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B1 noun 7 Min. Lesezeit

مخرج

makhraj

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At the A1 level, you don't need to worry about the complex mathematical or phonetic meanings of 'makhraj'. You might only see it if you are looking at a basic math book or if a teacher mentions it briefly. Think of it simply as 'the bottom part of a fraction'. It is a formal word. If you see a fraction like 1/2, the number 2 is the 'makhraj'. You won't use it in daily greetings or shopping, but it is a good word to recognize as you start to see numbers and shapes in Persian. Just remember: it's a technical word for 'the base' of something mathematical.

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By A2, you are expanding your vocabulary to include school-related terms. 'Makhraj' becomes more important if you discuss education or simple math. You should know that 'makhraj' is the denominator and its partner is 'surat' (the numerator). You might also hear it in a very basic way in a religious context, referring to how to say a letter correctly. At this level, just focus on the math meaning. If someone says 'makhraj-e moshtarak' (common denominator), they are usually talking about math problems. It is a noun, and it doesn't change much in simple sentences.

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At the B1 level, you should be comfortable using 'makhraj' in several ways. You understand it is the denominator in math, but you also start to see it in metaphorical contexts. For example, 'finding a common denominator' (makhraj-e moshtarak gereftan) is used when people are trying to find a compromise or a shared goal. You also begin to learn about 'makhraj-e horuf' (the articulation of letters) in your Persian pronunciation lessons. You should be able to identify that this word comes from the root 'to exit' and recognize its plural form 'makharej' which means 'expenses'.

At the B2 level, 'makhraj' is a word you use with precision. You can discuss mathematical concepts or phonetic rules using this term. You understand the nuances between 'makhraj' (a point of exit or base) and 'khoruj' (the act of exiting). In academic or professional discussions, you might use 'makhraj' to describe a technical outlet in engineering or anatomy. You are also proficient in using the idiom 'makhraj-e moshtarak' to describe political or social commonalities. You understand that this word carries a formal, slightly academic tone.

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For C1 learners, 'makhraj' is part of a sophisticated vocabulary. You use it in technical discussions about linguistics, specifically when debating the phonological history of Persian sounds. You are aware of its classical Arabic roots and how it has evolved in Persian literature. You can use it fluently in metaphors and understand its role in complex compound words. You also recognize that in the plural 'makharej', it is the standard term for fiscal expenditures in government or corporate reports. Your usage is precise and contextually appropriate.

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At the C2 level, you have a complete mastery of 'makhraj'. You can analyze classical Persian texts where the word might appear in its archaic sense of 'a way out' or 'a solution'. You can engage in high-level academic discourse on phonetics, discussing the 'makhraj' of various extinct or dialectal sounds. You understand the mathematical implications in advanced calculus or theoretical physics contexts. You can also play with the word in literature or poetry, utilizing its various meanings (base, exit, origin, expense) to create double meanings or sophisticated metaphors.

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Makhraj means 'denominator' in math.
It also means 'articulation point' in phonetics.
The phrase 'makhraj-e moshtarak' means 'common denominator'.
It is a formal word used in schools and technical fields.

The Persian word مخرج (pronounced makh-raj) is a versatile noun rooted in Arabic that primarily serves three distinct domains: mathematics, linguistics, and general physical space. In its most common academic application, it refers to the denominator of a fraction. Just as the denominator in English 'denominates' or names the parts, the Persian makhraj provides the base upon which the numerator (surat) sits. This mathematical utility makes it a staple word for students from primary school through advanced engineering.

Mathematical Context: In the expression 3/4, the number 4 is the makhraj. It represents the total number of equal parts into which a whole is divided.

برای جمع کردن دو کسر، ابتدا باید مخرج مشترک بگیرید.

Translation: To add two fractions, you must first find a common denominator.

Beyond the chalkboard, makhraj is a fundamental term in phonetics and linguistics. It refers to the 'point of articulation'—the specific part of the vocal tract (throat, tongue, teeth, lips) where a speech sound is produced. For anyone studying Persian or Arabic phonology, understanding the makhraj of each letter is essential for correct pronunciation. This usage is particularly prominent in religious contexts, such as Tajweed (the art of Quranic recitation), where the precise origin of sounds is a matter of spiritual and technical significance.

Linguistic Context: The makhraj of the letter 'B' in Persian is the meeting of the two lips.

Finally, in a more literal or archaic sense, makhraj can mean an outlet or exit. While modern Persian speakers usually prefer the word khoruj or khoruji for physical exits (like a door), makhraj persists in technical literature, anatomy (referring to bodily outlets), and metaphorical expressions. For instance, finding a 'common ground' or 'common denominator' in a social or political argument uses the phrase makhraj-e moshtarak, bridging the gap between math and human relations.

این لوله تنها مخرج آب از مخزن است.

Translation: This pipe is the only outlet for water from the tank.

Whether you are solving a math problem, perfecting your Persian accent, or discussing complex social issues, makhraj provides the structural foundation for the conversation. It is a word that signifies the origin, the base, and the point of departure.

Using مخرج correctly requires identifying whether you are in a formal, mathematical, or linguistic setting. In mathematics, it is almost always paired with its counterpart surat (numerator). When constructing sentences about fractions, the word makhraj functions as a standard noun that can take adjectives or be part of an Ezafe construction.

Fractional Usage: If you want to say 'The denominator is larger than the numerator,' you would say: Makhraj az surat bozorgtar ast.

اگر مخرج کسر صفر باشد، کسر تعریف‌نشده است.

Translation: If the denominator of a fraction is zero, the fraction is undefined.

In phonetics, you will often use the word in the context of learning or teaching. Teachers might tell students to 'pay attention to the makhraj of the letter Qaf.' Here, the word acts as a technical specification for physical movement. It is common to see it in instructional books about Persian grammar or Quranic studies.

استاد بر مخرج صحیح حروف تأکید داشت.

Translation: The professor emphasized the correct articulation point of the letters.

Metaphorically, the phrase makhraj-e moshtarak (common denominator) is extremely useful in debates. It describes finding a shared point between two conflicting ideas. You might say, 'We need to find a common denominator for our cooperation.' This elevates the word from simple math to high-level diplomatic and social discourse.

Metaphorical Usage: Finding a 'makhraj-e moshtarak' is the key to resolving many political disputes in Persian-speaking societies.

If you are a student in Iran, Afghanistan, or Tajikistan, the first place you will encounter مخرج is the mathematics classroom. From the age of ten onwards, teachers repeat this word daily while teaching fractions, decimals, and algebra. It is as fundamental to a Persian-speaking child's education as the word 'plus' or 'minus'.

بچه‌ها، وقتی مخرج‌ها مساوی نیستند، نمی‌توانید صورت‌ها را با هم جمع کنید.

Translation: Kids, when the denominators are not equal, you cannot add the numerators together.

The second most common environment is the religious school or mosque. In the study of Tajweed, which is the melodic and correct recitation of the Quran, the makhraj is the 'home' of the sound. Students are taught exactly where in the throat or mouth the air should be constricted to produce sounds like 'Ghayn' or 'Haa'. You will hear teachers say, 'Your makhraj for the letter 'Ayn' is too high in the throat.'

In modern media and political analysis, you will hear the term makhraj-e moshtarak during talk shows and debates. Analysts use it to describe the shared interests between nations or political parties. For example, a news anchor might ask, 'What is the common denominator between the economic policies of these two candidates?' This usage is very common in formal Persian news broadcasts like IRIB or BBC Persian.

News & Media: Analysts often seek a 'makhraj-e moshtarak' to explain complex geopolitical alliances.

Lastly, in technical engineering or medical fields, the word describes an outlet. A plumber might refer to the makhraj of a pipe system, or a doctor might use it in an anatomical sense. While less frequent in daily shopping or casual dining, it remains a vital term for anyone engaging with the Persian language at a professional or academic level.

One of the most frequent mistakes learners make is confusing مخرج (makhraj) with خارج (kharej). While both share the same root (K-R-J, meaning 'to go out'), kharej means 'outside' or 'abroad,' whereas makhraj is the 'place' or 'point' of exiting or the mathematical 'denominator'. You cannot use them interchangeably.

Wrong vs. Right: Wrong: Man be makhraj-e keshvar raftam. (I went to the denominator of the country.)
Right: Man be kharej az keshvar raftam. (I went abroad.)

Another common error is confusing makhraj with khoruj. Khoruj is the act of exiting or the 'Exit' sign you see above a door. If you are looking for the way out of a cinema, you should look for the khoruji sign, not the makhraj. Using makhraj in a mall might make people think you are looking for a math tutor or a speech therapist!

اشتباه متداول: استفاده از مخرج به جای خروجی اضطراری.

Translation: Common mistake: Using 'makhraj' instead of 'emergency exit'.

In mathematical contexts, learners sometimes swap makhraj (denominator) with surat (numerator). A helpful way to remember is that surat means 'face' or 'top' (at the top of the fraction), and makhraj is the 'foundation' or 'exit point' at the bottom. If you flip them, your math results will be the reciprocal of what you intended!

Lastly, be careful with the pronunciation. Some dialects might shift the vowels slightly, but in standard Persian, it is clearly makh-raj. Pronouncing it as mokh-rej changes the meaning to 'producer' or 'expeller' (rarely used), which can cause confusion in technical discussions.

While مخرج is the precise term for a denominator, there are several related words depending on the context. If you are speaking informally to a child about math, you might simply say adad-e payin (the bottom number), but this is not professional. In formal writing, makhraj is irreplaceable.

Comparison: Makhraj vs. Khoruj: Makhraj: Technical point of origin or mathematical base.
Khoruj: The general action of leaving or a physical exit door.

In the context of phonetics, synonyms are rare because makhraj is the standard technical term. However, you might hear mahal-e talaffoz (place of pronunciation). While mahal-e talaffoz is easier for beginners to understand, makhraj is what you will find in every textbook on the subject.

محل تلفظ (Mahal-e Talaffoz) vs مخرج (Makhraj)

Note: The former is descriptive, the latter is technical.

For the meaning of 'outlet' or 'expenditure,' the word makhraj is historically related to makharej (plural), which means 'expenses' or 'costs'. If you are talking about money going out of your pocket, you use the plural form makharej. This is a very common word in daily life, referring to the cost of living or business overheads.

Financial Connection: Makharej (Plural): Costs/Expenses. 'Makharej-e zendegi' means 'living expenses'.

How Formal Is It?

Wusstest du?

The same root gives us 'Kharj' (spending/cost) and 'Kharej' (outside). When you spend money, it 'exits' your wallet, and the 'makhraj' is the point of that exit!

Aussprachehilfe

UK /mæxˈɾædʒ/

US /mɑːxˈrædʒ/

The primary stress is on the second syllable 'raj'.

Reimt sich auf

ایرج (Iraj) اخرج (Akhraj) درج (Darj) خرج (Kharj) برج (Borj) فرج (Faraj) کرج (Karaj) مرج (Marj)

Häufige Fehler

Pronouncing 'kh' as a hard 'k' (it should be breathy).
Confusing it with 'Mokhrej' (which means producer).
Swapping the vowels to sound like 'Makhrej' (common in some dialects but less formal).
Failing to roll the 'r' slightly.
Pronouncing the 'j' too softly like 'zh'.

Schwierigkeitsgrad

Lesen 3/5

Easy to read but requires context to distinguish math from phonetics.

Schreiben 4/5

Requires correct spelling of the 'kh' (خ) and 'j' (ج).

Sprechen 4/5

The 'kh' sound can be tricky for English speakers.

Hören 3/5

Clear pronunciation in formal speech.

Was du als Nächstes lernen solltest

Voraussetzungen

عدد (Number) کسر (Fraction) حرف (Letter) خارج (Outside)

Als Nächstes lernen

صورت (Numerator) تقسیم (Division) تلفظ (Pronunciation) واج‌شناسی (Phonology)

Fortgeschritten

اتحاد (Identity/Algebra) تجزیه (Factorization) مخرج‌مشترک‌گیری (Common denominator finding)

Wichtige Grammatik

Ezafe Construction

مخرجِ کسر (Makhraj-e kasr)

Pluralization with -ha

مخرج‌ها (Makhraj-ha)

Arabic Broken Plural

مخارج (Makharej - used for expenses)

Compound Verbs with 'Gereftan'

مخرج مشترک گرفتن

Adjective placement

مخرجِ مشترک (Common denominator)

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Beispiele nach Niveau

این عدد مخرج کسر است.

This number is the denominator of the fraction.

Simple sentence with 'ast' (is).

مخرج کسر دو است.

The denominator of the fraction is two.

Subject + Complement + Verb.

صورت و مخرج را ببین.

Look at the numerator and denominator.

Imperative sentence.

مخرج کجاست؟

Where is the denominator?

Question with 'koja' (where).

مخرج این کسر بزرگ است.

The denominator of this fraction is big.

Adjective 'bozorg' modifying 'makhraj'.

یک مخرج بنویس.

Write a denominator.

Indefinite 'ye' (a/one).

مخرج نباید صفر باشد.

The denominator must not be zero.

Negative modal 'nabayad' (must not).

این مخرج کسر من است.

This is my fraction's denominator.

Possessive Ezafe construction.

مخرج این دو کسر با هم برابر است.

The denominators of these two fractions are equal.

Comparative 'ba ham barabar' (equal to each other).

او مخرج کسر را اشتباه نوشت.

He wrote the denominator of the fraction incorrectly.

Simple past tense 'nevesht'.

آیا مخرج مشترک را پیدا کردی؟

Did you find the common denominator?

Question in past tense.

مخرج کسر را تغییر بده.

Change the denominator of the fraction.

Compound verb 'taghyir dadan'.

مخرج حروف را در کلاس یاد گرفتیم.

We learned the articulation of letters in class.

Plural 'horuf' (letters).

این مخرج برای این صدا نیست.

This articulation point is not for this sound.

Negative 'nist' (is not).

مخرج کسر را در عدد دو ضرب کن.

Multiply the denominator of the fraction by the number two.

Imperative 'zarb kon'.

ما به دنبال یک مخرج مشترک هستیم.

We are looking for a common denominator.

Present continuous sense 'hastim'.

برای حل این مسئله، باید مخرج‌ها را یکسان کنیم.

To solve this problem, we must make the denominators the same.

Use of 'bayad' + subjunctive.

مخرج صحیح این حرف از ته گلو است.

The correct articulation of this letter is from the back of the throat.

Prepositional phrase 'az tah-e galu'.

آنها نتوانستند مخرج مشترکی برای صلح پیدا کنند.

They couldn't find a common denominator for peace.

Metaphorical usage.

مخرج کسر دوم را ساده کنید.

Simplify the denominator of the second fraction.

Ordinal number 'dovvom' (second).

تلفظ شما به دلیل مخرج اشتباه، نامفهوم است.

Your pronunciation is unclear because of the wrong articulation point.

Reasoning with 'be dalil-e'.

این کلمه مخرج‌های متفاوتی در گویش‌های مختلف دارد.

This word has different articulation points in different dialects.

Plural 'makhraj-ha'.

مخرج کسر نشان‌دهنده تعداد کل اجزا است.

The denominator of the fraction represents the total number of parts.

Present participle 'neshan-dahande'.

او مخرج تمام هزینه‌هایش را ثبت می‌کند.

He records the source of all his expenses.

Note: Here 'makhraj' is used slightly archaically for 'source/outlet'.

در ریاضیات پیشرفته، مخرج کسر می‌تواند یک عبارت جبری باشد.

In advanced mathematics, the denominator of a fraction can be an algebraic expression.

Formal register.

شناخت مخرج حروف برای قاریان قرآن الزامی است.

Knowing the articulation points of letters is mandatory for Quran reciters.

Gerund 'shenakht' (knowing).

سیاستمداران به دنبال مخرج مشترک برای همکاری‌های اقتصادی هستند.

Politicians are looking for a common denominator for economic cooperation.

Abstract usage.

اگر مخرج کسر به سمت بی‌نهایت برود، مقدار کسر به صفر نزدیک می‌شود.

If the denominator of the fraction goes toward infinity, the value of the fraction approaches zero.

Conditional 'agar' with 'beravad' (subjunctive).

مخرج این لوله به فاضلاب شهری متصل است.

The outlet of this pipe is connected to the city sewage system.

Technical usage.

نویسنده در این مقاله، مخرج مشترک تمام بحران‌ها را فقر می‌داند.

The author, in this article, considers poverty to be the common denominator of all crises.

Reporting verb 'midanad'.

مخرج این حرف با حرف 'ح' متفاوت است.

The articulation point of this letter is different from the letter 'H'.

Comparison with 'ba... motafavit'.

باید مخرج کسر را گویا کنید.

You must rationalize the denominator of the fraction.

Mathematical term 'guya kardan'.

تحلیل فونتیک زبان‌های باستانی نیازمند بررسی دقیق مخرج حروف است.

Phonetic analysis of ancient languages requires a careful examination of letter articulation points.

Academic register.

ایجاد یک مخرج مشترک فرهنگی می‌تواند به کاهش تنش‌های منطقه‌ای کمک کند.

Creating a cultural common denominator can help reduce regional tensions.

Complex noun phrase as subject.

در این فرمول، مخرج کسر تابعی از زمان تعریف شده است.

In this formula, the denominator of the fraction is defined as a function of time.

Passive construction 'ta'rif shode ast'.

او با مهارت تمام، مخرج هر واژه را با دقت ادا می‌کرد.

With complete skill, he pronounced the articulation point of every word with precision.

Adverbial phrase 'ba maharat-e tamam'.

مخرج‌های مالی دولت در سال گذشته به شدت افزایش یافت.

The government's financial expenditures increased sharply last year.

Plural noun in financial context.

این نظریه، مخرج مشترک تمام ادیان ابراهیمی را توحید می‌داند.

This theory considers monotheism to be the common denominator of all Abrahamic religions.

Philosophical context.

برای درک بهتر مفاهیم، باید مخرج کلام را یافت.

To better understand the concepts, one must find the 'makhraj' (origin/essence) of the speech.

Literary/Metaphorical usage.

تغییر در مخرج کسر باعث تغییر کلی در تراز مالی می‌شود.

A change in the denominator of the fraction causes a total change in the financial balance.

Cause and effect sentence.

واکاوی مخرج‌های واژگانی در متون کلاسیک، تحولات آوایی را آشکار می‌سازد.

Analyzing lexical articulation points in classical texts reveals phonetic evolutions.

Highly formal/Academic.

مخرج مشترک این دو گفتمان متضاد، در لایه‌های پنهان قدرت نهفته است.

The common denominator of these two opposing discourses lies in the hidden layers of power.

Sophisticated vocabulary ('gofteman', 'nahofte').

در محاسبات کوانتومی، مخرج کسرها اغلب شامل ثابت‌های فیزیکی پیچیده است.

In quantum calculations, the denominators of fractions often include complex physical constants.

Scientific context.

تمایز میان مخرج و منشأ در فلسفه زبان، موضوعی بحث‌برانگیز است.

The distinction between 'makhraj' (outlet/point) and 'mansha' (origin) in the philosophy of language is a controversial topic.

Philosophical terminology.

او به چنان درجه‌ای از تسلط رسیده بود که مخرج حروف را در خواب نیز رعایت می‌کرد.

He had reached such a degree of mastery that he observed the articulation points of letters even in his sleep.

Hyperbolic literary expression.

مخرج مشترک تمام این تراژدی‌ها، نسیان تاریخی جامعه است.

The common denominator of all these tragedies is the historical forgetfulness of society.

Abstract sociological observation.

در این ساختار معماری، مخرج آب به گونه‌ای طراحی شده که کمترین فرسایش را ایجاد کند.

In this architectural structure, the water outlet is designed in such a way as to create the least erosion.

Technical architectural description.

پژوهشگر بر این باور است که مخرج مشترک این دو گونه زبانی، ریشه در پهلوی اشکانی دارد.

The researcher believes that the common denominator of these two linguistic species is rooted in Parthian Pahlavi.

Historical linguistic context.

Häufige Kollokationen

مخرج مشترک

مخرج کسر

مخرج حروف

مخرج مشترک یافتن

مخرج صوتی

مخرج فاضلاب

مخرج طبیعی

مخرج کلام

گویا کردن مخرج

مخرج صفر

Häufige Phrasen

مخرج مشترک گرفتن

— To find a common denominator (math) or to find common ground (metaphor).

برای حل این مشکل سیاسی باید مخرج مشترک بگیریم.

مخرج حروف تهلقی

— Articulation points of throat letters in phonetics.

مخرج حروف حلقی در انتهای گلو است.

مخرج کسر بزرگ

— A large denominator, often implying a small total value.

هر چه مخرج کسر بزرگتر باشد، مقدار کسر کمتر است.

ساده کردن مخرج

— To simplify the denominator.

قبل از محاسبه، مخرج را ساده کن.

مخرج نهایی

— The final outlet or final denominator.

مخرج نهایی این لوله‌ها به دریا می‌رسد.

مخرج یکسان

— Identical denominator.

این دو کسر مخرج یکسان دارند.

مخرج متفاوت

— Different denominator.

جمع کردن کسرهای با مخرج متفاوت سخت‌تر است.

مخرج نامعلوم

— Unknown denominator.

در این معادله، مخرج نامعلوم است.

مخرج گویا

— Rational denominator.

جواب نهایی باید مخرج گویا داشته باشد.

مخرج مشترک فرهنگی

— Cultural common ground.

موسیقی مخرج مشترک فرهنگی ماست.

Wird oft verwechselt mit

مخرج vs خارج (Kharej)

Means 'outside' or 'abroad'. Often confused because of the same root.

مخرج vs خروجی (Khoruji)

Means a physical exit door or electronic outlet. Makhraj is more technical or mathematical.

مخرج vs مخرج (Mokhrej)

The active participle meaning 'one who expels' or 'producer'. Very rare in common Persian.

Redewendungen & Ausdrücke

"مخرج مشترک داشتن"

— To have something in common, especially in a way that allows for cooperation.

این دو حزب با هم مخرج مشترک دارند.

formal

"مخرج کلام را گرفتن"

— To get to the point or the essence of what someone is saying.

بالاخره مخرج کلام او را فهمیدم.

literary

"بی‌مخرج و مدخل"

— Something that has no clear beginning or end; confusing.

حرف‌هایش بی‌مخرج و مدخل بود.

archaic

"مخرج پیدا کردن"

— To find a way out of a difficult situation.

باید برای این بن‌بست یک مخرج پیدا کنیم.

neutral

"مخرج مشترک گرفتن از اختلافات"

— To find a way to reconcile or group different problems together.

او سعی کرد از تمام اختلافات ما مخرج مشترک بگیرد.

formal

"در مخرج ماندن"

— To be stuck at the base or not making progress (rare/slang).

توی مخرج این مسئله گیر کرده‌ام.

informal

"مخرج زدن"

— To create an outlet or opening (technical).

باید برای این تانک یک مخرج جدید بزنیم.

technical

"از یک مخرج بودن"

— To come from the same source or origin.

تمام این مشکلات از یک مخرج هستند.

neutral

"مخرج کسر زندگی"

— A metaphorical way of referring to the base or fundamental needs of life.

پول مخرج کسر زندگی نیست، اما مهم است.

poetic

"مخرج کلامش یکی بود"

— He kept saying the same thing; he had one main point.

هر چه گفت، مخرج کلامش یکی بود.

neutral

Leicht verwechselbar

مخرج vs صورت (Surat)

It's the partner of makhraj in fractions.

Surat is the top (numerator), Makhraj is the bottom (denominator).

صورت کسر سه و مخرج آن چهار است.

مخرج vs مخارج (Makharej)

It is the plural of makhraj but has a specific meaning.

Makharej almost always refers to 'expenses' or 'costs' in daily life.

مخارج سفر بسیار زیاد بود.

مخرج vs خروج (Khoruj)

Both relate to 'exiting'.

Khoruj is the 'act' of leaving; Makhraj is the 'point' or 'place' or 'denominator'.

خروج از اتاق ممنوع است.

مخرج vs مجرا (Majra)

Both can mean a passage or outlet.

Majra is a 'channel' or 'course' (like a river), while makhraj is specifically the 'outlet'.

این مجرای آب به مخرج اصلی می‌رسد.

مخرج vs منبع (Manba)

Sometimes people confuse the source with the outlet.

Manba is the 'source' (input), Makhraj is the 'outlet' (output).

منبع رودخانه در کوه و مخرج آن در دریاست.

Satzmuster

این [noun] مخرج است.

این عدد مخرج است.

مخرج کسر [number] است.

مخرج کسر ده است.

باید برای [noun] مخرج مشترک بگیریم.

باید برای کسرها مخرج مشترک بگیریم.

مخرج این حرف در [location] است.

مخرج این حرف در گلو است.

اگر مخرج [condition]، آنگاه [result].

اگر مخرج صفر باشد، کسر تعریف نمی‌شود.

مخرج مشترکِ [concept] و [concept] در [concept] نهفته است.

مخرج مشترک هنر و سیاست در جامعه نهفته است.

با تکیه بر مخرجِ [noun]، می‌توان [verb].

با تکیه بر مخرج کلام، می‌توان حقیقت را یافت.

واکاویِ مخرج‌هایِ [noun] نشان‌دهنده [noun] است.

واکاوی مخرج‌های آوایی نشان‌دهنده تحول زبان است.

Wortfamilie

Substantive

خروج (Exit)

خروجی (Outlet)

مخارج (Expenses)

خارج (Outside)

Verben

خارج شدن (To exit)

خارج کردن (To extract/take out)

Adjektive

خارجی (Foreign/External)

خارج از مرکز (Eccentric)

Verwandt

کسر (Fraction)

صورت (Numerator)

تلفظ (Pronunciation)

واج (Phoneme)

حساب (Arithmetic)

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So verwendest du es

frequency

High in educational and technical contexts; medium in general speech.

Häufige Fehler

Using 'kharej' for denominator. → makhraj
Kharej means 'outside'; makhraj is the technical term for denominator.
Saying 'makhraj' for a building exit. → khoruji
Makhraj is technical/math; khoruji is for doors/signs.
Confusing surat and makhraj. → surat (top), makhraj (bottom)
Learners often flip the two terms in math problems.
Pronouncing it 'makh-raz'. → makh-raj
The last letter is a 'j' sound, not a 'z'.
Using 'makhraj' for 'expenses' in singular. → makharej (plural)
While 'makhraj' is the root, the plural 'makharej' is the standard term for costs.

Tipps

Using Ezafe

Always use the Ezafe (short 'e' sound) when linking makhraj to another noun, like 'makhraj-e kasr'.

Math Pairs

Learn 'surat' and 'makhraj' together as a pair. It makes remembering them much easier.

The 'Kh' Sound

Don't be afraid to make a little noise in your throat for the 'kh'. It's a very common sound in Persian.

Metaphorical Use

Use 'makhraj-e moshtarak' in debates to sound more fluent and sophisticated.

Spelling

Remember that makhraj ends with 'jim' (ج), not 'che' (چ) or 'ze' (ز).

Religious Context

If you hear this word in a mosque, it's almost certainly about how to pronounce the Quran correctly.

Expenses

If you see 'makharej' in a bank app, it means your spending/expenses.

The Root

Connecting 'makhraj' to 'exit' will help you understand all its technical meanings.

Rationalizing

The phrase 'guya kardan-e makhraj' is a common high school math term you might encounter.

Visualizing

Visualize the 'makhraj' as the basement of a house where the 'exit' is located.

Einprägen

Eselsbrücke

Imagine a fraction as a building. The 'Surat' (Face) is looking out the top window, and the 'Makhraj' is the 'Exit' (Garage) at the bottom.

Visuelle Assoziation

Picture the letter 'M' in Makhraj as looking like a pair of legs at the bottom of a fraction, supporting the whole thing.

Word Web

Math Fraction Denominator Exit Outlet Phonetics Articulation Expense

Herausforderung

Try to find a 'makhraj-e moshtarak' (common denominator) between your favorite hobby and your job, and write a sentence about it in Persian.

Wortherkunft

Derived from the Arabic root 'خ-ر-ج' (K-R-J), which relates to the concept of 'going out' or 'exiting'. In Arabic, 'makhraj' is a 'noun of place' (Ism al-Makan), meaning 'the place from which something exits'.

Ursprüngliche Bedeutung: A place of exit or an outlet.

Semitic (Arabic) root, adopted into Persian.

Kultureller Kontext

No specific sensitivities, but ensure you don't confuse it with 'makharej' (expenses) in a context where money isn't being discussed.

English speakers use 'denominator' which comes from 'naming'. Persian uses 'makhraj' which comes from 'exiting'. This reflects different conceptual approaches to math.

Used extensively in the works of Al-Khwarizmi (the father of Algebra). Commonly found in 'Tajweed' manuals for Quranic recitation. Frequently used in modern Iranian political talk shows like 'Pargar'.

Im Alltag üben

Kontexte aus dem Alltag

Math Class

مخرج کسر
مخرج مشترک
ساده کردن مخرج
ضرب در مخرج

Linguistics Class

مخرج حروف
محل مخرج
تولید صدا در مخرج
اصلاح مخرج

Plumbing/Engineering

مخرج لوله
مخرج آب
بستن مخرج
مخرج اضطراری

Politics/Debate

مخرج مشترک یافتن
مخرج مشترک سیاسی
رسیدن به مخرج مشترک
مخرج کلام

Finance

مخارج زندگی
کنترل مخارج
کاهش مخارج
مخارج سالانه

Gesprächseinstiege

"چطور می‌توانیم برای این دو کسر مخرج مشترک بگیریم؟"

"آیا می‌دانید مخرج حرف 'ق' دقیقاً کجاست؟"

"به نظر شما مخرج مشترک تمام این مشکلات اقتصادی چیست؟"

"آیا مخرج این لوله به فاضلاب اصلی وصل است؟"

"چگونه مخرج کسر را در این مسئله گویا کردی؟"

Tagebuch-Impulse

درباره زمانی بنویسید که مجبور بودید در یک بحث، مخرج مشترکی با دیگران پیدا کنید.

تفاوت بین صورت و مخرج کسر را به زبان ساده برای یک کودک توضیح دهید.

چرا یادگیری مخرج حروف برای یادگیری یک زبان جدید مهم است؟

لیستی از مخارج (هزینه‌های) ماهانه خود تهیه کنید و مخرج اصلی آن‌ها را بیابید.

اگر زندگی یک کسر بود، مخرج کسر زندگی شما چه چیزی می‌بود؟

Häufig gestellte Fragen

10 Fragen

No, while it is the most common use in school, it also means the point where a sound is produced in speech (phonetics) and can refer to a physical outlet in technical contexts.

The regular plural is 'makhraj-ha'. The Arabic broken plural 'makharej' is also used, but it usually means 'expenses' or 'costs' in modern Persian.

You say 'makhraj-e moshtarak' (مخرج مشترک). It is used for both math and finding common ground between people.

Usually no. For a door, use 'khoruji' (خروجی). 'Makhraj' is more for a pipe's outlet or a technical exit point.

The opposite is 'surat' (صورت), which means the numerator.

It refers to the 'exit point' of air when making a sound. Each letter has a specific 'makhraj' in the mouth or throat.

Not directly, but 'makhraj-e kalam' can mean the 'bottom line' or 'essence' of what someone is saying.

Yes, it is a technical and formal word. In very casual speech, people might say 'adad-e payin' (the bottom number) for math.

It is spelled 'مخرج' (Mim-Khe-Re-Jim).

No, it is a raspy sound made in the throat, like the 'ch' in 'Loch Ness' or the Spanish 'j' in 'Juan'.

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