Math Terms

CP Formula — How to Find Cost Price, Examples

The CP formula recovers the cost price of an item from its selling price and a profit or loss: CP = SP - profit, CP = SP + loss, and from a percentage, CP = 100/(100 + profit%) × SP or 100/(100 - loss%) × SP. This article derives all four forms, defines every term, and works six examples plus the percentage mistakes that flip answers.

Isosceles Triangle Formula — Area, Perimeter, Height

The isosceles triangle formula set is: area = 1/2bh (or b/2√(a² - (b²)/4) from the equal side a and base b), perimeter = 2a + b, and height = √(a² - (b²)/4). This article gives each formula, derives the height and area straight from the Pythagorean theorem, works six examples from one-step to a word problem, and clears up the mistakes that cost the most marks.

What Is a Chord? Definition, Properties & Examples

A chord is a straight line segment whose two endpoints both lie on a curve — most often a circle. This article defines the term, gives the chord-length formulas, lays out the key chord properties, works six examples, and clears up the chord-versus-diameter mix-up that trips students.

What Is a Vector? Definition, Magnitude & Examples

A vector is a quantity that has both a size (magnitude) and a direction — like a velocity of 60 km/h heading north. This article defines the term, shows how vectors are written and drawn, gives the magnitude formula, walks the basic operations, works six examples, and clears up the vector-versus-scalar confusion.

What Is an Axiom? Definition, Examples & Uses

An axiom is a statement accepted as true without proof, used as a starting point from which everything else is proved. This article defines the term, separates axioms from postulates and theorems, lists Euclid's and Peano's famous axioms, works six examples, and clears up where students go wrong.

What Is a Triangle? Definition, Types & Properties

A triangle is a closed, flat shape with three straight sides, three corners, and three interior angles that always add up to 180°. This article defines the term, sorts triangles by side length and by angle, works six examples, and clears up the mistakes students make most.

What Is a Quadrilateral? Definition, Types & Examples

A quadrilateral is a closed, flat shape with exactly four straight sides, four corners, and four interior angles that always add up to 360°. This article defines the term, sorts the family, works six examples, and clears up where students slip.

What Is a Sequence in Math? Definition, Examples

A sequence is an ordered list of numbers that follows a rule, where each number is called a term. This article covers what a sequence is, why order matters, the main types, how to find any term with a rule, and six worked examples.

What Is a Formula in Math? Definition, Examples

A formula is a rule, written with mathematical symbols, that relates two or more quantities so you can compute one from the others. This article covers what a formula is, how it differs from an equation, how to read and rearrange one, and six worked examples across geometry, algebra, and everyday life.

What Is a Millennium? Definition, Years, Examples

A millennium is a unit of time equal to 1,000 years. This article covers what a millennium is, how it compares to a decade and a century, how to convert between them, why the third millennium began in 2001 rather than 2000, and worked examples for measuring long stretches of time.

What Is a Term in Math? Definition, Examples

A term is a single number, a single variable, or numbers and variables multiplied together — one of the building blocks an expression is made from, separated by plus or minus signs. This article covers what a term is, how to count them, like versus unlike terms, and six worked examples.

What Is an Independent Variable? Definition, Examples

An independent variable is the value you choose freely — the input that drives everything else. This article explains what an independent variable is, how it differs from the dependent variable, where it sits on a graph, and walks through six worked examples plus the mistakes students make most.

What Is the Distributive Property? Formula & Examples

The distributive property says that multiplying a number by a sum gives the same result as multiplying each addend separately and adding — a(b + c) = ab + ac. This article covers the formula over addition and subtraction, how it works with variables and negatives, six worked examples, and the slips that cost marks.

What Is a Denominator? Definition & Examples

The denominator is the bottom number of a fraction; it tells you how many equal parts the whole has been divided into. This article covers the definition, numerator versus denominator, why a denominator can never be zero, common denominators, six worked examples, and the common slips.

What Is Average? Definition, Formula & Examples

The average of a set of numbers is their sum divided by how many numbers there are — also called the arithmetic mean. This article covers the average formula, how it differs from the median and mode, six worked examples, and the slips that throw the answer off.

What Is a Multiple? Definition, Examples & Properties

A multiple of a number is what you get when you multiply that number by any integer — the multiples of 3 are 3, 6, 9, 12, …. This article covers the definition, multiples versus factors, common multiples and the LCM, six worked examples, and the mix-ups that cost marks.

What Is Proportion? Definition, Formula & Examples

A proportion is an equation that says two ratios are equal, written a/b = c/d or a : b :: c : d. This article covers the definition, the cross-multiplication rule, direct and inverse proportion, continued proportion, six worked examples, and the slips that cost marks.

What is Congruence — Definition, Symbol & Examples

Congruence in math means two figures have exactly the same shape and the same size — one can be moved (slid, rotated, or flipped) to match the other perfectly. This article gives the formal definition, walks through congruent line segments, angles, and shapes, lists the five triangle-congruence criteria (SSS, SAS, ASA, AAS, RHS), the difference between congruence and similarity, three worked examples, and the most common mistakes.

Radius of a Circle: Definition, Formula, Examples

The radius of a circle is the distance from its centre to any point on the boundary, and it is exactly half the diameter. This article covers the definition, the three formulas for finding the radius, how it ties to the circle equation, six worked examples, and the common mistakes.

What Is a Numerator? Definition, Meaning, Examples

A numerator is the top number of a fraction — the count of how many equal parts you actually have out of the whole. This article covers the precise definition, the numerator's relationship with the denominator, what happens when the numerator is 0 or equal to the denominator, three worked examples, and the mistakes students make most often.

What Is Width in Math? Definition, Formula, Examples

In math, width is the measurement of an object from one side to the other — a one-dimensional quantity taken perpendicular to the length. This article covers the precise definition, the difference between width, length, and depth, width in 2D and 3D shapes, three worked examples (Quick / Standard / Stretch), and the mistakes students make most often.

What Is an Improper Fraction? Definition & Examples

An improper fraction is a fraction whose numerator is greater than or equal to its denominator — for example, 7/4, 11/3, or 5/5. This article covers the precise definition, the conversion between improper fractions and mixed numbers, three worked examples why "improper" is a misleading name, and the mistakes students make most often.

What Is a Mixed Number? Definition, Parts, Examples

A mixed number is a number written as a whole number paired with a proper fraction — for example, 21/4, read as "two and one-quarter." This article covers the precise definition, the three parts of a mixed number, conversions to and from improper fractions, three worked examples, and the mistakes students make most often.

What Is Length in Math? Definition, Units, Examples

In math, length is the measurement of how far one end of an object is from the other — a one-dimensional quantity expressed in metres, centimetres, feet, or any chosen unit. This article covers the precise definition, the SI unit, common conversions, three worked examples, the difference between length, width, and height, and the mistakes students make most often.

What is Greatest Common Factor (GCF) — Definition & Methods

The Greatest Common Factor (GCF) — also called Highest Common Factor (HCF) or Greatest Common Divisor (GCD) — of two or more integers is the largest positive integer that divides each of them without remainder. This article gives the formal definition, walks through three methods to find it, distinguishes GCF from LCM, shows three worked examples, and clears up the most common mistakes.

What is Altitude in Math — Definition, Formula & Examples

An altitude in geometry is a line segment drawn from a vertex perpendicular to the opposite side. This article gives the formal definition, walks through the three altitudes of a triangle and the orthocenter they meet at, lists altitude formulas for equilateral, isosceles, and right triangles, shows how altitude appears in the area formula A = 1/2 × base × height, three worked examples, and clears up the most common confusions.

What is Function in Math — Definition, Types & Examples

A function in math is a rule that assigns to every input value exactly one output value — written y = f(x) where x is the input and y is the output. This article gives the formal definition, distinguishes a function from a general relation, covers domain and range, the vertical line test, the most-used function families, three worked examples, and the common confusions.

What is Meter — Definition, Conversion & Examples in Math

A meter (symbol m) is the SI base unit of length — the international standard for measuring distance — equal to 100 centimetres, 1000 millimetres, and approximately 3.281 feet. This article gives the formal definition, the metric prefix ladder, conversion to imperial units, three worked examples, and the most common conversion mistakes.

What is Polygon — Definition, Types, Properties & Examples

A polygon is a closed, two-dimensional figure made entirely of straight line segments — no curves, no open ends. This article gives the formal definition, walks through classification by number of sides (triangle → decagon), regular vs irregular, convex vs concave, the interior-angle-sum formula (n - 2) × 180°, three worked examples (Quick / Standard / Stretch), and the most common mistakes.

What is Roman Numerals — Rules, Chart & Conversion

Roman numerals are a number system using seven Latin letters — I (1), V (5), X (10), L (50), C (100), D (500), M (1,000) — combined with addition and subtraction rules to write any whole number. This article gives the formal definition, the four rules (addition, subtraction, repetition, vinculum), a full 1–1,000 chart, three worked conversions (Quick / Standard / Stretch), and the common mistakes to avoid.

What is Parameter in Math — Definition & Examples

A parameter is a quantity that appears inside a mathematical expression as a fixed value while the variables change — like the m and b in y = mx + b, or r in the circle equation. This article gives the formal definition, distinguishes parameters from variables, explains parametric equations and statistical parameters, walks through three worked examples (Quick / Standard / Stretch), and clears up the common confusions.

What is Unit in Math — Definition, Meanings & Examples

A unit in math means one of something — a single, standardised quantity used as a reference for counting or measuring. This article covers the five most-used senses of "unit" (place-value, measurement, unit fraction, unit rate, unit cell), gives examples for each, walks through three worked examples (Quick / Standard / Stretch), and names the common confusions.

What is Surface Area — Definition, Formulas & Examples

Surface area is the total area of every face or curved surface that covers a three-dimensional shape, measured in square units. This article gives the formal definition, distinguishes total / lateral / curved surface area, lists formulas for the seven most common solids, walks through three worked examples (Quick / Standard / Stretch), and names the slips that cost marks.

What is Dimension in Math — Definition, Types & Examples

A dimension in math is the number of independent coordinates you need to pinpoint a single location inside an object — zero for a point, one for a line, two for a flat shape, three for a solid. This article gives the formal definition, walks through 0D, 1D, 2D, 3D and a glimpse of higher dimensions, explains the difference between dimensions of a space and dimensions of a shape (length-breadth-height), shows three worked examples, and clears up the most common confusions.

What is Pentagon — Definition, Properties & Formulas

A pentagon is a closed two-dimensional polygon with exactly five straight sides, five vertices, and five interior angles that sum to 540°. This article gives the formal definition, walks through regular vs irregular, convex vs concave, the interior-and-exterior-angle facts, the area formula for a regular pentagon, three worked examples (Quick / Standard / Stretch), and the most common slips.

What is Diagonal — Definition, Formula & Examples in Math

A diagonal is a straight line segment that joins two non-adjacent (non-consecutive) vertices of a polygon or polyhedron. This article gives the formal definition, the count formula n(n-3)/2, length formulas for the square (a√2), rectangle (√(l² + b²)), and cube (a√3), three worked examples (Quick / Standard / Stretch), the properties of diagonals across common quadrilaterals, and the most common mistakes.

What Is a Number? — Definition & Types of Numbers

A number is a mathematical object used to count, measure, order, or label — represented by a symbol called a numeral (like 7, π, 3/4). This article gives the definition, walks through the eight number-type families (natural, whole, integer, rational, irrational, real, imaginary, complex) and how they nest inside each other, shows how the Hindu-Arabic system works, three worked examples, and the most common confusions.

What is Ratio — Definition, Formula & Examples in Math

A ratio is a comparison of two (or more) quantities of the same kind, written as a : b or as the fraction a/b, that tells you how big one quantity is relative to the other. This article covers the definition, the three notations (a:b, a/b, a to b), part-to-part vs part-to-whole types, simplification with the GCD, equivalent ratios, three worked examples (Quick / Standard / Stretch), the difference between ratio and proportion, and the slips that cost marks.

What is a Trapezoid – Definition, Properties & Formula

This article explains what a trapezoid is — a quadrilateral with exactly one pair of parallel sides — and covers its key properties, angle relationships, midsegment theorem, and area formula with worked examples. You will be able to identify a trapezoid, distinguish it from a parallelogram, and solve any standard exam problem involving its measurements.

What is Diameter – Definition, Formula & Examples

This article explains what diameter is — the longest chord of a circle, equal to twice the radius — and shows how the diameter formula connects to circumference and area, with worked examples throughout. You will leave with a clear, exam-ready understanding of diameter and how it relates to every other circle measurement.

What is a Line in Math? Definition, Types, Examples

A line in math is a straight, one-dimensional figure that extends infinitely in both directions. It has no width or thickness — only length. A line is one of the most fundamental objects in geometry, alongside the point and the plane

What is Difference in Math? Definition, Examples

In math, the difference is the result of subtraction** — the answer you get when you subtract one number from another. In 10 - 4 = 6, the 6 is the difference. The number you start with is called the minuend (10), the number being subtracted is the subtrahend (4), and the result is the difference.

What is a Scalene Triangle? Definition, Properties

A scalene triangle is a triangle with no equal sides and no equal angles — every side is a different length, every angle is a different measure. The three angles still sum to 180°. Area is computed by A = 1/2bh or by Heron's formula A = √(s(s-a)(s-b)(s-c)).

What is a Sphere? Definition, Volume, Surface Area

A sphere is a perfectly round 3D shape — the set of all points in space at the same distance from a fixed centre. That distance is the radius r. The volume of a sphere is V = 4/3π r³ and the surface area is SA = 4π r². A sphere has the *smallest surface area* enclosing a given volume — which is why bubbles are spherical.

What is a Variable in Math? Definition, Types

A variable in math is a letter that stands for an unknown or changing value — typically x, y, z, a, b, or n. Variables are the language of algebra. There are two main types: independent variables (the input you choose) and dependent variables (the output that depends on the input).

What is a Reciprocal? Definition, Formula, Examples

The reciprocal of a number is 1 divided by that number. For any non-zero number x, its reciprocal is 1/x, written as x⁻¹. When a number is multiplied by its reciprocal, the result is always 1 — that's why the reciprocal is also called the multiplicative inverse. To find the reciprocal of a fraction, flip it: the reciprocal of a/b is b/a. The number 0 has no reciprocal.

What is Vertical? Definition, Equation, Examples

Vertical in math means straight up-and-down, perpendicular to the horizon. A vertical line on the coordinate plane is parallel to the y-axis. Every point on the line has the same x-coordinate. The equation is x = a where a is a constant. Vertical lines have undefined slope (not zero — undefined).

What is an Isosceles Triangle? Definition, Properties

An isosceles triangle is a triangle with two sides of equal length — called the legs — and two equal angles opposite those sides — called the base angles. The third side is the base, and the angle between the two legs is the vertex angle. Six properties follow from this single definition.

What is the Radius of a Circle? Definition, Formula

The **radius** of a circle is the distance from the centre to any point on the circumference. It is exactly **half the diameter**: r = d/2. The radius is the most fundamental measurement of a circle — area (A = π r²), circumference (C = 2π r), and every other circle formula depends on it.

What is Horizontal? Definition, Meaning, Examples

Horizontal in math means parallel to the horizon — running left-to-right (or right-to-left) without rising or falling. A horizontal line is parallel to the x-axis, has the equation y = b where b is constant, and has slope 0.

What is Calculus? Definition, Branches, Examples

Calculus is the branch of mathematics that studies continuous change — how quantities change over time, or how shapes accumulate area or volume. It has two main branches: differential calculus and integral calculus. The two are connected by the Fundamental Theorem of Calculus.

What is an Algorithm? Definition, Examples

An algorithm is a finite, well-defined sequence of instructions that solves a specific problem or performs a computation. The word comes from al-Khwarizmi, a 9th-century Persian mathematician whose name was Latinised as Algoritmi.

What is Area? Definition, Formula, Examples

Area is the size of a two-dimensional surface — how much space a flat shape occupies. It is measured in *square units* (m², cm², ft², in²). The most-used area formulas are: square (A = a²), rectangle (A = l × w), triangle (A = 1/2 × b × h), and circle (A = π r²).

What is a Percent? Definition, Formula, Examples

percent (symbol: %) is a way to express a number as a fraction of 100. Percent means "per hundred" — so 25% means 25 out of 100, or 25/100 = 0.25. The formula to convert a fraction to a percentage is (part)/(whole) × 100.

What is a Solution in Math – Definition & Examples

This article explains what a solution in math means — a value or set of values that satisfies an equation or inequality — and walks through examples across one-variable equations, systems, and inequalities. You will understand the formal definition, how to verify a solution, and why some equations have no solution or infinitely many.

What is Square Root – Definition, Formula & Examples

This article explains what square root means — the value that, multiplied by itself, gives the original number — and covers the square root formula, notation, and worked examples from perfect squares to estimating irrationals. You will understand the concept, the symbol, and the methods for finding square roots by hand and by calculator.

What is Perimeter – Definition, Formula & Examples

This article explains what perimeter is — the total length of a shape's boundary — and provides the perimeter formula for every standard polygon and circle, with worked examples that progress from straightforward to multi-step problems. You will leave with the definitions, formulas, and practice you need to solve any perimeter question with confidence.

What is a Real Number – Definition, Types & Examples

What is Frequency – Definition, Formula & Examples

What is Pi (π)? Definition, Value & Formula

Pi (π) is the ratio of any circle's circumference to its diameter, approximately 3.14159 or 22/7. It's an irrational, transcendental constant — its decimal expansion never ends and never repeats.

Symmetry in Math: Types, Lines of Symmetry & Examples

Symmetry in math is the property of a shape or object that looks unchanged after a transformation - reflection, rotation, or translation. The five main types are reflection, rotational, translational, point, and glide reflection symmetry, each defined by how the shape stays the same when moved.

Integer – Definition, Types, Examples & Properties

An integer is a whole number - positive, negative, or zero - with no fractional or decimal part, written as the set ℤ = {..., −3, −2, −1, 0, 1, 2, 3, ...}. Integers follow closure, commutative, associative, distributive, identity, and additive inverse properties, and form the foundation for arithmetic, the number line, and all rational numbers.

What is Probability? Definition, Formula & Examples

Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain), calculated using the formula P(E) = n(E) / n(S) - favourable outcomes divided by total outcomes. The three main types are theoretical (reasoned), experimental (observed from trials), and axiomatic (rule-based), and the concept underpins everything from coin tosses to weather forecasting and machine learning.

Volume in Math: Definition, Formula & Examples

Volume is the amount of 3D space an object occupies, measured in cubic units (cm³, m³). For most regular shapes it equals base area × height - cube (a³), cuboid (l × b × h), cylinder (πr²h) - while spheres use (4/3)πr³, cones are one-third of a cylinder, and irregular shapes are measured by water displacement.

Whole Numbers: Definition, Symbol, Properties & Examples

A whole number is a non-negative integer with no fractional or decimal part. The set of whole numbers is W = {0, 1, 2, 3, 4, 5, ...}, beginning at 0 and continuing infinitely. Numbers like 7, 42, and 1000 are whole numbers. Numbers like −3, 1/2, and 0.7 are not.

Parallelogram: Definition, Properties & Formulas

A parallelogram is a quadrilateral (a four-sided polygon) in which both pairs of opposite sides are parallel and equal in length. The word comes from the Greek parallēló-grammon, meaning "shape of parallel lines.

Vertex in Maths: Definition, Examples, and Types Explained

Odd Numbers: Definition, List (1–100), Properties & Examples

An odd number is any whole number that leaves a remainder of 1 when divided by 2 — ending in 1, 3, 5, 7, or 9 (like 1, 3, 5, 7, 9, 11... 99). They follow the form 2n + 1, can be consecutive (3, 5, 7) or composite (9, 15, 21), and obey simple rules: odd + odd = even, odd × odd = odd.

What is an Even Number? Definition, List & Examples

An even number is any integer that can be divided by 2 with no remainder. Examples include 2, 4, 6, 8, 0, and −12. Every even number can be written in the form n = 2k, where k is an integer.

What is a Rational Number? Examples and Types

Rational numbers are numbers expressible as p/q (integers, q ≠ 0) and cover integers, fractions, terminating decimals, and repeating decimals - denoted by Q. They split into positive, negative, zero, and standard form; stay closed under addition, subtraction, multiplication, and non-zero division; and differ from irrationals (π, √2) whose decimals never terminate or repeat.

What is a Composite Number? Definition, List & Examples

A composite number in maths is a whole number greater than 1 with 3 or more factors (like 4, 6, 9, 12). The smallest composite number is 4, and there are 74 composite numbers between 1 and 100.

What is a Natural Number? Definition, Examples & Properties

A natural number is any number used for counting, starting from 1 and going on forever - written as the set N = {1, 2, 3, 4, 5, ...}. They don't include negatives, decimals, or fractions, and whether 0 counts depends on the convention your textbook follows.

Median in Maths: Definition, Formula & Examples

The median is the middle value of an ordered data set. For ungrouped data with odd n, it's the ((n+1)/2)ᵗʰ term; for even n, it's the average of the two middle terms; for grouped data, use Median = l + [((n/2) − cf) / f] × h.

Rhombus – Definition, Properties, Formulas & Examples

A rhombus is a four-sided shape with all four sides equal in length, opposite sides parallel, and diagonals that bisect each other at right angles. Its area is (d₁ × d₂) / 2 and its perimeter is 4a, where d₁ and d₂ are the diagonals and a is the side length.

What is Mode in Maths? Definition, Formula, and Examples

Mode is the value that appears most often in a dataset - 7 is the mode of 4, 7, 7, 9, 12. Unlike mean and median, mode also works on non-numerical data like colors, blood types, or favorite subjects.

What is an Irrational Number? Definition, Examples & Properties

An irrational number is a real number that cannot be written as a ratio of two integers (p/q form), and its decimal expansion never terminates and never repeats. Common examples include √2, π, e, and the golden ratio φ.