An equation in math is like a balanced scale, showing that two things are exactly the same in value. For example, '2 + 2 = 4' is a simple equation.
It often includes letters called 'variables' that stand for numbers we don't know yet, like 'x + 5 = 10'. You need to find the value of 'x' that makes it true.
Metaphorically, if you're talking about a situation, an equation means there are many different parts that you have to think about and put together carefully to understand it or find a solution.
It's like figuring out how all the different pieces of a puzzle fit to make a complete picture. All these factors need to be balanced for something to work out.
§ Understanding the Noun "Equation"
The word equation primarily functions as a noun, and it carries two distinct but related meanings: one literal in mathematics and another metaphorical for complex situations. Understanding these nuances is key to using it effectively in sentences.
§ Grammatical Forms and Usage
As a noun, "equation" can be singular or plural (equations). It is a countable noun, meaning you can have one equation, two equations, and so on. Its primary role in a sentence will be as a subject, object, or part of a prepositional phrase.
- Subject
- The equation was difficult to solve.
- Object
- She presented a complex equation during the lecture.
§ Prepositions Commonly Used with "Equation"
While "equation" doesn't have a fixed set of prepositions it always pairs with, certain prepositions are commonly used depending on the context. These often describe the nature of the equation, what it pertains to, or how it is being discussed.
- Equation *for* something: This typically refers to the purpose or outcome of the equation, especially in a mathematical sense.
The physicist derived a new equation for predicting climate change.
- Equation *of* something: This often describes what the equation represents or defines.
He studied the equation of motion in classical mechanics.
- Equation *involving* something: Used when specifying the elements or variables included in the equation.
The research focused on an equation involving several unknown variables.
- *In* an equation: Refers to something being contained within or part of the equation.
The constant 'c' represents the speed of light in that famous equation.
- Equation *between* two things: Highlights the relationship or balance between two distinct elements in the metaphorical sense.
Finding the right balance between work and life is a complex equation for many.
§ Contextual Usage: Mathematical vs. Metaphorical
The context will always dictate whether you're using "equation" in its literal mathematical sense or its metaphorical sense. Pay attention to the surrounding words and phrases to ensure clarity.
- Mathematical Context
- This usage will often be found in academic, scientific, or technical texts. It will frequently be accompanied by terms like 'solve,' 'variables,' 'constants,' 'formula,' 'theorem,' or names of mathematical fields.
The students struggled to solve the quadratic equation.
- Metaphorical Context
- In this sense, "equation" refers to a complex interplay of factors that need to be balanced or understood to achieve a certain outcome. It's common in discussions about strategy, problem-solving, economics, social issues, or personal decisions.
Success in business is often a delicate equation of innovation, timing, and market demand.
§ Common Phrases and Collocations
Here are some common phrases where "equation" is frequently found:
- To solve an equation: (Mathematical) To find the values of the variables that make the equation true.
The goal of the assignment was to solve the differential equation.
- To balance the equation: (Metaphorical) To find a satisfactory compromise or equilibrium among various factors.
Management is trying to balance the equation of cost, quality, and speed.
- To be part of the equation: (Metaphorical) To be one of the important factors or considerations in a situation.
Customer satisfaction is always a crucial part of the business equation.
- A new equation: (Both) Can refer to a newly discovered mathematical equation or a new set of circumstances and factors that need to be considered.
The rise of AI has introduced a completely new equation for the job market.
By paying attention to these grammatical considerations, prepositions, and contextual cues, you can confidently and accurately use the word "equation" in both its mathematical and metaphorical senses.
按水平分级的例句
2 + 2 = 4 is a simple equation.
Dos más dos es igual a cuatro es una ecuación simple.
This sentence uses basic numbers and the equals sign to demonstrate a simple mathematical equation.
We learned about equations in math class.
Aprendimos sobre ecuaciones en la clase de matemáticas.
This sentence introduces the concept of learning about equations in a school setting.
Solving the equation helped me find the answer.
Resolver la ecuación me ayudó a encontrar la respuesta.
This sentence shows the action of 'solving' an equation to get a result.
The teacher wrote an equation on the board.
La maestra escribió una ecuación en la pizarra.
This sentence uses a common classroom scenario to illustrate where an equation might be seen.
He tried to solve the difficult equation.
Él intentó resolver la ecuación difícil.
This sentence adds the adjective 'difficult' to describe the equation, showing a challenge.
Finding a good job is part of the equation for happiness.
Encontrar un buen trabajo es parte de la ecuación para la felicidad.
This sentence uses 'equation' metaphorically, referring to factors that contribute to happiness.
Many things are in the equation to make a perfect cake.
Muchas cosas están en la ecuación para hacer un pastel perfecto.
This sentence also uses 'equation' metaphorically, implying various ingredients and steps are needed.
Time and effort are important parts of the success equation.
El tiempo y el esfuerzo son partes importantes de la ecuación del éxito.
This sentence uses 'equation' metaphorically to represent the elements required for success.
Solving a complex mathematical equation can be a deeply satisfying intellectual challenge, requiring both logic and intuition.
To solve a complex mathematical equation is a challenge. You need logic and intuition.
Here, 'equation' is used in its primary mathematical sense, as a statement of equality.
The economic equation for a stable recovery involves a delicate balance of inflation, interest rates, and employment figures.
The economy needs a stable recovery. This involves balancing inflation, interest rates, and employment.
This sentence uses 'equation' metaphorically to describe a complex economic situation where factors need to be balanced.
In this ethical dilemma, there's no easy answer; it's a moral equation where every choice has significant consequences.
This is a difficult ethical problem. Every choice has big results.
Here, 'moral equation' refers to a situation where different moral factors must be weighed.
Developing a sustainable energy plan for the city is a complicated equation, factoring in environmental impact, cost, and public acceptance.
Making a sustainable energy plan is hard. You must think about the environment, cost, and if people will accept it.
The phrase 'complicated equation' highlights the multi-faceted nature of the planning process.
The physicist spent years trying to formulate a grand unifying equation that would explain all the fundamental forces of the universe.
The scientist tried for years to make one big equation to explain all forces in the universe.
This example uses 'equation' in its scientific context, representing a formula.
Finding the perfect work-life balance is a personal equation that often changes over time as priorities shift.
Finding a good work-life balance is different for everyone. It changes as your priorities change.
'Personal equation' is a metaphorical use, indicating a unique balance of factors for an individual.
The political equation for winning the election includes effective campaigning, a clear message, and strong public support.
To win the election, you need good campaigning, a clear message, and strong public support.
Here, 'political equation' refers to the combination of elements needed for political success.
She realized that honesty was a crucial variable in the equation of trust within any lasting relationship.
She understood that honesty is very important for trust in any long relationship.
This sentence uses 'equation' metaphorically to represent the components of trust, with honesty as a 'variable'.
Solving a complex differential equation can take days, even for experienced mathematicians, due to the intricate relationships between variables.
Solucionar una ecuación diferencial compleja puede tomar días, incluso para matemáticos experimentados, debido a las intrincadas relaciones entre las variables.
Here, 'equation' is used in its literal mathematical sense, with 'differential' specifying the type.
The economic equation for sustainable growth involves balancing innovation, resource management, and social equity.
La ecuación económica para el crecimiento sostenible implica equilibrar la innovación, la gestión de recursos y la equidad social.
This sentence uses 'equation' metaphorically to represent a complex balance of factors in economics. 'For' indicates purpose.
Finding the right equation for a harmonious work-life balance is a perpetual challenge for many professionals.
Encontrar la ecuación adecuada para un equilibrio armonioso entre el trabajo y la vida personal es un desafío perpetuo para muchos profesionales.
Again, 'equation' is used metaphorically, referring to the optimal combination of elements. 'Right' emphasizes suitability.
The physicist spent years trying to formulate a grand unified equation that would explain all fundamental forces of nature.
El físico pasó años tratando de formular una gran ecuación unificada que explicara todas las fuerzas fundamentales de la naturaleza.
'Unified equation' refers to a theoretical mathematical statement that brings together different phenomena.
Success in the startup world is a complex equation of innovation, funding, market timing, and a bit of luck.
El éxito en el mundo de las startups es una ecuación compleja de innovación, financiación, momento del mercado y un poco de suerte.
Here, 'equation' is a metaphor for the combination of critical elements. 'Of' lists the contributing factors.
The political equation shifted dramatically after the recent elections, necessitating new alliances and strategies.
La ecuación política cambió drásticamente después de las recientes elecciones, lo que requirió nuevas alianzas y estrategias.
'Political equation' is a metaphorical expression for the balance of power and relationships within a political system.
Teachers often emphasize the importance of showing all steps in solving an algebraic equation to ensure understanding.
Los profesores a menudo enfatizan la importancia de mostrar todos los pasos al resolver una ecuación algebraica para asegurar la comprensión.
This is a literal use of 'equation' in a mathematical context, with 'algebraic' specifying the type. 'In solving' acts as a prepositional phrase.
The critical equation for long-term ecological preservation is understanding the delicate interdependencies within ecosystems.
La ecuación crítica para la preservación ecológica a largo plazo es comprender las delicadas interdependencias dentro de los ecosistemas.
'Critical equation' metaphorically refers to the most crucial factor or understanding needed. 'For' indicates the area of application.
近义词
反义词
自我测试 48 个问题
The math problem had an easy ___.
An equation is used in math problems.
We need to find the answer to this ___.
An equation is something you solve to find an answer.
Can you solve the ___? It has numbers and a plus sign.
An equation often has numbers and math symbols.
The teacher wrote a simple ___ on the board.
Teachers write equations for students to solve.
This ___ is 2 + 2 = 4.
2 + 2 = 4 is an example of a simple equation.
Learning math means understanding ___.
Equations are a fundamental part of learning mathematics.
Write a simple sentence using the word 'equation' to talk about numbers. For example: 'The equation is 2 + 2 = 4.'
Well written! Good try! Check the sample answer below.
Sample answer
My math equation is 1 + 1 = 2.
Complete the sentence: 'This math problem needs an ____ to solve it.'
Well written! Good try! Check the sample answer below.
Sample answer
This math problem needs an equation to solve it.
Write a sentence using 'equation' to show that two things are equal. For example: 'This is an equation: X = Y.'
Well written! Good try! Check the sample answer below.
Sample answer
The equation shows that 5 equals 5.
What does an equation have?
Read this passage:
In math class, we learn about equations. An equation has an equals sign, like 3 + 4 = 7. It shows that two parts are the same.
What does an equation have?
The passage says, 'An equation has an equals sign.'
The passage says, 'An equation has an equals sign.'
What did the equation help the student understand?
Read this passage:
My teacher wrote an equation on the board: 5 + 5 = 10. It helped me understand how to add numbers.
What did the equation help the student understand?
The passage states, 'It helped me understand how to add numbers.'
The passage states, 'It helped me understand how to add numbers.'
What is an equation?
Read this passage:
An equation is a math sentence. It tells us that what is on one side of the equals sign is the same as what is on the other side.
What is an equation?
The passage explains, 'An equation is a math sentence.'
The passage explains, 'An equation is a math sentence.'
The correct order forms a simple sentence about a math equation.
This sentence describes what an equation contains.
This sentence expresses a preference for solving equations.
Listen for the word related to a mathematical problem.
Listen for the word that means a complex situation.
Listen for the word referring to a scientific formula.
Read this aloud:
The equation for success often includes hard work and dedication.
Focus: e-QUA-tion
你说的：
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Read this aloud:
We need to find a solution to this complex equation.
Focus: e-QUA-tion
你说的：
Speech recognition is not supported in your browser. Try Chrome or Edge.
Read this aloud:
Balancing family and career can be a difficult equation.
Focus: e-QUA-tion
你说的：
Speech recognition is not supported in your browser. Try Chrome or Edge.
The complex international situation is a delicate ___ that requires careful diplomacy.
In this context, 'equation' refers to a complex situation where many factors need to be balanced, aligning with the metaphorical definition of the word.
Solving a quadratic ___ can involve factoring, completing the square, or using the quadratic formula.
Here, 'equation' is used in its mathematical sense, referring to a statement of equality between two expressions.
The coach tried to find the right ___ of players to create a winning team.
Metaphorically, 'equation' can refer to the combination of elements needed to achieve a desired outcome, much like finding the right balance of factors.
Before we can proceed, we need to solve this ___ and find the value of 'x'.
This sentence directly refers to the mathematical process of solving an 'equation' to find an unknown value.
For a successful business, customer satisfaction is a crucial part of the ___.
In this metaphorical sense, 'equation' represents the essential factors that contribute to a successful outcome.
The scientist spent hours trying to balance the chemical ___ for the experiment.
In chemistry, 'equation' refers to a representation of a chemical reaction, showing the reactants and products in a balanced form.
Which of the following best represents a mathematical equation?
An equation asserts the equality of two expressions, as shown in option A.
In a metaphorical sense, 'equation' refers to a situation that requires:
Metaphorically, an equation implies a complex situation where various factors need to be carefully considered and balanced.
Which sentence uses 'equation' in its metaphorical sense?
Option A uses 'equation' to describe a complex social situation that needs balancing, which is the metaphorical meaning.
A mathematical equation always involves at least one variable.
While many equations involve variables, simple arithmetic statements like '2 + 2 = 4' are also equations and don't necessarily contain variables.
The metaphorical use of 'equation' suggests a straightforward and uncomplicated situation.
Metaphorically, 'equation' implies a complex situation with multiple factors that need to be balanced, not a simple one.
In the sentence 'The equation for success includes hard work and perseverance,' 'equation' is used metaphorically.
Here, 'equation' refers to a combination of factors leading to a result, which is its metaphorical meaning.
The discovery of a new variable completely altered the ______ of the long-standing cosmological model.
In this context, 'equation' is used metaphorically to refer to the complex balance of factors in the cosmological model, which was disrupted by the new discovery.
Solving this complex statistical ______ requires advanced computational methods and a deep understanding of probability theory.
Here, 'equation' refers to a mathematical statement involving variables that needs to be solved.
For the company to achieve sustainable growth, integrating environmental concerns into their business model is a critical ______.
Metaphorically, 'equation' refers to the complex situation where environmental factors must be balanced with business objectives for sustainable growth.
The physicist spent decades trying to unify the four fundamental forces into a single, elegant ______.
In this scientific context, 'equation' denotes a mathematical statement expressing the relationship between physical quantities.
Success in this competitive industry is a complex ______ of innovation, market timing, and effective leadership.
Metaphorically, 'equation' describes the combination of multiple critical factors that must be balanced for success.
To determine the projectile's trajectory, we must first solve the differential ______ that describes its motion under gravity.
This refers to a mathematical statement used to model the motion of the projectile.
This phrase refers to the intricate balance of factors that determine prices in an economy.
The sentence emphasizes the necessity of a thorough analysis of all components when dealing with a complex situation or mathematical problem.
This sentence uses 'equation' metaphorically to describe the delicate equilibrium needed in a multifaceted situation to achieve a positive outcome.
/ 48 correct
Perfect score!
例句
Finding a balance between work and family life is a difficult equation for many parents to solve.
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这个词在其他语言中
更多Math词汇
divisions
B1Divisions refer to the acts of separating something into multiple parts or the specific sections that result from such a process. It can also describe disagreements between groups of people or major departments within a large organization or military structure.
proportion
A2比例是指整体的一部分，通常与总量进行比较。它也描述了两个不同事物的大小或数量之间的关系。
count
A2指计算事物的总数。也可以表示某事物在特定情况下具有重要性或价值。
addition
B2The act of joining or putting something with something else to increase the size, number, or amount. It can also refer to a person or thing that is added to improve or supplement an existing group or object.
add
A1把东西加到一起增加总数、大小、质量，或进行数学加法。
formula
C1指表达数学或化学关系的规则集合，或实现特定结果的既定方法。常用来比喻达成成功的固定模式。
percentage
C2A percentage is a rate, number, or amount in each hundred, used to express a proportion or ratio relative to a whole. In academic contexts, it specifically refers to the quantitative measurement of a subset compared to the total population or data set.
variable
C1A variable is an element, feature, or factor that is liable to vary or change, especially in the context of a scientific experiment or mathematical calculation. It represents a quantity or characteristic that can have different values depending on the circumstances.
random
B2指做事没有明确的计划或模式，凭偶然性发生。表示一种无目的、无规律的状态。
parameter
B2指界定系统或过程运作范围的限制或基准。是设定任务条件的可测量因素。
