chéngyǐ: 乘以 - To Multiply By

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• Summary: Learn how to say “multiply by” in Chinese with the essential mathematical term 乘以 (chéngyǐ). This page breaks down the characters, explains its use in equations like “3 乘以 5” (3 times 5), and explores the cultural significance of mathematics in China. Perfect for students, this guide provides clear example sentences and distinguishes 乘以 (chéngyǐ) from similar terms, helping you master basic mathematical operations in Mandarin Chinese.

• Pinyin (with tone marks): chéngyǐ
• Part of Speech: Verb
• HSK Level: N/A (Fundamental term for basic numeracy, but not on a specific HSK list)
• Concise Definition: To multiply a number by another number.
• In a Nutshell: 乘以 (chéngyǐ) is the standard and formal way to express “multiplied by” in a mathematical context. It directly translates to “multiply by” and is used in the structure: `Number A 乘以 Number B`. It's the term you would see in a textbook and hear in a classroom when learning math.

• 乘 (chéng): In a mathematical context, this character means “to multiply.” Its original meaning is “to ride” (like a horse or a vehicle). You can think of multiplication as one number “riding” on top of another to increase its value.
• 以 (yǐ): This is a very common classical and formal function word that means “by means of,” “with,” or “by.” In this compound, it clearly specifies what number is being used for the multiplication.
• The two characters combine literally to mean “multiply by,” creating a clear and unambiguous mathematical instruction.

While 乘以 (chéngyǐ) is a universal mathematical term, its usage is tied to the high value placed on numeracy and mathematics in Chinese culture and education. From a very young age, Chinese children learn the `九九乘法表 (jiǔjiǔ chéngfǎ biǎo)`, the “nine-nine multiplication table.” This isn't just a table; it's a rhythmic chant that is memorized by rote until it becomes second nature. This rigorous, foundational training emphasizes speed and accuracy in mental calculation. In the West, while multiplication tables are also taught, there is often more emphasis on conceptual understanding over rote memorization in modern pedagogy. In China, the belief is that absolute mastery of the basics through memorization, using terms like 乘以, frees up mental capacity for more complex problem-solving later on. Therefore, hearing 乘以 might evoke a sense of foundational, rigorous, and essential education for a native Chinese speaker.

• In Education: This is the primary context. 乘以 is the standard term used in textbooks, by teachers, and on exams from primary school through university.
  • Example: 老师说：“请计算七乘以八。” (Lǎoshī shuō: “Qǐng jìsuàn qī chéngyǐ bā.”) - The teacher said: “Please calculate seven multiplied by eight.”
• Formal & Technical Settings: In business, engineering, or finance, when precise calculations are discussed, 乘以 is used to avoid ambiguity.
  • Example: The cost is the unit price multiplied by the quantity. (成本是单价乘以数量。 - Chéngběn shì dānjià chéngyǐ shùliàng.)
• Informal Spoken Chinese: In casual, everyday conversation, it's common to drop the 以 (yǐ) and simply use 乘 (chéng).
  • Example: “三乘五是多少？” (Sān chéng wǔ shì duōshǎo?) - “What's three times five?” This is quicker and more natural for simple mental math. Using the full 乘以 in this context would sound slightly overly formal, like saying “What is the product of three multiplied by five?”

• Example 1:
  • 五乘以二等于十。
  • Pinyin: Wǔ chéngyǐ èr děngyú shí.
  • English: Five multiplied by two equals ten.
  • Analysis: A basic, complete mathematical sentence showing the standard `A 乘以 B 等于 C` (A times B equals C) structure.
• Example 2:
  • 如果你把这个数字乘以三，你会得到什么？
  • Pinyin: Rúguǒ nǐ bǎ zhège shùzì chéngyǐ sān, nǐ huì dédào shénme?
  • English: If you multiply this number by three, what will you get?
  • Analysis: This example uses the common `把 (bǎ)` structure to bring the object (这个数字, this number) before the verb. This is a very natural way to phrase this kind of instruction in Chinese.
• Example 3:
  • 面积是长度乘以宽度计算出来的。
  • Pinyin: Miànjī shì chángdù chéngyǐ kuāndù jìsuàn chūlái de.
  • English: The area is calculated by multiplying the length by the width.
  • Analysis: This demonstrates its use in a formulaic or scientific context.
• Example 4:
  • 任何数乘以零都得零。
  • Pinyin: Rènhé shù chéngyǐ líng dōu dé líng.
  • English: Any number multiplied by zero is zero.
  • Analysis: A great example of a mathematical rule or principle being stated.
• Example 5:
  • 我需要将投资回报率乘以初始本金。
  • Pinyin: Wǒ xūyào jiāng tóuzī huíbàolǜ chéngyǐ chūshǐ běnjīn.
  • English: I need to multiply the return on investment by the initial principal.
  • Analysis: Shows the term's application in a financial or business context. `将 (jiāng)` is used here as a more formal version of `把 (bǎ)`.
• Example 6:
  • 1.5 乘以 4 等于 6。
  • Pinyin: Yī diǎn wǔ chéngyǐ sì děngyú liù.
  • English: 1.5 multiplied by 4 equals 6.
  • Analysis: Demonstrates the usage with decimal numbers. `点 (diǎn)` means “point.”
• Example 7:
  • 请把所有这些费用加起来，然后乘以税率。
  • Pinyin: Qǐng bǎ suǒyǒu zhèxiē fèiyòng jiā qǐlái, ránhòu chéngyǐ shuìlǜ.
  • English: Please add up all these costs, and then multiply by the tax rate.
  • Analysis: This shows 乘以 as part of a multi-step calculation.
• Example 8:
  • 负三乘以负二等于正六。
  • Pinyin: Fù sān chéngyǐ fù èr děngyú zhèng liù.
  • English: Negative three multiplied by negative two equals positive six.
  • Analysis: An example using negative (`负 fù`) and positive (`正 zhèng`) numbers.
• Example 9:
  • 在代数中，我们学习如何将变量x乘以变量y。
  • Pinyin: Zài dàishù zhōng, wǒmen xuéxí rúhé jiāng biànliàng x chéngyǐ biànliàng y.
  • English: In algebra, we learn how to multiply the variable x by the variable y.
  • Analysis: Use of the term in a higher-level academic subject, here with variables.
• Example 10:
  • 这台机器的效率乘以工作时间就是总产量。
  • Pinyin: Zhè tái jīqì de xiàolǜ chéngyǐ gōngzuò shíjiān jiùshì zǒng chǎnliàng.
  • English: This machine's efficiency multiplied by its operating time is the total output.
  • Analysis: This example shows a more abstract, conceptual use of multiplication outside of pure numbers.

• 乘以 (chéngyǐ) vs. 乘 (chéng): This is the most common point of confusion.
  • 乘以 (chéngyǐ): “multiplied by”. More formal, written, and grammatically complete. The structure is `A 乘以 B` (A is multiplied by B).
  • 乘 (chéng): “multiply” or “times”. More colloquial and common in spoken language. `A 乘 B` (A times B).
  • For a beginner, it's safest to use 乘以 in written sentences and 乘 when speaking casually.
• Word Order is Fixed: In English, you can say “multiply A by B” or “B times A” and they mean the same thing. In Chinese, the order `A 乘以 B` is fixed. A is the number being multiplied (the multiplicand), and B is the number doing the multiplying (the multiplier).
  • Correct: `把 10 乘以 5` (bǎ shí chéngyǐ wǔ) - Multiply 10 by 5.
  • Incorrect: `乘以 5 这个 10` - This word order is completely unnatural and wrong.
• Not to be confused with 倍 (bèi): 乘以 (chéngyǐ) is the action of multiplying. 倍 (bèi) is the result or multiple.
  • `10 乘以 2 等于 20。` (10 multiplied by 2 equals 20.) - The action.
  • `20 是 10 的两倍。` (20 shì 10 de liǎng bèi.) - 20 is two times (double) 10. - The state/result.

• 加 (jiā) - To add; plus. The first operation in `加减乘除`.
• 减 (jiǎn) - To subtract; minus.
• 除以 (chúyǐ) - To divide by. The direct counterpart to `乘以`.
• 等于 (děngyú) - To be equal to; equals.
• 乘法 (chéngfǎ) - The noun “multiplication.” While `乘以` is the verb, `乘法` is the concept itself.
• 九九乘法表 (jiǔjiǔ chéngfǎ biǎo) - The “nine-nine multiplication table,” a cornerstone of Chinese primary education.
• 倍 (bèi) - A measure word for “times” or “-fold” (e.g., `三倍` - three times, triple).
• 积 (jī) - The product; the result of a multiplication problem.
• 数学 (shùxué) - Mathematics.
• 计算 (jìsuàn) - To calculate; to compute.