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A2 noun 11분 분량

equação

예시
설명 equação in your Level:
At the A1 level, learners encounter 'equação' strictly as a mathematical term. It is introduced alongside basic school vocabulary like 'escola' (school), 'professor' (teacher), and 'matemática' (mathematics). A beginner might learn to say 'Eu tenho uma equação de matemática' (I have a math equation) or 'A equação é difícil' (The equation is difficult). The focus is on recognizing the word, knowing its feminine gender (a equação), and understanding its plural form (as equações). At this stage, learners do not need to worry about the metaphorical uses of the word. The goal is simple vocabulary acquisition and basic sentence construction using common verbs like 'ter' (to have) and 'ser' (to be). Pronunciation practice is also crucial, specifically mastering the nasal 'ão' sound, which is often challenging for English speakers.
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At the A2 level, learners begin to use 'equação' in slightly more complex sentences and with action verbs. They learn to say 'Eu preciso resolver a equação' (I need to solve the equation) or 'O professor escreveu a equação no quadro' (The teacher wrote the equation on the board). They start to understand collocations like 'resolver uma equação' (solve an equation). Learners at this stage can describe their daily routines and school activities, making 'equação' a useful word for talking about homework or classes. They also become more comfortable with the plural form 'equações' and ensure noun-adjective agreement, such as saying 'equações difíceis' (difficult equations). The focus remains largely literal, but sentence structures become more fluid and descriptive.
At the B1 level, the metaphorical use of 'equação' begins to emerge. Learners start to understand that 'equação' can refer to a complex situation or problem in everyday life, not just in math. They might hear or read sentences like 'O dinheiro é uma parte importante da equação' (Money is an important part of the equation). They learn idioms and phrases such as 'tirar da equação' (to take out of the equation). At this intermediate stage, learners can express opinions and discuss abstract concepts, allowing them to use 'equação' to describe balancing work and life, or solving logistical problems. They also encounter the word more frequently in news articles and podcasts, broadening their comprehension of its versatility in the Portuguese language.
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At the B2 level, learners are expected to use 'equação' confidently in both literal and figurative contexts. They can engage in detailed discussions about politics, economics, and society, where terms like 'equação política' (political equation) or 'equação econômica' (economic equation) are commonplace. They understand nuances and can use advanced vocabulary alongside 'equação', such as 'variáveis' (variables), 'fatores' (factors), and 'equilibrar' (to balance). A B2 learner might write an essay stating, 'Para resolver a equação do aquecimento global, precisamos de cooperação internacional' (To solve the equation of global warming, we need international cooperation). Their pronunciation of the 'ção' ending should be clear and natural, and they make no mistakes regarding the word's gender or pluralization.
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At the C1 level, the use of 'equação' is highly sophisticated and nuanced. Learners encounter the word in academic texts, literature, and high-level professional environments. They understand complex collocations like 'equação diferencial' (differential equation) in scientific contexts, and sophisticated metaphors in literary contexts. They can subtly manipulate the word to convey specific meanings, such as describing a delicate diplomatic negotiation as a 'frágil equação' (fragile equation). At this advanced level, learners have a deep intuitive grasp of when to use 'equação' versus alternatives like 'dilema', 'paradoxo', or 'quebra-cabeça' (puzzle), depending on the exact stylistic and rhetorical effect they wish to achieve in their writing or speech.
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At the C2 level, learners possess near-native mastery of the word 'equação'. They understand its etymology and can play with its meaning in creative and poetic ways. They can effortlessly parse highly technical or philosophical texts where 'equação' is used to define the fundamental nature of reality or human existence. A C2 speaker might use the word in spontaneous, complex debates, employing idiomatic expressions flawlessly. They recognize regional variations in pronunciation or usage, although 'equação' is standard across the Lusophone world. Their usage is characterized by precision, elegance, and a complete absence of grammatical or contextual errors, reflecting a profound integration of the word into their comprehensive Portuguese vocabulary.
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예시
The Portuguese word 'equação' translates directly to 'equation' in English. In its most literal and primary sense, it refers to a mathematical statement asserting that two expressions are equal, typically separated by an equals sign. However, the usage of 'equação' extends far beyond the confines of a mathematics classroom. In everyday Portuguese, people frequently use this word metaphorically to describe a complex situation, a problem that needs solving, or a scenario involving multiple variables and factors that must be balanced. When someone says they need to 'resolver esta equação' (solve this equation) in a business meeting, they are not talking about algebra; they are talking about finding a solution to a multifaceted problem. Understanding how to use 'equação' in both its literal and figurative senses is crucial for learners who want to achieve fluency and sound natural in Portuguese conversations.
Literal Use
In mathematics, an 'equação' is a formula that expresses the equality of two expressions, such as 2x + 3 = 7. Students learn to solve these from a young age.
Figurative Use
In daily life, it means a complex problem or situation. For example, balancing a household budget is often referred to as a difficult 'equação' to solve.
Idiomatic Context
Taking someone or something 'out of the equation' (tirar da equação) means to remove a variable or person from consideration to simplify a problem.

A professora escreveu a equação no quadro negro para que todos os alunos pudessem copiá-la.

Se você tirar o medo da equação, o que você faria hoje?

O governo está tentando resolver a complexa equação da economia nacional.

Nós precisamos encontrar o valor de X nesta equação de segundo grau.

O amor e a confiança são partes fundamentais dessa equação familiar.

This word is deeply embedded in both academic and colloquial language. When you listen to Portuguese speakers discussing politics, they might talk about the 'equação política' (political equation) meaning the balance of power and alliances. In sports, commentators might discuss the 'equação do campeonato', referring to the points and results needed for a team to win the title. Therefore, mastering the word 'equação' allows you to express complex ideas about problem-solving, balance, and strategic thinking in Portuguese. It is a versatile noun that elevates your vocabulary from simple, concrete descriptions to more abstract, analytical conversations. Whether you are studying algebra or navigating the complexities of human relationships, 'equação' is a word you will encounter and use frequently.
Using the word 'equação' correctly in Portuguese sentences requires an understanding of its gender, its pluralization, and the common verbs and adjectives that typically accompany it. Because it is a feminine noun ending in '-ção', it must be preceded by feminine articles such as 'a' (the) or 'uma' (a/an). The plural form is 'equações', which is a standard transformation for words with this suffix. When constructing sentences, the most common verb paired with 'equação' is 'resolver' (to solve). You will frequently hear phrases like 'resolver a equação' (solve the equation). Other common verbs include 'montar' (to set up/assemble), 'simplificar' (to simplify), and 'equilibrar' (to balance).
With Verbs of Action
Use verbs like resolver, formular, or entender. Example: Eu preciso resolver esta equação antes do exame.
With Descriptive Adjectives
Adjectives like complexa, simples, difícil, and matemática are common. Example: É uma equação muito complexa para mim.
In Prepositional Phrases
Phrases like 'parte da equação' (part of the equation) are very common. Example: O tempo é uma parte importante da equação.

O aluno não conseguiu resolver a equação de matemática.

Temos que incluir os custos de transporte na equação.

A nova política mudou completamente a equação eleitoral.

Se você adicionar estresse à equação, o resultado será negativo.

A equação química precisa ser balanceada antes do experimento.

When writing sentences, it is also important to consider the prepositions that follow 'equação'. Usually, we say 'equação de' (equation of) when specifying the type, such as 'equação de segundo grau' (quadratic equation). Metaphorically, you might say 'a equação do sucesso' (the equation of success), implying the formula or combination of factors required to achieve success. By practicing these collocations and sentence structures, you will be able to integrate 'equação' seamlessly into your spoken and written Portuguese, whether you are discussing a literal math problem or a complex life situation.
The word 'equação' is ubiquitous in Portuguese-speaking environments, spanning from educational institutions to corporate boardrooms and everyday casual conversations. The most obvious place you will encounter this word is in schools and universities. Mathematics, physics, and chemistry classes are filled with references to 'equações'. Teachers will ask students to solve them, balance them, and understand their variables. However, the true richness of the word reveals itself outside the classroom. In news broadcasts, journalists frequently use 'equação' to describe political and economic scenarios. You might hear a news anchor discussing the 'equação financeira' (financial equation) of a struggling company or the 'equação política' (political equation) facing a president trying to pass a new law.
Educational Settings
Math, science, and engineering classes. This is where the literal meaning is used almost exclusively, focusing on numbers, variables, and formulas.
Business and Economics
Used to describe financial models, market strategies, and the balance of risk and reward in corporate decision-making.
Everyday Conversations
Used metaphorically to describe life's problems, relationship dynamics, or any situation requiring a balance of different factors.

Na aula de física, aprendemos uma nova equação sobre a gravidade.

O analista financeiro disse que a equação de lucros da empresa está errada.

Para o treinador, a equação é simples: se ganharmos, somos campeões.

O diretor de marketing apresentou a equação de vendas para o próximo trimestre.

Nós precisamos tirar o orgulho da equação para resolver essa briga.

You will also hear this word in self-help and motivational contexts. Speakers might talk about the 'equação da felicidade' (equation of happiness), breaking down complex emotional states into simpler, manageable variables. In sports commentary, the 'equação' often refers to the mathematical probability of a team advancing in a tournament. Understanding these diverse contexts is essential. It shows that 'equação' is not a dry, academic term confined to textbooks, but a vibrant, dynamic word used to conceptualize and articulate the complexities of modern life in the Portuguese-speaking world. Recognizing its metaphorical power will significantly enhance your listening comprehension and your ability to engage in deep, meaningful conversations.
When learning the word 'equação', English speakers and other learners of Portuguese tend to make a few predictable mistakes. The most prominent errors revolve around gender, spelling, and pronunciation. Because the English word 'equation' does not have a grammatical gender, learners often default to using the masculine article 'o', saying 'o equação'. This is incorrect; 'equação' is strictly feminine, so it must be 'a equação'. Another common mistake is related to spelling. The Portuguese language uses the cedilla (ç) and the tilde (~) to create specific sounds. Learners sometimes write 'equassão', 'equacão', or 'equacao', forgetting the diacritics. These spelling errors can also lead to pronunciation errors. The 'ção' ending is a nasal diphthong that does not exist in English, and mastering it requires practice.
Gender Mistakes
Using 'o equação' instead of 'a equação'. Always remember that nouns ending in '-ção' are almost universally feminine in Portuguese.
Spelling Mistakes
Forgetting the cedilla (ç) or the tilde (~). Writing 'equacao' is incorrect and changes how the word is read by native speakers.
Pluralization Mistakes
Saying 'equaçãos' instead of 'equações'. The suffix '-ção' changes to '-ções' in the plural form.

Incorreto: O equação é difícil. Correto: A equação é difícil.

Incorreto: Eu resolvi as equaçãos. Correto: Eu resolvi as equações.

Ele escreveu a equação corretamente no teste.

A professora corrigiu a equação que estava no quadro.

Nós precisamos entender a equação antes de tentar resolvê-la.

Another subtle mistake is using 'equação' when another word would be more appropriate. For example, if you are talking about a simple arithmetic sum like 2 + 2, calling it an 'equação' might sound overly formal or technically incorrect to a native speaker. In such cases, 'conta' (sum/calculation) or 'cálculo' (calculation) is much more natural. 'Equação' implies a level of complexity, specifically the presence of an unknown variable that needs to be found. By being mindful of its gender, spelling, pronunciation, and exact meaning, you can avoid these common pitfalls and use 'equação' with confidence and precision.
While 'equação' is a specific and powerful word, there are several similar words and alternatives in Portuguese that you might use depending on the exact context. Knowing these alternatives helps you avoid repetition and allows you to express nuances in meaning. The most common alternatives are 'fórmula' (formula), 'cálculo' (calculation), 'conta' (sum/bill/math problem), and 'problema' (problem). Each of these words has a slightly different connotation. A 'fórmula' is a set rule or established method, whereas an 'equação' is a statement of equality that often needs solving. A 'cálculo' refers to the process of computing a result, which is broader than an equation. 'Conta' is a very informal word used for simple math or a restaurant bill.
Fórmula (Formula)
Used when referring to a fixed mathematical rule or a recipe for success. Example: A fórmula da água é H2O.
Cálculo (Calculation)
Refers to the act of calculating or the result of a mathematical process. Example: O cálculo estrutural do prédio está pronto.
Conta (Math problem / Bill)
A very common, informal word for simple arithmetic. Example: A criança está aprendendo a fazer contas de somar.

Em vez de usar uma equação complexa, ele fez um cálculo simples.

A equação de Einstein é a fórmula mais famosa do mundo.

Resolver esse problema é muito mais difícil do que resolver uma equação.

A matemática envolve muitas fórmulas, cálculos e equações.

A equação da vida não tem uma fórmula exata.

Understanding these distinctions helps you choose the right word for the right situation. If you are reading a scientific paper, 'equação' and 'fórmula' will be prevalent. If you are helping a child with elementary homework, you will talk about 'contas'. If you are discussing a philosophical issue, you might use 'equação' metaphorically, or simply call it a 'problema' or 'questão' (question/issue). Expanding your vocabulary with these related terms ensures that your Portuguese is rich, varied, and appropriate for the specific context of your conversation.
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수준별 예문

1

A equação é muito difícil.

The equation is very difficult.

Uses the feminine article 'A' and the verb 'ser' in the present tense.

2

Eu tenho uma equação para resolver.

I have an equation to solve.

Uses the indefinite article 'uma' and the verb 'ter'.

3

Onde está a equação?

Where is the equation?

Simple question structure using 'Onde está'.

4

Ela escreve a equação.

She writes the equation.

Present tense of the verb 'escrever'.

5

Esta é uma equação simples.

This is a simple equation.

Demonstrative pronoun 'Esta' agreeing with the feminine noun.

6

As equações são fáceis.

The equations are easy.

Plural form 'equações' and plural adjective 'fáceis'.

7

Eu não entendo a equação.

I do not understand the equation.

Negative sentence with the verb 'entender'.

8

A professora lê a equação.

The teacher reads the equation.

Present tense of the verb 'ler'.

1

Eu preciso resolver esta equação hoje.

I need to solve this equation today.

Modal verb 'precisar' followed by the infinitive 'resolver'.

2

O aluno copiou a equação do quadro negro.

The student copied the equation from the blackboard.

Past tense of 'copiar' and preposition 'de' + 'o' (do).

3

Nós aprendemos uma nova equação na escola.

We learned a new equation at school.

Past tense of 'aprender' and adjective 'nova' preceding the noun.

4

Você sabe a resposta para essa equação?

Do you know the answer to that equation?

Question using the verb 'saber' and preposition 'para'.

5

A equação matemática estava errada.

The mathematical equation was wrong.

Imperfect past tense of 'estar' and adjective agreement.

6

Eles estão estudando equações difíceis.

They are studying difficult equations.

Present continuous tense using 'estar' + gerund.

7

Por favor, explique a equação novamente.

Please explain the equation again.

Imperative form of 'explicar'.

8

A equação tem duas variáveis diferentes.

The equation has two different variables.

Use of the verb 'ter' to indicate possession or composition.

1

O tempo é uma parte vital dessa equação.

Time is a vital part of that equation.

Metaphorical use of 'equação' to mean a complex situation.

2

Temos que tirar os sentimentos da equação.

We have to take feelings out of the equation.

Idiomatic expression 'tirar da equação'.

3

A equação financeira da empresa não faz sentido.

The company's financial equation doesn't make sense.

Use of 'equação' in a business/economic context.

4

Resolver a equação do trânsito é o maior desafio do prefeito.

Solving the traffic equation is the mayor's biggest challenge.

Using 'equação' to describe a public policy problem.

5

Se você adicionar estresse à equação, tudo piora.

If you add stress to the equation, everything gets worse.

Conditional 'Se' clause and metaphorical addition.

6

Eles tentaram equilibrar a equação, mas falharam.

They tried to balance the equation, but failed.

Past tense with the verb 'equilibrar'.

7

A equação química precisa ser balanceada com cuidado.

The chemical equation needs to be balanced carefully.

Passive voice 'ser balanceada'.

8

Qual é a equação para o sucesso nesta carreira?

What is the equation for success in this career?

Philosophical/metaphorical question structure.

1

A complexa equação política exigiu meses de negociações diplomáticas.

The complex political equation required months of diplomatic negotiations.

Advanced vocabulary and past perfect tense.

2

Para os cientistas, a equação de Einstein mudou a nossa compreensão do universo.

For scientists, Einstein's equation changed our understanding of the universe.

Historical reference and complex sentence structure.

3

O gerente percebeu que o custo logístico era a variável oculta na equação.

The manager realized that the logistical cost was the hidden variable in the equation.

Corporate context using related terms like 'variável'.

4

A sustentabilidade deve ser introduzida na equação do desenvolvimento urbano.

Sustainability must be introduced into the equation of urban development.

Passive voice with modal verb 'deve ser introduzida'.

5

Embora a equação parecesse simples, a sua resolução provou ser quase impossível.

Although the equation seemed simple, its resolution proved to be almost impossible.

Concession clause with 'Embora' and imperfect subjunctive 'parecesse'.

6

Eles estão tentando formular uma equação que preveja o comportamento do mercado.

They are trying to formulate an equation that predicts market behavior.

Present subjunctive 'preveja' in a relative clause.

7

A nova lei altera fundamentalmente a equação de risco e retorno para os investidores.

The new law fundamentally alters the risk and return equation for investors.

Advanced vocabulary 'altera fundamentalmente'.

8

Não podemos ignorar a equação demográfica ao planejar o futuro da previdência.

We cannot ignore the demographic equation when planning the future of social security.

Infinitive clause 'ao planejar'.

1

A hermenêutica do texto revela uma equação existencial profunda sobre a condição humana.

The hermeneutics of the text reveals a profound existential equation about the human condition.

Academic and literary vocabulary 'hermenêutica', 'existencial'.

2

O modelo macroeconômico baseia-se numa equação estocástica diferencial de extrema complexidade.

The macroeconomic model is based on a stochastic differential equation of extreme complexity.

Highly technical scientific vocabulary.

3

Ao desconstruir a narrativa, o crítico expôs a frágil equação de poder que sustentava o regime.

By deconstructing the narrative, the critic exposed the fragile power equation that sustained the regime.

Advanced literary and political analysis context.

4

A mitigação das mudanças climáticas impõe uma equação cujas variáveis são não apenas tecnológicas, mas éticas.

Climate change mitigation imposes an equation whose variables are not only technological, but ethical.

Use of the relative pronoun 'cujas' (whose).

5

O paradoxo inerente a esta equação social reside na dicotomia entre liberdade e segurança.

The inherent paradox in this social equation lies in the dichotomy between freedom and security.

Sophisticated philosophical phrasing.

6

A resolução dessa equação diplomática demandará uma sinergia sem precedentes entre as nações.

The resolution of this diplomatic equation will demand unprecedented synergy among nations.

Future tense 'demandará' and advanced noun 'sinergia'.

7

Ele reduziu a complexidade do comportamento humano a uma mera equação utilitarista.

He reduced the complexity of human behavior to a mere utilitarian equation.

Critical tone using 'mera' (mere) and 'utilitarista'.

8

A equação de Schrödinger permanece como o pilar fundamental da mecânica quântica moderna.

Schrödinger's equation remains the fundamental pillar of modern quantum mechanics.

Specific scientific reference with formal structure.

1

A sublimação da dor em arte é, talvez, a equação mais insondável da psique humana.

The sublimation of pain into art is, perhaps, the most unfathomable equation of the human psyche.

Poetic and psychological vocabulary 'sublimação', 'insondável'.

2

O autor manipula a equação temporal da narrativa com uma destreza que beira o genial.

The author manipulates the narrative's temporal equation with a dexterity that borders on genius.

Literary critique style phrasing.

3

Na tessitura do cosmos, cada buraco negro representa uma singularidade onde a equação da relatividade colapsa.

In the fabric of the cosmos, each black hole represents a singularity where the equation of relativity collapses.

Astrophysical context with poetic phrasing 'tessitura do cosmos'.

4

A falácia do argumento reside em postular uma equação linear para um fenômeno eminentemente caótico.

The fallacy of the argument lies in postulating a linear equation for an eminently chaotic phenomenon.

Academic debate and logical analysis vocabulary.

5

Desvendar a equação ontológica do ser tem sido o escopo primordial da filosofia ocidental.

Unraveling the ontological equation of being has been the primordial scope of Western philosophy.

Philosophical terminology 'ontológica', 'escopo primordial'.

6

A sinfonia resolve a sua própria tensão interna através de uma equação harmônica de rara beleza.

The symphony resolves its own internal tension through a harmonic equation of rare beauty.

Musical analysis using mathematical metaphor.

7

O estadista compreendeu que a equação da paz exigia concessões que a plebe consideraria anátemas.

The statesman understood that the equation of peace required concessions that the plebs would consider anathemas.

Historical and political context with archaic/formal words 'plebe', 'anátemas'.

8

A inexorabilidade da morte é a única constante verdadeira na efêmera equação da vida.

The inexorability of death is the only true constant in the ephemeral equation of life.

Highly poetic and existential reflection.

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