| symbol | latex code | explanation | |
|---|---|---|---|
+ | + | Addition | |
− | - | Subtraction; also negation of a single number | |
× | \times | Multiplication — common in elementary contexts | |
· | \cdot | Multiplication — preferred beyond elementary work, where × could be confused with the letter x (properties of operations) | |
ab | ab | Juxtaposition — writing factors side by side also denotes multiplication | |
÷ | \div | Division — an operation producing a quotient; contrast with the divisibility bar | | |
a / b | a/b | Division written with a slash — the inline form of a fraction | |
± | \pm | Plus or minus — both values at once | |
= | = | Equal to | |
≠ | \neq | Not equal to | |
< | < | Less than — read 'is less than' | |
> | > | Greater than — read 'is greater than' (comparing fractions) | |
≤ | \leq | Less than or equal to | |
≥ | \geq | Greater than or equal to | |
≈ | \approx | Approximately equal to | |
a | b | a \mid b | a divides b — a statement, true or false, not an operation (terminology and notation) | |
a ∤ b | a \nmid b | a does not divide b — the negation uses a slashed bar | |
gcd(a, b) | \gcd(a, b) | Greatest common divisor of a and b (GCD) | |
lcm(a, b) | \operatorname{lcm}(a, b) | Least common multiple of a and b (LCM) | |
σ(n) | \sigma(n) | Sum of all positive divisors of n (sum of factors) | |
a mod n | a \bmod n | The modulo operation — produces the remainder of a divided by n (modulo notation) | |
a % n | a \% n | The programming form of the modulo operation, used by C, Java, Python, JavaScript and most languages | |
a ≡ b (mod n) | a \equiv b \pmod{n} | Congruence — a statement that a and b leave the same remainder modulo n (congruence); an assertion, not a computation | |
a⁄b (stacked) | \frac{a}{b} | Fraction — numerator over denominator; the horizontal line is the fraction bar or vinculum (what is a fraction) | |
a/b (inline) | a/b | The slash form of the same fraction, used in running text | |
2¾ | 2\tfrac{3}{4} | Mixed number — a whole part written next to a proper fraction; here adjacency means addition, not multiplication (mixed numbers) | |
b⁄a | \frac{b}{a} | Reciprocal of a⁄b — numerator and denominator swapped (dividing fractions) | |
(a⁄b)/(c⁄d) | \frac{\;\frac{a}{b}\;}{\;\frac{c}{d}\;} | Complex fraction — the longer main bar separates the overall numerator and denominator (complex fractions) | |
% | \% | Percent — parts per hundred | |
0.75 | 0.75 | Decimal notation — the decimal point separates whole and fractional parts | |
0.3̅ | 0.\overline{3} | Repeating decimal — the overline marks the repeating block |