of a mathematical expression. They show which operations should be performed first. For example, in 2 × (3 + 4), you add 3 and 4 first because they are inside the parentheses, and then multiply the result by 2.
13. Factorial (!)
The factorial symbol !!! is used to multiply a series of descending natural numbers. For example, 5! =5 × 4 × 3 × 2 × 1 = 120.
14. Modulus (mod)
The modulus operation finds the remainder after division. For instance, 14 mod 3 is 2 because 14 divided by 3 is 4 with a remainder of 2.