Division is a math operation that tells how many equal groups you can make or how many are in each group. In English, we describe division using the ideas of sharing equally and splitting into equal parts. A division statement connects four roles: the number being divided, the number you divide by, the result, and sometimes what is left over.

English division vocabulary names each part of the operation so you can read and explain a calculation clearly. The same idea can be expressed with different words depending on whether you focus on groups, sharing, or measurement. Knowing the standard terms helps you understand textbooks, word problems, and spoken explanations.

Word/Phrase	🇨🇳 中文 词/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
dividend	🧩 被除数	the number being divided	🧩 the number being divided	12 is the dividend in 12 ÷ 3	🧩 12 是 12 ÷ 3 中的被除数
divisor	🧩 除数	the number you divide by	🧩 the number you divide by	3 is the divisor in 12 ÷ 3	🧩 3 是 12 ÷ 3 中的除数
quotient	🧩 商	the answer to a division	🧩 the answer to a division	4 is the quotient in 12 ÷ 3	🧩 4 是 12 ÷ 3 中的商
remainder	🧩 余数	what is left after equal groups	🧩 相等分组后剩下的部分	14 ÷ 3 has remainder 2	🧩 14 ÷ 3 的余数是 2
factor	🧩 因数	a number that divides another number exactly	🧩 能整除另一个数的数	3 is a factor of 12	🧩 3 是 12 的一个因数
multiple	🧩 倍数	a result of multiplying a number	🧩 某数相乘得到的结果	12 is a multiple of 3	🧩 12 是 3 的一个倍数

Division can be written with different symbols in English materials. You should be able to say each symbol aloud and recognize that they all represent the same operation. Some symbols are more common in school, while others appear more in higher math or on calculators.

Word/Phrase	🇨🇳 中文 词/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
÷	🧩 ÷	division sign, said as divided by	🧩 除号，读作“divided by”	12 ÷ 3 is twelve divided by three	🧩 12 ÷ 3 表示 12 除以 3
/	🧩 /	slash used for division, often in typing	🧩 用于表示除法的斜杠，常在打字时使用	12/3 is twelve over three	🧩 12/3 表示 12 除以 3
a fraction bar	🧩 分数线	division written as a fraction	🧩 将除法写成分数	12 over 3 equals 4	🧩 12/3 等于 4
long division bracket	🧩 长除法括号	layout for step by step division	🧩 逐步除法的排版	3 goes into 12	🧩 3 能进入 12 的次数

English has several natural sentence patterns for division, and each highlights a different viewpoint. Choose the pattern that matches what you want to emphasize, such as the operation, the result, or the equal sharing idea. Being consistent with wording makes explanations easier to follow.

Word/Phrase	🇨🇳 中文 词/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
divided by	🧩 divided by	standard way to read ÷	🧩 读 ÷ 的标准方式	Twelve divided by three equals four	🧩 Twelve divided by three equals four
over	🧩 over	common for / and fractions	🧩 在 / 与分数中常见	Twelve over three equals four	🧩 Twelve over three equals four
split into	🧩 split into	focuses on dividing into equal groups	🧩 侧重将其分成相等的组	Split 12 into 3 equal groups	🧩 将 12 分成 3 个相等的组
shared equally among	🧩 shared equally among	focuses on fair sharing	🧩 侧重于公平分配	12 cookies shared equally among 3 kids	🧩 12 片饼干在 3 个孩子之间平均分配
goes into	🧩 goes into	common in long division speech	🧩 长除法口语中常见	Three goes into twelve four times	🧩 3 能在 12 中进入 4 次
per	🧩 per	expresses a unit rate from division	🧩 表示通过除法得到的单位价格	12 dollars for 3 items is 4 dollars per item	🧩 12 美元买 3 件，单位价格为每件 4 美元

Division results in English are described differently depending on whether the division is exact. If a remainder appears, English often names it explicitly, especially in school math. The same remainder can also be expressed as a fraction or a decimal, so you should recognize these as equivalent ways to report the result.

Rule	🇨🇳 中文 规则	Example	🇨🇳 中文 示例
If the divisor divides the dividend exactly, say the quotient with no remainder	📌 If the divisor divides the dividend exactly, say the quotient with no remainder	12 ÷ 3 = 4, the division is exact	📌 12 ÷ 3 = 4，除法是整除的
If something is left, state the remainder using remainder or r	📌 If something is left, state the remainder using remainder or r	14 ÷ 3 = 4 remainder 2, or 4 r 2	📌 14 ÷ 3 = 4 remainder 2, or 4 r 2
You can convert a remainder to a mixed number	📌 You can convert a remainder to a mixed number	14 ÷ 3 = 4 2/3	📌 14 ÷ 3 = 4 2/3
You can convert a remainder to a decimal when appropriate	📌 You can convert a remainder to a decimal when appropriate	14 ÷ 3 ≈ 4.67	📌 14 ÷ 3 ≈ 4.67

Long division uses special spoken vocabulary to describe each step. English explanations often follow a predictable sequence so listeners can track where each number comes from. Understanding these phrases helps you follow classroom instruction and written solution walkthroughs.

Word/Phrase	🇨🇳 中文 词/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
goes into	🧩 goes into	asks how many times the divisor fits	🧩 询问除数能容纳多少次	4 goes into 20 five times	🧩 4 能把 20 除以 5 次
times	🧩 times	multiplication step inside division	🧩 除法内部的乘法步骤	5 times 4 is 20	🧩 5 乘以 4 等于 20
subtract	🧩 subtract	remove the product to find what remains	🧩 移去积以找出剩余	Subtract 20 from 20	🧩 从 20 中减去 20
bring down	🧩 bring down	move the next digit into the working number	🧩 将下一位数字带入工作数字	Bring down the 6	🧩 把 6 提到被除数中
repeat the steps	🧩 repeat the steps	continue until all digits are used	🧩 继续直到所有数字都被使用	Repeat until you reach the last digit	🧩 直到到达最后一位数字重复步骤

Word problems often describe division without showing a symbol, so you must recognize division meaning from vocabulary. Some problems ask for the number of groups, while others ask for the size of each group. Identifying which quantity is unknown helps you set up the correct division expression.

Rule	🇨🇳 中文 规则	Example	🇨🇳 中文 示例
If the problem says shared equally, it signals division	📌 If the problem says shared equally, it signals division	15 stickers shared equally among 5 friends	📌 15 贴纸平均分给 5 个朋友
If it asks how many each, it usually asks for the quotient	📌 If it asks how many each, it usually asks for the quotient	How many stickers does each friend get	📌 每个朋友得到多少张贴纸
If it asks how many groups, divide to find the number of groups	📌 If it asks how many groups, divide to find the number of groups	How many boxes can you fill with 24 apples if each holds 6	📌 如果每盒装 6 个苹果，24 个苹果可以装满多少盒？
Words like per often mean division to find a unit rate	📌 Words like per often mean division to find a unit rate	120 miles in 3 hours is 40 miles per hour	📌 120 miles in 3 hours is 40 miles per hour

In English math language, division is the inverse of multiplication, meaning one operation undoes the other. This relationship is used to check answers and to explain why division facts connect to multiplication facts. Understanding inverse language helps you follow explanations about fact families and checking work.

Rule	🇨🇳 中文 规则	Example	🇨🇳 中文 示例
If a ÷ b = c, then c × b = a	📌 If a ÷ b = c, then c × b = a	If 12 ÷ 3 = 4, then 4 × 3 = 12	📌 If 12 ÷ 3 = 4, then 4 × 3 = 12
Use multiplication to check a division result	📌 Use multiplication to check a division result	Check 14 ÷ 3: 4 × 3 = 12, plus remainder 2 makes 14	📌 Check 14 ÷ 3: 4 × 3 = 12, plus remainder 2 makes 14
Exact division means the divisor is a factor of the dividend	📌 Exact division means the divisor is a factor of the dividend	3 is a factor of 12 because 12 ÷ 3 is an integer	📌 3 is a factor of 12 because 12 ÷ 3 is an integer

English often treats a fraction as a division statement, where the numerator is divided by the denominator. This connects division vocabulary to fraction vocabulary like numerator and denominator. Recognizing this equivalence helps when rewriting expressions and interpreting math text.

Word/Phrase	🇨🇳 中文 词/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
numerator	🧩 numerator	top number in a fraction, the dividend	🧩 分数中的分子，即被除数	In 3/4, 3 is the numerator	🧩 在 3/4 中，3 是分子
denominator	🧩 denominator	bottom number in a fraction, the divisor	🧩 分数中的分母，即除数	In 3/4, 4 is the denominator	🧩 在 3/4 中，4 是分母
fraction equals division	🧩 fraction equals division	a/b means a divided by b	🧩 a/b means a divided by b	3/4 means three divided by four	🧩 3/4 means three divided by four
simplify	🧩 simplify	reduce a fraction by dividing by a common factor	🧩 通过公因子约简分数	6/8 simplifies to 3/4	🧩 6/8 化简为 3/4

When division produces decimals, English explanations often mention place value and rounding. In real life contexts, you may also hear approximation language to show the result is not exact. Knowing these terms helps you interpret calculator results and measurements.

Word/Phrase	🇨🇳 中文 词/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
decimal point	🧩 decimal point	dot that separates whole and fractional parts	🧩 将整数部分和小数部分分开的点	4.5 has a decimal point	🧩 4.5 有小数点
terminate	🧩 terminate	decimal ends after a certain place	🧩 小数在某一位后就结束	1 ÷ 4 = 0.25, it terminates	🧩 1 ÷ 4 = 0.25，它是有限小数
repeat	🧩 repeat	decimal pattern continues	🧩 小数模式继续	1 ÷ 3 = 0.333..., it repeats	🧩 1 ÷ 3 = 0.333...，它是循环小数
round to	🧩 round to	shorten a decimal to a place value	🧩 将小数四舍五入到某一位	Round 4.666... to 4.67	🧩 将 4.666... 四舍五入为 4.67
approximately	🧩 approximately	indicates an estimate close to the value	🧩 表示接近该值的估算	14 ÷ 3 is approximately 4.67	🧩 14 ÷ 3 大约等于 4.67