Mathematical operations are actions you do to numbers to get a result. The four core operations are addition, subtraction, multiplication, and division. Each operation has a symbol, a common verb you say in English, and a name for its result. Learning these lets you understand and describe most basic calculations clearly.

Word/Phrase	🇨🇳 中文 词语/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
addition	➕ 加法	Putting numbers together to get a total	把数字放在一起得到一个总和	7 + 5 is addition	➕ 7 + 5 是加法
subtraction	➖ 减法	Taking one number away from another to find the difference	从一个数中减去另一个数以得到差值	10 − 3 is subtraction	➖ 10 − 3 是减法
multiplication	✖️ 乘法	Repeated addition to get a product	通过重复相加得到乘积	4 × 6 is multiplication	✖️ 4 × 6 是乘法
division	➗ 除法	Splitting into equal parts to get a quotient	将一个数字分成相等的部分以得到商	20 ÷ 4 is division	➗ 20 ÷ 4 是除法

In English, you often describe operations with verbs instead of only symbols. These verbs appear in spoken math, word problems, and instructions. Many verbs have close meanings, but some fit certain operations better than others. Knowing the common verb for each operation helps you translate a sentence into an equation.

Word/Phrase	🇨🇳 中文 词语/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
add	🧩 加	Do addition	进行加法	Add 2 and 8	🧩 将 2 与 8 相加
plus	🧩 加法	Added to	被加到	3 plus 9 equals 12	🧩 3 加 9 等于 12
subtract	🧩 减法	Do subtraction	做减法	Subtract 5 from 12	🧩 从 12 中减去 5
minus	🧩 减法符号	Subtracted from	从…减去	15 minus 4 equals 11	🧩 15 减 4 等于 11
multiply	🧩 乘法	Do multiplication	做乘法	Multiply 7 by 3	🧩 将 7 乘以 3
times	🧩 乘以	Multiplied by	乘以	6 times 5 is 30	🧩 6 乘 5 等于 30
divide	🧩 除法	Do division	做除法	Divide 24 by 6	🧩 将 24 除以 6
divided by	🧩 被除以	Separated into equal parts	被除以	18 divided by 3 is 6	🧩 18 除以 3 等于 6

English uses specific nouns for the result of an operation. These words show up in textbooks, instructions, and explanations. Using the correct result word makes your math writing sound precise. Some result words are used more in formal math than in everyday speech.

Word/Phrase	🇨🇳 中文 词语/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
sum	🏁 和	Result of addition	加法的结果	The sum of 4 and 9 is 13	🏁 4 与 9 的和是 13
total	🏁 总数	Final amount after adding	在加法后的最终数量	The total is 27	🏁 总数是 27
difference	🏁 差值	Result of subtraction	减法的结果	The difference between 10 and 6 is 4	🏁 10 与 6 的差值是 4
product	🏁 积	Result of multiplication	乘法的结果	The product of 3 and 8 is 24	🏁 3 与 8 的积是 24
quotient	🏁 商	Result of division	除法的结果	The quotient of 20 and 5 is 4	🏁 20 与 5 的商是 4
remainder	🏁 余数	Amount left over after division	除法后剩余的数量	17 divided by 5 has a remainder of 2	🏁 17 除以 5 的余数是 2

The equals sign shows that two expressions have the same value. In English you can say equals, is, is equal to, or results in, depending on context. In equations, both sides must balance, even if they look different. This idea is important for reading and writing math statements correctly.

Word/Phrase	🇨🇳 中文 词语/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
equals	⚖️ 等于	Has the same value as	与…具有相同的数值	8 + 1 equals 9	⚖️ 8 + 1 等于 9
is	⚖️ 是	Informal way to state equality	非正式表述相等的方式	2 times 6 is 12	⚖️ 2 次 6 等于 12
is equal to	⚖️ is equal to	More formal way to state equality	更正式的相等表达	3 + 4 is equal to 7	⚖️ 3 + 4 等于 7
results in	⚖️ 结果是	Focuses on the outcome	关注结果	9 − 2 results in 7	⚖️ 9 − 2 的结果是 7

When an expression has multiple operations, English follows a standard order to avoid confusion. Parentheses come first, then exponents, then multiplication and division, then addition and subtraction. Multiplication and division share the same level, so you work left to right. Addition and subtraction also share a level, so you work left to right.

Rule	🇨🇳 中文 规则	Example	🇨🇳 中文 示例
Do parentheses first	📌 括号优先	(3 + 5) × 2	📌 (3 + 5) × 2
Do exponents next	📌 指数优先	2^3 + 1	📌 2^3 + 1
Do multiplication and division left to right	📌 从左到右进行乘法和除法	12 ÷ 3 × 2	📌 12 ÷ 3 × 2
Do addition and subtraction left to right	📌 从左到右进行加法和减法	10 − 4 + 1	📌 10 − 4 + 1

Word problems often use prepositions that change the order of numbers in an operation. The pattern subtract A from B means B − A, not A − B. The phrase divide A by B means A ÷ B. Learning these fixed patterns prevents common interpretation errors when turning English into equations.

Rule	🇨🇳 中文 规则	Example	🇨🇳 中文 示例
Subtract A from B means B − A	🧭 从 B 中减去 A 表示 B − A	Subtract 3 from 10 means 10 − 3	🧭 从 10 中减去 3 表示 10 − 3
Divide A by B means A ÷ B	🧭 将 A 除以 B 表示 A ÷ B	Divide 20 by 4 means 20 ÷ 4	🧭 将 20 除以 4 表示 20 ÷ 4
Multiply A by B means A × B	🧭 将 A 乘以 B 表示 A × B	Multiply 6 by 7 means 6 × 7	🧭 将 6 乘以 7 表示 6 × 7
Add A to B means B + A	🧭 将 A 加到 B 表示 B + A	Add 5 to 12 means 12 + 5	🧭 将 5 加到 12 表示 12 + 5

English connects division and fractions closely: a fraction bar can mean divided by. You may hear over to describe a fraction, especially in spoken math. You also need language for numerator and denominator to describe fraction parts clearly. This vocabulary helps when reading formulas and simplifying expressions.

Word/Phrase	🇨🇳 中文 词语/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
fraction bar	🧮 fraction bar	The line meaning division in a fraction	分数线表示分数中的除法	3/4 means 3 divided by 4	🧮 3/4 表示 3 除以 4
over	🧮 over	Spoken way to read a fraction	用于朗读分数的口语表达	5/8 is five over eight	🧮 5/8 是五分之八
numerator	🧮 numerator	Top number in a fraction	分数中的分子	In 7/9, 7 is the numerator	🧮 在 7/9 中，7 是分子
denominator	🧮 denominator	Bottom number in a fraction	分数中的分母	In 7/9, 9 is the denominator	🧮 在 7/9 中，9 是分母

Beyond the four core operations, English frequently uses exponent and root vocabulary. Exponents describe repeated multiplication, and roots undo powers. You will see terms like squared and cubed often in geometry and measurement. Knowing these words helps you read expressions with superscripts and radical symbols.

Word/Phrase	🇨🇳 中文 词语/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
exponent	⬆️ exponent	A power showing repeated multiplication	表示重复乘法的幂	In 2^5, 5 is the exponent	⬆️ 在 2^5 中，5 是指数
squared	⬆️ squared	Power of 2	2 的幂	7^2 is seven squared	⬆️ 7^2 是七的平方
cubed	⬆️ cubed	Power of 3	3 的幂	4^3 is four cubed	⬆️ 4^3 是四的立方
square root	🌱 square root	A number that squared gives the original number	把平方后得到原数的数	The square root of 25 is 5	🌱 25 的平方根是 5
cube root	🌱 cube root	A number that cubed gives the original number	将其立方得到原数的数	The cube root of 27 is 3	🌱 27 的立方根是 3

Operations with negative numbers use clear sign language in English. You may say negative five for −5, and you may also hear minus five in casual speech. When reading expressions, minus can mean subtraction or a negative sign, depending on position. Being careful with these terms helps you interpret equations correctly.

Rule	🇨🇳 中文 规则	Example	🇨🇳 中文 示例
Negative describes the sign of a number	➖ 负号描述一个数的符号	Negative 6 means −6	➖ 负数 6 表示 −6
Minus often describes subtraction between two numbers	➖ 减号常用于描述两个数之间的减法	8 minus 3 means 8 − 3	➖ 8 减 3 表示 8 − 3
A negative sign can appear inside parentheses	➖ 负号可以出现在括号内	4 × (−2)	➖ 4 × (−2)
You can say plus negative to show addition with a negative number	➖ 你可以说“加负数”来表示带着负数的加法	7 + (−3) is seven plus negative three	➖ 7 + (−3) 表示七加负三

Math in real life often uses approximate answers. English uses words like round, estimate, and approximately to show you are not giving an exact value. You also need phrases for decimal places to explain how you rounded. This language is common in measurement, money, and data.

Word/Phrase	🇨🇳 中文 词语/短语	Definition	🇨🇳 中文 定义	Example	🇨🇳 中文 示例
round	🎯 round	Change a number to a nearby simpler number	将数字改为附近更简单的数字	Round 3.47 to 3.5	🎯 将 3.47 四舍五入为 3.5
estimate	🎯 estimate	Find a close value without exact calculation	在不进行精确计算的情况下找出接近的数值	Estimate 198 × 5 as about 200 × 5	🎯 198 × 5 估算为约 200 × 5
approximately	🎯 approximately	Not exact, close to	不是精确的，接近	The result is approximately 62	🎯 结果大约是 62
decimal place	🎯 decimal place	A position after the decimal point	小数位	4.736 rounded to two decimal places is 4.74	🎯 将 4.736 四舍五入到两位小数是 4.74