equation

equation — noun

1. a written statement in mathematics that uses symbols and an equals sign to show

1.nounB1
Definition

a written statement in mathematics that uses symbols and an equals sign to show that two sets of numbers or quantities are the same in value.

Example

The teacher wrote the equation 3x + 5 = 20 on the board for the class to solve.

countable: solve + equation

Kevin spent the whole evening working on a quadratic equation from his maths homework.

Common collocations
  • solve an equation
  • quadratic equation
  • linear equation
  • mathematical equation
  • simple equation
  • both sides of the equation
Synonyms
  • formula

    a formula is a rule expressed in symbols, often giving a relationship (e.g. area = length × width); an equation shows equality between two specific values

  • statement

    more general — a statement can be in words or symbols; equation is specific to symbolic equality

Grammar Patterns

equation + equals sign + result

Usage Note

A mathematical equation always contains an equals sign (=) and expresses a relationship between two sides. By contrast, an expression (such as 3x + 5) has no equals sign.

Common Mistakes

Solve the expression 3x + 5 = 20.
Solve the equation 3x + 5 = 20.
An expression has no equals sign; an equation always has one.

2. a written representation of a chemical reaction using symbols and formulas that

2.nounB2
Definition

a written representation of a chemical reaction using symbols and formulas that shows which substances react and what new substances are produced.

Example

The chemical equation for burning methane is CH4 + 2O2 → CO2 + 2H2O.

domain: chemistry — chemical equation

Amani balanced the chemical equation by adjusting the number of each type of molecule.

collocation: balance + equation

Common collocations
  • balance an equation
  • chemical equation
  • write an equation
  • reactants in an equation
  • products of an equation
Synonyms
  • chemical formula

    a formula shows the composition of a single substance (e.g. H₂O); an equation shows the transformation between multiple substances

Grammar Patterns

equation + arrow + product

Usage Note

A chemical equation uses an arrow (→) rather than an equals sign (=). The substances on the left are reactants; those on the right are products. Distinguish from equation/1 (mathematical), which uses numbers and an equals sign.

Common Mistakes

Write the chemical formula for combustion.
Write the chemical equation for combustion.
A formula (e.g. H₂O) shows one substance; an equation shows the whole reaction.

3. a set of connected factors or issues that you need to think about together to un

3.nounB2
Definition

a set of connected factors or issues that you need to think about together to understand something or decide what to do.

Example

When planning the wedding, the budget equation included the venue, the food, and the flowers.

metaphorical: the + noun + equation

The political equation in the region became more complicated after the new trade agreement.

Common collocations
  • part of the equation
  • change the equation
  • factor into the equation
  • the budget equation
  • the political equation
  • the human equation
Synonyms
  • situation

    more general — equation emphasises that multiple factors interact and need to be weighed together

  • scenario

    scenario suggests a possible or imagined set of events; equation focuses on the balancing of factors

  • mix

    informal — a mix of ingredients/factors is similar, but equation has the added sense of trade-offs and balance

Grammar Patterns

the + equation + of + factors

part of the equation

Usage Note

This is a metaphorical extension of the mathematical sense. Often used with the definite article ('the equation') or a possessive ('our equation'). Common in business, politics, and everyday decision-making contexts.

Common Mistakes

The human equation is hard to solve.
The human factor in the equation makes the situation harder to predict.
When using equation metaphorically, make clear what factors are involved rather than treating it as a vague synonym for 'situation'.

4. the process of viewing two separate items as equal in value, meaning, or importa

4.nounC1
Definition

the process of viewing two separate items as equal in value, meaning, or importance.

Example

The simple equation of wealth with happiness is a common but misleading belief in society.

pattern: the equation of X with Y

Marta rejected the easy equation of success with a large salary or a fancy title.

Common collocations
  • equation of X with Y
  • simple equation
  • easy equation
  • dangerous equation
  • reject the equation
Synonyms
  • identification

    suggests seeing two things as essentially identical; equation allows for comparison without full identity

  • comparison

    broader — comparison examines similarities and differences; equation asserts sameness

Antonyms
  • distinction

    the act of pointing out differences rather than treating things as the same

Grammar Patterns

the equation of X (with) Y

Usage Note

Typically used in fixed constructions with 'of … and …' or 'of … with …'. Frequently appears in academic or formal writing about concepts, ideologies, or values. The focus is on the act of mentally putting two things in the same category.

Common Mistakes

The equation between hard work and success is wrong.
The equation of hard work with success is misleading.
Use 'equation of X with Y' (not 'equation between') when referring to the act of equating.

Word family

Synonym discussion

Sense: noun/1

In mathematics, an equation is a statement that two quantities are equal, always containing an equals sign (=). A formula is a rule or relationship expressed in symbols, such as area = length × width — it can be thought of as a type of equation that gives a general rule rather than a one-off problem. An expression is a group of mathematical symbols without an equals sign (e.g. 3x + 5) — it represents a quantity but does not assert equality. A calculation is the process of working out a numerical answer, such as adding up a column of numbers. In short: every equation and every formula contains an expression on each side, but not every expression is part of an equation.

equation ↗formula ↗expression ↗calculation ↗

Common collocations

Nouns

Prepositions

Etymology

LatinOld FrenchEnglish

Equation comes from the Latin word aequatio, meaning 'making equal' or 'leveling'. This in turn comes from aequus, meaning 'equal' or 'level'. The word entered English through Old French around the 14th century, originally referring to the astrological concept of equal hours of day and night. The mathematical sense — a statement showing equality between quantities — emerged in the late 16th century. The chemical sense developed in the 19th century as scientists began using symbolic notation to describe reactions.