这里把四则运算（加减乘除）和乘方、开方、指数和对数运算的相关（美式）英语单词和短语做一个简要汇总。另外，补充了一些关于代数恒等式和法则的表达。

count v. 数(shu3) determine the total number of (a collection of items)

arithmetic n. art of counting 算术 adj. arithmetic/arithmetical

operation n. 运算 a process in which a number, quantity, expression, etc., is altered or manipulated according to formal rules, such as those of addition, multiplication, and differentiation.

unary operation 一元运算 one input, one output (e.g. take the absolute value, take the opposite, take the reciprocal, etc.)

binary operation 二元运算 two inputs, one output (e.g. addition, subtraction, multiplication, division, etc.)

3+4 means the number we get if we start with 3 and count on 4 times.

Q: What number do we get if we count on 4 times from the number 3 ?

add v. 加，加上; add y to x : 把 y 加到 x 上； y added to x : x+y .

e.g. add x to both sides of the equation. 方程两边同时加上一个数x.

addend n. 加数

augend n. 被加数

注：在教学中很少用到 augend 这个词，由于加法交换律的缘故，相加的每一个数都可以叫加数(addend).

plus prep. with the addition of 加 x plus y : x+y .

包含词根 plus 的单词：surplus (late Middle English: from Old French sourplus, from medieval Latin superplus, from super- ‘in addition’+plus ‘more’.)

sum n. 和（结果）the sum of x and y : x+y ; v. 求和; summation n. 求和

包含词根 add 的单词：addendum (pl. addenda, late 17th century: Latin, ‘that which is to be added’, gerundive of addere)

sum function 和函数 (f+g)(x):=f(x)+g(x) .

z is y more than x : z 比 x 多 y , z=x+y . 单独说 y more than x 就是比 x 多 y , 也就是 x+y ; 如果不说多多少，就变成了比较两数大小的不等式 z is more/greater than x : z 比 x 大，也就是 z 大于 x , z>x .

increase v. 增加； increase x by y : 在 x 基础上增加 y ; x increased by y : x+y ; 注意区别 increase x to y : 在 x 基础上增加到 y

总结起来 x+y 一共有5种说法:

1. y added to x (add y to x );

2. x plus y ;

3. the sum of x and y ;

we can also say (usually when y>0 )

4. y more than x ;

5. x increased by y .

e.g. The sum of the (two) roots of a quadratic equation ax^2+bx+c=0 equals the opposite/negative of the linear coefficient b over the quadratic coefficient a, i.e. -\dfrac{b}{a} .

Subtraction is the inverse operation of addition.

7-4 means counting backward 4 times from 7 , or the number that when increased by 4 equals 7 .

Q: What number plus 4 equals 7 ?

subtract v. 减，减去; subtract y from x : 从 x 中减去 y ; y subtracted from x : x-y

e.g. Subtract x from each side of the equation 方程两边同时减去一个数 x .

subtrahend n. 减数

minuend n. 被减数

minus prep. with the subtraction of 减

difference n. 差（结果）the difference of x and y : x-y

common difference 公差

difference function 差函数 (f-g)(x):=f(x)-g(x)

difference equation 差分方程

decrease v. 减少；decrease x by y : 在 x 基础上减少 y ; x decreased by y : x-y ; 注意区别 decrease x to y : 在 x 基础上减少到 y .

z is y less than x : z 比 x 少 y , z=x-y , 单独说 y less than x 就是比 x 少 y , 也就是 x-y ; 如果不说少多少，就变成了比较两数大小的不等式 z is less than x : z 比 x 小，也就是 z 小于 x, zy>0 )

4. x decreased by y ;

5. y less than x .

The difference of x and y is positive if and only if x is greater than y .

注意：less 和 lesser (not so great or important as the other or the rest) 不同；If there are two numbers x