双语数学概念上.docx
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双语数学概念上.docx
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双语数学概念上
双语数学概念用语(上)
本文来自:
疯狂英语www.crazyenglish.org
详细出处参考:
http:
//www.crazyenglish.org/zhuanyeyingyu/kejiao/2009/0310/39990.html
(资料引用共享,本站尚未校订)
一、运算
1、各种符号
.period句号,comma逗号
:
colon冒号;semicolon分号
!
exclamation惊叹号?
questionmark问号
 ̄hyphen连字符'apostrophe省略号;所有格符号
—dash破折号‘’singlequotationmarks单引号
“”doublequotationmarks双引号...ellipsis省略号
()parentheses圆括号[]squarebrackets方括号
《》Frenchquotes法文引号;书名号¨tandemcolon双点号
"ditto同上‖parallel双线号
/virgule斜线号&ampersand=and~swungdash代字号
§section;division分节号→arrow箭号;参见号
plussign加号minussign减号
+plus加号;正号-minus减号;负号
±plusorminus正负号×ismultipliedby乘号
÷isdividedby除号=isequalto等于号
≠isnotequalto不等于号=isequivalentto全等于号
≌isequaltoorapproximatelyequalto等于或约等于号
≈isapproximatelyequalto约等于号
<islessthan小于号>ismorethan大于号
≮isnotlessthan不小于号≯isnotmorethan不大于号
≤islessthanorequalto小于或等于号ismorethanorequalto大于或等于号
等于equals,isequalto,isequivalentto
大于isgreaterthan;小于islesserthan
大于等于isequalorgreaterthan;小于等于isequalorlesserthan
运算符operator
2.“加”用plus,and或add表示;“等于”用is,make,equal等词表示。
addingthefollowing:
求和
加plus(介词.),add(动词),addition(名词);被加数augend,summand;加数addend;和sum
2+3=?
可表示为:
Howmuchistwoplusthree?
2+3=5Twoplusthreeisfive.Twoandthreeareequaltofive.
Twoandthreemakefive.Twoaddedtothreeequalsfive.
Ifweaddtwoto/andthree,wegetfive.
commutativepropertyofaddition加法交换率:
changingtheorderoftheaddendsdoesnotchangethesum..
associativepropertyofaddition:
Ifa,bandcarerealnumbers,then(a+b)+c=a+(b+c).changingthemannerofcombiningaddendsdoesn’tchangethesum.
3.“减”用minus或takefrom表示minuend被减数,subtrahend减数difference差
减minus(介词),subtract(动词),subtraction(名词)
10-6=?
Howmuchistenminussix?
10-6=4Tenminussixisfour.
Takesixfromtenandtheremainderisfour.
Six(taken)fromtenisfour.十减去六等于四
4.“乘”用time(动词)或multiply表示
乘times(介词),multiply(动词),multiplication(名词);被乘数multiplicand,faciend;因数factors,乘数multiplicator;multiplier;积product
3X4=?
Howmuchisthreetimesfour?
3X4=12Threetimesfouristwelve.
Multiplythreebyfour,wegettwelve.
Threemultipliedbyfourmakestwelve.三乘以四等于十二
Inamultiplicationequation,thesearethetwo(ormore)numberswhicharemultipliedtogether.
Anynumbermultipliedby1isitself.
Tomultiplyanumberbyten,simplyaddazeroattheendoftheoriginalnumber.
0和任何数相乘都得0。
Commutativepropertyofmultiplication乘法交换率:
Ifaandbarerealnumbers,thena×b=b×a,changingtheorderofthefactorsdoesnotchangetheproduct.
Isadditioncommutative?
Issubtractioncommutative?
Ismultiplicationcommutative?
Isdivisioncommutative?
associativepropertyofmultiplication结合率:
Ifa,bandcarerealnumbers,thena(bc)=(ab)c.changingthegroupingofmultiplyingfactorsdoesnotchangetheproduct.
distributivepropertyofmultiplicationoveraddition乘法对加法的分配率:
Ifa,bandcarerealnumbers,thena(b+c)=ab+ac.
Foreveryrealnumber”a”:
a+0=a.0istheidentityelementforaddition.
Foreveryrealnumber“a”:
a×1=a.1istheidentityelementformultiplication.
5.“除”用divide的过去分词形式表示
除dividedby(介词.),divide(动词),division(名词)
可被整除的数divisible;被整除dividedevenly;被除数dividend;除数divisor;余数remainder;商quotient
16÷4=?
Howmuchissixteendividedbyfour?
16÷4=4Sixteendividedbyfourisfour.
Sixteendividedbyfourequals/gives/makesfour.
6.表示“n次方”的说法:
指数用序数词,底数用基数词。
10的7次方theseventhpoweroften(tentotheseventhpower)
6的10次方thetenthpowerofsix(sixtothetenthpower)
Azerofactoralwaysgivesazeroproduct.
Theproductoftworealnumbersmaybe0onlyifonefactoris0.
Dividingbyzeroisnotdifined.a/0anda÷0arenotdefined.
Zerodividedbyanynon-zerorealnumberequalszero.
Forthepairofnumbers,selectthecorrectsymbol(=,≤greaterthanorequalto≥lessthan
Oneislessthanonehundred.
Forty-fourisgreaterthansix.
Nineequalsthreetimesthree.
7、Theorderofoperationsregardingaddition,subtraction,multiplicationetc运算顺序:
1)parentheses:
docalculationswithingroupingsymbolssuchas:
()[]{}.
2)Multiplication&Divisionfromlefttoright.3)Addition&Subtractionfromlefttoright.
记“PleaseExcuseMyDearAuntSally”(括号、指数、乘法、除法、加法、减法)
Hint:
Remember“PleaseExcuseMyDearAuntSally”
(parentheses;Exponents;Multiplication;Division;Addition;Subtraction)
Expressthefollowing,usingmathematicalphrases:
用数学语言表达
1)Tenincreasedbytheproductofsixandthree
2)Eightdecreasedbythequotientoffourandtwo.
3)Theproductofsixandfivedecreasedbythesumofeightandfour.
8、explainhowtoroundnumbers.解释如何四舍五入
近似值approximation估算estimation
Togiveanapproximatevalue.即取一个近似值。
将一个整数四舍五入到所要求的位数值,若所要求位数右边的数字小于5,则将其约去,若大于或等于5,则进一位。
Whenroundinganumbertoagivenplacevalue:
ifthedigittotherightoftheonegivenislessthanorequaltofive,youroundup.
Example:
round67tothenearestten’splace.”7”isgreaterthan“5”,soround“67”upto“70”.
Roundthenumber5842tothenearesthundred.Thefourintheten’splaceislessthanfive,soyourounddownto5800.
进位carry
截尾truncation
四舍五入round
下舍入rounddown
上舍入roundup
有效数字significantdigit
无效数字insignificantdigit
9、验算Howcanyouusemultiplicationtochecktheresultofadivisionproblem?
example:
41/9=
1)multiplythequotientbythedivisor4x9=36
2)addtheremaindertotheproductofitem1above36+5=41
二、整数
1、数
数字digit;零null,zero,nought,nil
数number;整数wholenumber,integer
正positive;正数positivenumber;正整数positivewholenumber
负negative(anumberthatislessthanzero);负数negativenumber;非负的nonnegative;负整数negativewholenumber;oppositenumbers相反数;
realnumbers实数;numberline数轴;origin原点
Arithmetic算术algebra代数geometry几何generated旋转average平均数
naturalnumber自然数:
Thesameasacountingnumber.Itisamemberoftheset{0,1,2,3,4……}
rationalnumber有理数:
Anumberthatcanberepresentedbyafraction(分数).Thisincludesallterminatingandrepeatingdecimals.
整数integer:
Anypositiveornegativenumberorzero.Amemberoftheset{…,-3,-2,-1,0,1,2,3,…}.
整数wholenumbers:
Allthe“naturalnumbers”pluszero.
irrationalnumber无理数:
Anon-repeating(无限),non-terminating(不循环)decimal.
实数realnumber:
Anyrationalorirrationalnumber.
连续整数consecutivenumber
Counting(连续的数)ornaturalnumbers(自然数):
Thenumbersyoucountwith.:
1,2,3,…(etc)
Evennumbers;eveninteger,偶数:
Wholenumbersdivisiblebytwo.0,2,4,…
Oddnumbers;oddinteger,奇数:
Wholenumbersnotdivisiblebytwo.
primenumber质数:
Anumberwhichhasnofactorsotherthanitselfor1.
Listallofthenon-primenumbers(合数)between15and30
primenumber质数:
Anumberwhichhasexactlytwowholenumberfactors?
oneanditself.
primefactor质因数:
Afactorofanumberwhichisalsoaprimenumber. 49hasfactorsof1,7,49.
合数Compositenumbere.g.4,6,8,9,10,12,14,15…
listthedigitsinournumberssystem列出数字系统中的阿拉伯数字。
Thereareten:
0,1,2,3,4,5,6,7,8,9。
Combinationsoftheseareusedtomakeupallnumbers这些阿拉伯数字构成了所有的数。
2、十进制decimalsystem
二进制binarysystem
十六进制hexadecimalsystem
一位数1-digitnumber两位数2-digitnumber
listplacevaluesforthefollowingnumber:
123456789列出下面这个数各位数字的位值。
Placevaluestellusbywhichpowerof10tomultiplyadigit位值的意思是,一个数的相邻两位之间相差10倍。
9—one’splace个位
8—ten’splace十位,8isinthetensplace
7—hundred’splace
6—thousand’splace
5—tenthousand’splace,5isinthetenthousandsplace
4—100thousand’splace
3—million’splace
2—10million’splace
1—100million’splace亿位
3、正负数
如何用正负数来表示相反的情况?
Howaresignednumbersusedtorepresentopposingsituations?
1)Oppositessuchasupanddownorleftandrightcanberepresentedby“+”and“-”.Ifupisrepresentedby“+”,thendowncanberepresentedby“-”.
2)Eventhoughthedistanceisrepresentedas+25and?
15,thetotalmilestraveledis40(25+15).
(+25)→
←(-15)
3)Adepositorincreaseisrepresentedas+
4)Streetlevelisconsideredzero.Travelingdownonelevelwouldbeexpressedas?
1.
将下列正负数按从小到大顺序排列
Placethesesignednumbersinorderfrommostnegativetomostpositive.
Onanumberlinethevaluesofnegativenumbersdecreasefromtheorigin(0)totheleft.thevaluesofpositivenumbersincreasefromtheorigin(0)totheright.
absolutevalue绝对值:
Thedistance(alwayspositive)betweenanumberandzero(theorigin)onanumberline.
Whatisthesymbolforabsolutevalue?
Thesymbol│x│meansabsolutevalueofthetermxinside.
4、代数
expression表达式:
Arelationship(关系式)representedwithnumbersand/orsymbols.
equation等式:
Asentencethatusesthesymbol“=”tostatsthattheresultoftheexpressionsontheleftsideisthesameastheresultoftheexpressionsontherightside.
inequality不等于:
Twonumbersthatarenotequaltoeachother.Onenumbermaybegreaterthantheothernumberorlessthantheothernumber.
Expressasanequation列方程式
Anumberincreasedbysixequals63.Whatisthenumber?
三、分数fraction
3----分子numerator
——----分数线fractionstrokeorfractionline
4-----分母denominator
1.分数是由基数词和序数词一起来表示的。
基数词作分子,序数词作分母,除了分子是“1”以外,其它情况下序数词都要用复数形式。
3/4threefourths或threequarters
1/3onethird或athird
24/25twenty-fourtwenty-fifths
31/4threeandonefourth或threeandonequarter
1/2ahalf
1/4onequarter或aquarter
11/2oneandahalf
11/4oneandaquarter
2.当分数后面接名词时,如果分数表示的值大于1,名词用复数;小于1,名词用单数。
11/2hours一个半小时(读作oneandahalfhours)
23/4meters二又四分之三米(读作twoandthree-fourthsmeters)
4/5meter五分之四米
5/6inch六分之五英寸
真分数properfraction;假分数improperfraction;
带分数mixednumber:
wholepart整数部分;fractionpart分数部分
simplifythismixednumber化简带分数
普通分数vulgarfraction,commonfraction;
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