equation

/ɪˈkweɪʒn/ (bre, ipa) · /ɪˈkweɪʒn/ (ame, ipa) · /i-ˈkwā-zhən also -shən/ (ame, mw)

equation — 名詞

  • equationsingular
  • equationsplural

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

1.名詞B1
釋義

方程式

數學中表示等式的符號敘述

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.

例句

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

老師在黑板上寫了方程式 3x + 5 = 20，要全班同學解題。

countable: solve + equation

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

Kevin 花了整個晚上解數學作業裡的一道二次方程式。

同義詞
  • 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

文法句型

equation + equals sign + result

用法筆記

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.

常見錯誤

❌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.名詞B2
釋義

化學方程式

用化學符號表示反應的式子

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

例句

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

甲烷燃燒的化學方程式是 CH4 + 2O2 → CO2 + 2H2O。

domain: chemistry — chemical equation

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

Amani 調整了每種分子的數量，使化學方程式達到平衡。

collocation: balance + equation

同義詞
  • chemical formula

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

文法句型

equation + arrow + product

用法筆記

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.

常見錯誤

❌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.名詞B2
釋義

變數組合

需考量多種因素的複雜狀況

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

例句

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

規劃婚禮時，預算的變數組合包括場地、餐點和鮮花。

metaphorical: the + noun + equation

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

新的貿易協定簽訂後，該地區政治方面的變數組合變得更加複雜。

同義詞
  • 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

文法句型

the + equation + of + factors

part of the equation

用法筆記

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.

常見錯誤

❌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.名詞C1
釋義

等同

將某事物視為與另一事物相等

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

例句

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

把財富等同於快樂這種簡單的想法，在社會中很常見但容易誤導人。

pattern: the equation of X with Y

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

Marta 拒絕將成功簡單地等同於高薪或華麗的職稱。

同義詞
  • 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

反義詞
  • distinction

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

文法句型

the equation of X (with) Y

用法筆記

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.

常見錯誤

❌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.