1.加減乘除等于英語怎么表示

這里把四則運算（加減乘除）和乘方、開方、指數(shù)和對數(shù)運算的相關(guān)（美式）英語單詞和短語做一個簡要匯總另外，補充了一些關(guān)于代數(shù)恒等式和法則的表達0. 數(shù)數(shù)(Counting)count v. 數(shù)(shu3) determine the total number of (a collection o老濕影院免費體驗f items)。

2.加減乘除等于英語怎么說

arithmetic n. art of counting 算術(shù) adj. arithmetic/arithmeticalMiddle English: from Old French arismetique

3.加減等于的英文怎么寫

, based on Latin arithmetica, from Greek arithmētikē (tekhnē)‘(art) of counting’, from arithmos ‘number’.

4.加減乘除的英文怎么寫

operation n. 運算 a process in which a number, 老濕影院免費體驗quantity, expression, etc., is altered or manipulated according to formal rules, such as those of addition, multiplication, and differentiation.

5.加,減,乘,除,等于用英語怎么說

late Middle English: via Old French from Latin operatio(n-), from the verb operari ‘expend labor on’unary operation

6.加減乘除的英文分別是什么

一元運算 one 老濕影院免費體驗input, one output (e.g. take the absolute value, take the opposite, take the reciprocal, etc.)

7.加減等于的英語怎么讀

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

8.加減乘除等于用英文怎么寫

1. 加法(Addition)3+43+4 means the number we get if we start with 33 and count老濕影院免費體驗 on 44 times.Q: What number do we get if we count on

9.加減乘除等于英語怎么讀

44 times from the number 33 ?add v. 加，加上; add yy to xx : 把 yy 加到 xx 上； yy added to xx : x+yx+y .late Middle English: from Latin

10.加減乘除等于的英文怎么讀

addere, from ad-‘to’+ the base of dare ‘put’.e.g. add x to both sides of the equation. 方程兩邊同時老濕影院免費體驗加上一個數(shù)x.

addend n. 加數(shù)late 17th century: from Latin addendus ‘to be added’, gerundive of addere.augend n. 被加數(shù)late 19th century: via German from Latin

augendus, gerundive of augere ‘to increase’.注：在教學(xué)中很少用到 augend 這個詞，由于加法交換律的緣故，相加的每一個數(shù)都可以叫加數(shù)(addend).plus

prep. with the addition of 加 xx plus yy : x+yx+y .m老濕影院免費體驗id 16th century: from Latin, literally ‘more’.包含詞根 plus 的單詞：surplus (late Middle English: from Old French

sourplus, from medieval Latin superplus, from super- ‘in addition’+plus ‘more’.)sum n. 和（結(jié)果）the sum of

xx and yy : x+yx+y ; v. 求和; summation n. 求和Middle English: via Old French from Latin summa ‘m老濕影院免費體驗ain part, sum total’, feminine of

summus ‘highest’.包含詞根 add 的單詞：addendum (pl. addenda, late 17th century: Latin, ‘that which is to be added’, gerundive of

addere)sum function 和函數(shù) (f+g)(x):=f(x)+g(x)(f+g)(x):=f(x)+g(x) .zz is y more thanxx : zz 比 xx 多 yy ,

z=x+yz=x+y . 單獨說 yy more than xx 就是比 xx 多 yy , 老濕影院免費體驗也就是 x+yx+y ; 如果不說多多少，就變成了比較兩數(shù)大小的不等式 zz is more/greater than

xx : zz 比 xx 大，也就是 zz 大于 xx , x">z>xz>x .increase v. 增加； increase xx by yy : 在 xx 基礎(chǔ)上增加 yy ; xx increased by

yy : x+yx+y ; 注意區(qū)別 increase xx to yy : 在 xx 基礎(chǔ)上增加到 yyMiddle English (formerly also asencrease): from Old French

encreistre, from Latin老濕影院免費體驗 increscere, from in- ‘into’ + crescere ‘grow’.總結(jié)起來x+yx+y 一共有5種說法: 1. yy added to

xx (add yy to xx); 2. xx plus yy ; 3. the sum of xx and yy; we can also say (usually when 0">y>0y>0)4.

yy more than xx;5. xx increased by yy.e.g. The sum of the (two) roots of a quadratic equation ax2+bx+

c=0ax^2+bx+c=0 e老濕影院免費體驗quals the opposite/negative of the linear coefficient bb over the quadratic coefficient

aa, i.e. ?ba-\dfrac{a} .2. 減法(Subtraction)Subtraction is the inverse operation of addition.7?47-4 means counting backward

44 times from 77 , or the number that when increased by 44 equals 77 .Q: What number plus老濕影院免費體驗 44 equals 7

7 ?subtract v. 減，減去; subtract yy from xx : 從 xx 中減去 yy ; yy subtracted from xx : x?yx-ymid 16th century: from Latin

subtract- ‘drawn away’, from sub- ‘from below’ + trahere‘ to draw’.e.g. Subtract xx from each side of the equation 方程兩邊同時減去一個數(shù)

xx .subtrahend n. 減數(shù)late 17th century: from Lat老濕影院免費體驗in subtrahendus ‘to be taken away’, gerundive of subtrahere.

minuend n. 被減數(shù)early 18th century: from Latin minuendus, gerundive of minuere ‘diminish’.minus prep. with the subtraction of 減

late15th century: from Latin, neuter of minor ‘less’.difference n. 差（結(jié)果）the difference of xx and yy :

x?yx-yMiddle E老濕影院免費體驗nglish: via Old French from Latin differentia.common difference 公差difference function 差函數(shù)

(f?g)(x):=f(x)?g(x)(f-g)(x):=f(x)-g(x)difference equation 差分方程decrease v. 減少；decrease xx by yy : 在 xx

基礎(chǔ)上減少 yy ; xx decreased by yy : x?yx-y ; 注意區(qū)別 decrease xx to yy : 在 xx 基礎(chǔ)上減少到 yy .zz is yyless thanx

x : zz 比 x老濕影院免費體驗x 少 yy , z=x?yz=x-y , 單獨說 yy less than xx 就是比 xx 少 yy , 也就是 x?yx-y ; 如果不說少多少，就變成了比較兩數(shù)大小的不等式

zz is less than xx : zz 比 xx 小，也就是 zz 小于 xx, z

yy from xx); 2. xx minus yy; 3. the difference of xx and yy; we can also say (usually when 0">y>0y>0)

4. xx decreased by yy;5. yy less than xx.The difference of xx 老濕影院免費體驗and yy is positive if and only if xx is greater than

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

x

xx .3. 乘法(Multiplication)Multiplication is repeated addition.3×4=123\times 4=12 means 33 groups of 4

4 is 1212 : 4+4+4=124+4+4=12 .What is the sum 老濕影院免費體驗of 33 groups of 44 ? What is the sum of three 44 s?multiply

v. 乘，乘上; multiply xx by yy : 乘 xx 以 yy ; xx multiplied by yy : xx 乘以 yy .Middle English: from Old French

multiplier, from Latin multiplicare.e.g. If we multiply both sides of an inequality by a positive number, the direction of the inequality老濕影院免費體驗 is preserved. 不等式兩邊同時乘以一個正數(shù)，不等號方向不變。

multiplicand n. 被乘數(shù) late 16th century: from medieval Latin multiplicandus ‘to be multiplied’, gerundive of Latin

multiplicare.multiplier n. 乘數(shù)注：在英語數(shù)學(xué)里，被乘數(shù)寫在后面，乘數(shù)寫在前面，只在小學(xué)數(shù)學(xué)中區(qū)別注：由于乘法交換律的緣故，被乘數(shù)和乘數(shù)都可以叫說 factor (乘積因子)factor

n. 既可以表示因數(shù)/約數(shù)，也可以表示因式; factor v. 因數(shù)/因式分解; fac老濕影院免費體驗torization n.common factor 公因數(shù)/公因式 greatest common factor

最大公因數(shù)/最大公因式factor theorem 因式定理：多項式 f(x)f(x) 的零點 aa 和一次因式 x?ax-a 的對應(yīng)關(guān)系multiple n. 倍數(shù)，倍式mid 17th century: from French, from late Latin

multiplus, alteration of Latin multiplex.common multiple 公倍數(shù)/公倍式 least common multiple 最小公倍數(shù)/最小公倍式times

prep. mu老濕影院免費體驗ltiplied by 乘以late 19th century (in a sense relating to the number of times that a specific dimension is to be repeated in quantitive surveying): use as a verb of

times expressing multiplication (dating from late Middle English).product n. 乘積（結(jié)果）the product of xx and

yy : xyxylate Middle English (as a老濕影院免費體驗 mathematical term): from Latin productum ‘something produced’, neuter past participle (used as anoun) of

producere ‘bring forth’.scalar multiplication 數(shù)乘（用數(shù)去乘）; scalar product 數(shù)量積（得到的乘積是一個數(shù)）product function

積函數(shù) (fg)(x):=f(x)g(x)(fg)(x):=f(x)g(x) .product rule 乘法法則 (fg)′(x)=f′(x)g(x)+f(x)g′(x)(fg)(x)=老濕影院免費體驗f(x)g(x)+f(x)g(x)

.英語中倍數(shù)的表達（知乎上有人總結(jié)過，這里就不贅述了）總結(jié)起來xyxy一共有三種說法:1. xx multiplied by yy (multiply xx by yy); 2. xx times y

y; 3. the product of xx and yy.The product of the (two) roots of a quadratic equation ax2+bx+c=0ax^2+bx+c=0

equals the constant cc divided by the quadratic coefficient aa, i.e. ca\dfra老濕影院免費體驗c{c}{a} .4. 除法(Division)

Division is the inverse operation of multiplication.12÷4=312\div 4=3 means when 1212 is divided into

44 equal groups, there will be 33 in each group; Or when 1212 is divided into groups of 44 , there will be

33 groups.How many are there in each group if 1212 is divided into 44 老濕影院免費體驗groups? How many groups are there if

1212 is divided in to groups of 44 ? What number times 44 equals 1212 ?divide v. 除；divide xx by yy : 除

xx 以 yyMiddle English (as a verb): from Latin dividere ‘force apart, remove’. The noun dates from the mid 17th century.

e.g. If we divide both sides of an inequali老濕影院免費體驗ty by a negative number, the direction of the inequality is reversed. 不等式兩邊同時除以一個負(fù)數(shù)，不等號方向改變。

divided by prep. pr. 除以 xx divided by yy : xx 除以 yydivisible adj. that can be evenly divided by 可整除的dividend

n. 被除數(shù)，被除式late 15th century (in the general sense ‘portion, share’): from Anglo-Norman French divide老濕影院免費體驗nde

, from Latin dividendum ‘something to be divided’, from the verb dividere.Zero can be a dividend or a numerator.

divisor n. 除數(shù)，除式；也表示整數(shù)的約數(shù)因數(shù)，或整式的因式late Middle English: from French diviseur or Latin divisor, from dividere.

Zero can never be a divisor or a denominator.quotient n. 商（結(jié)果）the quotient of老濕影院免費體驗 xx and yy : xy\dfrac{x}{y}

, 也可以讀成 the ratio (比) of xx to yy .late Middle English: from Latin quotiens ‘how many times’ (from quot

‘how many’), by confusion with participial forms ending in-ens,-ent-.quotient function 商函數(shù) (fg)(x):=f

(x)g(x)\left(\dfrac{f}{g}\right)(x):=\dfrac{f(x)}{g(x)}quotient rule 老濕影院免費體驗除法法則 (fg)′(x)=f′(x)g(x)?f(x)g′(x

)[g(x)]2\left(\dfrac{f}{g}\right)(x)=\dfrac{f(x)g(x)-f(x)g(x)}{[g(x)]^2}quotient ring 商環(huán) quotient field (=field of fractions)

分式環(huán)/分式域quotient group 商群 quotient space 商空間IQ (intelligence quotient): a number representing a persons reasoning ability (measured using proble老濕影院免費體驗m-solving tests) as compared to the statistical norm or average for their age, taken as

100100 .EQ (emotional quotient): the level of a persons emotional intelligence, often as represented by a score in a standardized test.

long division 長除法 arithmetical division in which the divisor has two or more f老濕影院免費體驗igures, and a series of steps is made as successive groups of digits of the dividend are divided by the divisor, to avoid excessive mental calculation.

short division 短除法 arithmetical division in which the quotient is written directly without a succession of intermediate calculations (used to find pr老濕影院免費體驗ime factorization, g.c.f. or l.c.m.)

synthetic division 綜合除法remainder n. 余數(shù)，余式 e.g. The quotient of 1717 and 33 is 55 , with a remainder of

22 .late Middle English: from Anglo-Norman French, from Latin remanere.remainder theorem 余數(shù)定理：多項式 f(

x)f(x) 除以一次因式 x?ax-a 后得到的余數(shù) rr 等于 f(a)f(a) .Chinese remainder 老濕影院免費體驗theorem 中國剩余定理，孫子剩余定理In Sun Tzus example (stated in modern terminology), what is the smallest number that when divided by

33 leaves a remainder of 22 , when divided by 55 leaves a remainder of 33 , and when divided by 77 leaves a remainder of

22 ?注：由于除法和分?jǐn)?shù)的關(guān)系 xx divided by yy can be written as xy\dfra老濕影院免費體驗c{x}{y} (where xx is the numerator 分子, yy is the denominator 分母) and read as

xx over yy.總結(jié)起來xy\dfrac{x}{y}有如下四種說法: 1. xx divided by yy (divide xx by yy); 2. the quotient of xx and

yy; 3. xx over yy;4. the ratio of xxto yy .The quotient of two positive numbers xx and yy is greater than

11 if and only if老濕影院免費體驗 xx is greater than yy .5. nn 次方/冪( nnth Power)Exponentiation (指數(shù)運算) is repeated multiplication.

square v. 平方 square the number xx : 把數(shù) xx 平方 square both sides of the equation 把方程兩邊同時平方Middle English: shortening of Old French 。

esquare (noun), esquarre (past participle, used as an adjective), esquarre老濕影院免費體驗r (verb), based on Latin quadra

‘square’.xx squared： xx 平方 e.g. xx squared is the product of xx and itself.square n. 平方（結(jié)果）the square of

xx : xx 的平方；來源于正方形(square)的面積公式；square adj. 平方的 square meter 平方米；注：quadratic 二次的總結(jié)起來 x2x^2 有三種常見讀法:1.

xx squared (to square xx); 2. xx (raised) to the 22nd power/[pow老濕影院免費體驗er of] 22 (to raise x to the 22nd power/ [power of]

22); 3. (take) the square of xx. e.g. Pythagorean theorem: In a right triangle, the sum of squares of the lengths of the two legs (a and b) equals the square of the length of the hypotenuse (c).

In symbols, a2+b2=c2a^2+b^2=c^2 , read as " aa squared 老濕影院免費體驗plus bb squared equals cc squared".cube v. 立方 cube the number

xx ：把數(shù) xx 立方 cube both sides 兩邊同時立方mid 16th century: from Old French, or via Latin from Greek kubos.x

x cubed： xx 立方 e.g. xx cubed is the product of a number and its square.cube n. 立方（結(jié)果）the cube of xx :

xx 的立方；來源于立方體(cube)的體積公式cubic adj. 立方老濕影院免費體驗的，三次的 cubic meter 立方米; cubic equation 三次方程總結(jié)起來 x3x^3 有三種常見讀法:1.

xx cubed (to cube xx); 2. xx [raised] to the 33rd power/power of 33 (to raise xx to the 33rd power/[power of]

33); 3. [to take] the cube of xx.raise xx to the nnth power/power of nn : 取 xx 的 nn 次方/冪xx [raised] to the

nnth power/power of xx老濕影院免費體驗 : xx 的 nn 次方/冪 e.g. The nnth power of a number xx is the product of nn factors of

xxs multiplied together.(square: raise to the 22nd power/power of 22 ; cube: raise to the 33rd power/power of

33 )base n. 底數(shù) the base of xnx^n is the factor xx that is multiplied repeatedly.late Middle English: from Old老濕影院免費體驗 French

bas, from medieval Latin bassus ‘short’ (found in classical Latin as a cognomen). Early senses included ‘low, short’ and ‘of inferior quality’; from the latter arose a sense ‘low in the social scale’, and hence (mid 16th century) ‘reprehensibly cowardly, selfish, or mean’.

exponent n. 指數(shù) the e老濕影院免費體驗xponent of xnx^n is the number nn that indicates the number of repeated factor xx

.late 16th century (as an adjective in the sense ‘expounding’): from Latin exponent- ‘putting out’, from the verb

exponere.exponential adj. 指數(shù)的；exponential function 指數(shù)函數(shù)；exponential growth/decay 指數(shù)增長/衰減；exponential model老濕影院免費體驗 指數(shù)模型

power n. 方，冪（結(jié)果） xnx^n： nnth power of xx ; if nn is negative or non-integer, we say xx to the (power of)

nn , instead.Middle English: from Anglo-Norman French poeir, from an alteration of Latin posse‘be able’.

power function 冪函數(shù) y=axny=ax^npower series 冪級數(shù) ∑n=0∞cn(x?a)n\sum\limits_{n=0}^{\infty} 老濕影院免費體驗c_n(x-a)^npower rule

一般指對冪函數(shù)的求導(dǎo)公式 (xn)′=nxn?1(x^n)=nx^{n-1}power of a point 點 PP （關(guān)于一個圓 OO ）的冪，定義成 OP2?r2OP^2-r^2 .The radius of convergence of a power series can be determined by the ratio test.

idempotent 冪等的： A2=AA^2=AIn words: If a matrix squared equals the matrix itself, then we say this matrix i老濕影院免費體驗s idempotent.

late 19th century: from Latin idem ‘same’ + potent.If a matrix is idempotent, then its eigenvalues are either

00 or 11 (since its minimal polynomial is λ2?λ\lambda^2-\lambda ).nilpotent 冪零的 ：Ak=0A^k=0In words: If a matrix raised to a whole number equals zero matrix, then we say this matr老濕影院免費體驗ix is nilpotent.

If a matrix is nilpotent, then it has only 00 as its eigenvalue. (since its minimal polynomial is λk=

0\lambda^k=0 )late 19th century: from nil + Latin potens, potent- ‘power’.6. nn 次方根( nnth Root)Taking the

nnth root is the inverse operation of taking the nnth power.Q: What number to 老濕影院免費體驗the nnth power equals to the given number?

square root n. pr. 平方根; take the square root of xx : 取 xx 的平方根e.g. A square root of xx is a number yy

that when squared equals xx .principal square root n. pr. 算術(shù)平方根 (the nonnegative square root)Positive definite matrix has a unique square root which is also 老濕影院免費體驗positive definite.

cube root n. pr. 立方根; take the cube root of xx : 取 xx 的（實）立方根e.g. A cube root of x is a number y that when cubed equals

x .nth root n. pr. n 次方根：take the nth root of x ：取 x 的 n 次方根e.g. An n th root of a number x is a number

y that when raised to the nth power equals x .nth roots of u老濕影院免費體驗nity are e^{\frac{2k\pi i}{n}}=\cos\left(\frac{2k\pi}{n}\right)+i\sin\left(\frac{2k\pi}{n}\right)

, 0\leq k\leq n-1 .root n. 根，可以指一元方程的解(solution to an equation in one variable/unknown)Old English wrōtan

, of Germanicorigin; related to Old English wrōt ‘snout’, German Rüssel ‘snout’, and perhaps ultim老濕影院免費體驗ately to Latin

rodere ‘gnaw’.e.g. A zero of a polynomial function p(x) is a root of the corresponding polynomial equation

p(x)=0.radical n. 用根式表示的根；radical expression 根式 ；radical sign/symbol 根號 late Middle English (in the senses ‘forming the root’ and ‘inherent’): from late Latin

radicalis, from Latin 老濕影院免費體驗radix, radic- ‘root’.nested radical n. pr. radical of a radical, like \sqrt{a+\sqrt}

.e.g. The solutions to a reduced cubic equation x^3+px+q=0 can be found by using the cubic formula, written as a sum of two nested radicals, both containing a square root sign and a cube root sign:

x=\sqrt[3]{-\dfr老濕影院免費體驗ac{q}{2}+\sqrt{\dfrac{q^2}{4}+\dfrac{p^3}{27}}}+\sqrt[3]{-\dfrac{q}{2}-\sqrt{\dfrac{q^2}{4}+\dfrac{p^3}{27}}}

.Denesting nested radical: If a , b , and c are rational numbers and c is not the square of a rational number, there are two rational numbers

x and y , such that \sqrt{a+b\sqrt{c}}=\sqrt{x}+\s老濕影院免費體驗qrt{y} if and only if a^2-b^2c is the square of a rational number.

surd n. 不盡根 mid 16th century: from Latin surdus ‘deaf, mute’; as a mathematical term, translating Greek (Euclid)

alogos ‘irrational, speechless’, apparently via Arabic ji?r a?amm, literally ‘deaf root’.radicand n. 被開方數(shù) the radicand of 老濕影院免費體驗the radical

\sqrt[n]{x} is the number xe.g. The radicand of a radical with even index must be nonnegative.index (pl. indices)

n. 指數(shù) the index of the radical \sqrt[n]{x} is the number nlate Middle English: from Latin index, indic-

‘forefinger, informer, sign’, from in- ‘towards’+ a second element relate老濕影院免費體驗d to dicere ‘say’ or dicare

‘make known’;e.g. We can use the quadratic formula \dfrac{-b\pm \sqrt{b^2-4ac}}{2a} , read as the opposite/negative of

b plus minus the square root of b squared minus 4ac , the quantity over 2a , to find solutions to any quadratic equation

ax^2+bx+c=0,~a\neq 0, read as a (ti老濕影院免費體驗mes) x squared plus b (times) x plus c equals zero, with a nonzero.

logarithm 對數(shù) take logarithm to the base b of a ：取以 b 為底的 a 的對數(shù)early 17th century: from modern Latin logarithmus

, from Greek logos ‘reckoning, ratio’ + arithmos ‘number’.log base b of a: 以 b 為底的 a 的對數(shù)The logarithm to the base

b of a nu老濕影院免費體驗mber N is the exponent to which when b is raised equals N .Q: A given base b raised to what power equals a given number

N ? common logarithm 常用對數(shù) (base 10)；natural logarithm 自然對數(shù) (base e )logarithmic adj. 對數(shù)的；logarithmic function

對數(shù)函數(shù)；logarithmic spiral 對數(shù)螺旋7. 恒等式、不等式與運算法則sum of squares 平方和 a^2+b^2=(a老濕影院免費體驗+ib)(a-ib)In words: The sum of squares of two real numbers equals the product of a complex number with one of the two real numbers as its real part and the other as its imaginary part, and the conjugate of the complex number thus formed.

difference of squares 平方差 a^2-b^2=(a+b)(a-b)In words: The diffe老濕影院免費體驗rence of squares of two numbers equals the product of their sum and their difference.

sum of cubes 立方和 a^3+b^3=(a+b)(a^2-ab+b^2)In words: The sum of two cubes equals the product of their sum and the sum of their squares minus their product.

difference of cubes 立方差 a^3-b^3=(a-b)(a^2+ab+b^2)In words: Th老濕影院免費體驗e difference of two cubes equals the product of their difference and the sum of their squares plus their product.

perfect square formula 完全平方公式 (a\pm b)^2=a^2\pm 2ab+b^2In words: The square of the sum/difference of two numbers equals the sum of their squares plus/minus twice their product.

perfect cub老濕影院免費體驗e formula 完全立方公式(a+ b)^3=a^3+ 3a^2b+ 3ab^2+ b^3 , (a-b)^3=a^3-3a^2b+3ab^2-b^3 .In words: The cube of the sum of two numbers equals the sum of their cubes and two terms resulting from three times the square of one number times the other.

product of powers 方的積 a^m b^n the product of a to the power of m老濕影院免費體驗 and b to the n.power of a product 積的方

(ab)^n=a^nb^n the product of a and b, raised to the n.quotient of powers 方的商 \frac{a^m}{b^n} the quotient of a to the m and b to the n.

power of a quotient 商的方 \left(\frac{a}\right)^n=\frac{a^n}{b^n} the quotient of a and b, raised to the n equals the the quot老濕影院免費體驗ient of a to the n and b to the n.

power of a power 方的方 (a^m)^n=a^{mn} a to the m, and then to the n, equals to a to the mn.logarithm of a product equals sum of logarithms

\log_b(mn)=\log_b m+\log_b nlogarithm of a quotient equals difference of logarithms\log_b\left(\dfrac{m}{n}\right)=\log_b m -\log_老濕影院免費體驗b n

在三角學(xué)(trigonometry)中還有和差化積公式(sum-to-product identities)，積化和差公式 (product-to-sum identities)product property

乘法性質(zhì)（一般指乘法和其他運算交換順序）quotient property 除法性質(zhì)（一般指除法和其他運算交換順序）additive identity 加法恒等元 0 ： x+0=x=0+x .i.e. The sum of any number and the additive identity, no matter in what order we add, equals th老濕影院免費體驗e number itself.

additive inverse 加法逆元(對一般的數(shù)系而言就是相反數(shù)opposite)： x+(-x)=0=(-x)+xi.e. The sum of any number and its additive inverse, no matter in what order we add, equals the additive identity.

multiplicative identity 乘法恒等元 1 ： x\cdot 1=x=1\cdot x .i.e. Any number times the multiplicative identity equa老濕影院免費體驗ls the number itself.

multiplicative inverse 乘法逆元(對一般的數(shù)系而言就是倒數(shù)reciprocal)： x\cdot \dfrac{1}{x}=1=\dfrac{1}{x}\cdot x .i.e. The product of any number and its multiplicative inverse, no matter in what order we multiply, equals the multiplicative identity.

commutative property (AmE) 交換律 ～of addition x+y=老濕影院免費體驗y+x ; ～of multiplication xy=yxi.e. The sum of two numbers x and y is the same as the sum of the same two numbers, with the order reversed. (

x plus y equals y plus x ).i.e. The product of two numbers x and y equals the product of the same two numbers, with the order reversed. (

x times y equals y time老濕影院免費體驗s x ).mid 16th century (in the sense ‘relating to transactions between people’): from French

commutatif,-ive or medieval Latin commutativus, from commutat-‘exchanged’, from the verb commutare.associative property

(AmE) 結(jié)合律 ～of addition (x+y)+z=x+(y+z) ; ～of multiplication (xy)z=x(yz) .The sum of x and老濕影院免費體驗 y , and then plus

z , equals x plus the sum of y and z .i.e. When we add three numbers up, the sum of the first two numbers plus the third number has the same result as the sum of the last two numbers added to the first number.

The product of x and y , and then times z , equals x times the product of老濕影院免費體驗 y and z .i.e. When we multiply three numbers together, the product of the first two numbers times the third number has the same result as the first number multiplied by the product of the last two numbers.

distributive property (AmE) 分配律 x(y+z)=xy+xz .The product of x and the sum of y and z (the qua老濕影院免費體驗ntity y

plus z ) equals the product of x and y plus the product of x and z (or the sum of products x times z

and y times z ).late Middle English: from Old French distributif,-ive or late Latin distributivus, from Latin

distribut- ‘divided up’, from the verb distribuere.arithmetic mean：算術(shù)平均 \dfrac{1}{n}老濕影院免費體驗\sum\limits_{i=1}^n x_i =\dfrac{x_1+x_2+\cdots +x_n}{n}

In words: the sum of n numbers divided by n .geometric mean：幾何平均 \sqrt[n]{\prod_{i=1}^n x_i}=\sqrt[n]{x_1x_2\cdots x_n}

，其中 x_i\geq 0 , 1\leq i\leq nIn words: the product of n nonnegative numbers, taken the nth root.harmonic mean

：調(diào)和平均 \dfrac{n}{\老濕影院免費體驗sum\limits_{i=1}^n \dfrac{1}{x_i}}=\dfrac{n}{\dfrac{1}{x_1}+\dfrac{1}{x_2}+\cdots+\dfrac{1}{x_n}}

In words: the reciprocal of the arithmetic mean of the reciprocals of n numbers.power mean (generalized mean)

：冪平均 M_p(x_1,x_2,\cdots, x_n)=\left(\dfrac{1}{n}\sum\limits_{i=1}^n x_i^p\right)^{\frac{1}{p}}老濕影院免費體驗 ，其中 x_i\geq 0

， 1\leq i\leq n . 其中 M_1 是算術(shù)平均， M_0 是幾何平均（取極限）， M_{-1} 是調(diào)和平均， M_{+\infty} 是最大值， M_{-\infty} 是最小值In words: the arithmetic mean of 。

n numbers to the p , raised to the power of \dfrac{1}{p} .logarithmic mean：對數(shù)平均數(shù) \dfrac{x-y}{\ln x-\ln y}

，其中 x\neq y ，可以通過微分中值定理 (Mean Value Theorem of Diff老濕影院免費體驗erential Calculus) 推廣到任意 n 個數(shù)In words: the difference of two numbers divided by the difference of their logarithms.。