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1、第一章计算题训练基础篇知识要点：1、熟记分数和小数百分数最简比互化中的常见数1/8=0.125,1/4=0.25,3/8=0.375,1/2=0.5,5/8=0.6253/4=0.75,7/8=0.8752掌握简便运算技巧加法交换律和结合律a+b=b+a(ab)+c=a+(b+c)乘法交换律，结合律，分配律ab=ba(ab)c=a(bc)(a+b)c=ac+bc(a-b)c=ac-bc除法分配律(a+b)c=ac+bc(a-b)c=ac-bca-b-c=a-(b+c)a-(b-c)=a-b+cabc=a(bc)3 平方差公式：(a+b)(a-b)=a2b24 熟记100以内质数:2,3,5,7
2、,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,975熟记1-20的平方1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,4001-10的立方1,8,27,64,125,216,343,512,729,10002的1次方到10次方；3的1次方到8次方3,9,27,81,243,729,2187,65616掌握等差数列和=(首项+末项)X项数+2项数=(末项-首项)公差+1一用分配律凑整1719999279121022761371997999二用
3、结合律凑整2548125368375561240.125240.375799225312525三化多位数为一位数2722824.245484537814.2x45四凑整意识之分配律【例1】计算：200.9X20.08-200.8X20.07【巩固】计算:20.0931.52,009317+200.93.68=【巩固】计算:2.009x43+20.09x2.9+200.9x0.28=【巩固】计算:19993.14199.931.4+19.99314.【巩固】计算:199.919.98-199.819.97【巩固】计算:10.373.41.719.26=【例2】计算：6.258.27163.750
4、.8278【巩固】计算:20.0962+200.93.9-7x2.87=【巩固】计算:2.89x47+1.53-1.4x1.1+24x0.11+288x0.53-0.1=【巩固】计算:2237.5+22.312.5+2304-0.72.5+1=【巩固】计算：19.9837+199.82.3+9.9980【巩固】计算：3790.038+1590.00621+3.79x0.121【巩固】计算78.16x1.45+3.14x21.84+169x0.7816【巩固】计算:7.8I61.45+3.142.184+1.697.816=【巩固】计算：147.758.4+4.792+4092.1+0.9521
5、479【例3】计算：1253.6-79+833.6【例4】计算8.11.3-81.3+1.91.3+11.91.3【例5】(2)2003200111120037337【例6】计算：5L28.1+119.25+5370.19【例7计算：2237.5+22.312.5+2304-0.72.5+l【巩固】1.2517.6+360.8264125=【例8】计算：2007-(8.58,5-1.51.5)10160-03.【巩固】计算(980X65320)(66+98X64)【巩固】2004.051997.05-2001.051999.05【巩固】(873x477-198)+(476x874+199)【例
6、9】计算：1.23452+0.765522.4690.7655.第二节配对和凑整意识知识要点:哪些数需要配对？I分母相同的2能抵消的3能约分的4能凑整的5整数与整数,分数与分数6加数与加数，减数与减数模块一：分组凑整思想例191.5+88.8+90.2+270.4+89.6+186.7+91.8【巩固】2006+2006+2006+2006+994+994+994+0994=【例2】计算【例3】计算56.43+12.96+13.574.338.965.67【巩固】3.17+7.48-2.38+0.53-3.48-1.62+5.3【例4】计算1+0.99-0.98-0.970.96+0.95-0
7、.94-0.93+0.04+0.03-0.02-0.01模块二、加补凑整思想【例5同学们，你们有什么好办法又快又准的算出下面各题的答案？把你的好方法讲一讲！也当一次小老师！(1) 0.9+0.99+0.999+0.9999+0.99999(2) 1.996+19.97+199.8(3) 0.7+9.7+99.7+999999999.7【巩固】请你认真计算下面两道题看谁算得最准确(1)9.99629.98169.9+3999.5(2)89+899+8999+89999+899999模块三、位值原理例6(123456789.987654321+234567891.198765432+9123456
8、78.876543219)9【例7】124.68+324.68+524.68+724.68+924.68【巩固】325.24+425.24+625.24+925.24+525.24模块四、基准数思想【例8计算().9+0.99+0.999+0.9999+0.99999【巩固】1.996+19.97+199.8例io!+WWWKL12223333312+199519951995+19951+1995例11kfa+2+2+23420JU45AYf2+3+20)U53+一201818+192019+一20五综合训练57例1、57-JO2001-l-44巩固练习：1997x19971998601-l-
9、55彳列2、200597.75+4010l.12537llll+77779巩固练习：4.72.8+3.69.4999778+333666例3、199208-198209巩固练习：3567-34681324、-39+-25+-35551119巩固练习：17X至+llJoJO例5、123434-341212巩固练习：201820181998-19981998X2018例 6、 12312312312415731巩固练习：15731573-15741575例7、159-105535353104巩固练习:169Illlll131313+200420022003例8、1477101+100x103巩固练
10、习:13557HF7x9299x1011-5-+62_9_11_1212-20+30-42”1956-72+90例9、zl 1(-+- 8 9+w+x+m+TT+9+w+x+m+巩固练习：弓+3；+(1+；+9；)-(l+g+K+$x(；+3-)X(H11)(1)(-H11)2320102320123201232010；1317.62011.4(2011.412.5)2.45-(0.13l400)9992+19998llll+99998573+69757236361573697-124727220100.31.2I20120.520129799X49984211423+lo-+71377132
11、Q3-(7.753.3759.253-)927816.251.7+0.751.71,4l-17.6+36-+2.6412.5452009 2010)200920101227427 7 277121(19.2 + 13) 6.25 + (40.8 + 26)6-3 15 U 30 29 - + 0.375 + 38 8 37373739 空+ 148x 也+ 48 卫1491491492 5 .3 7 n 4 951-71-+ 91-3 34 45 5201120112011201210015-+ 198198- + 1131992001-328(3282.5)1.20.752.50.08575
12、-7.50.1(6-5.43+4.57-)-(1-)1.444252469456.879443.48+60l0.0357.15x2.5x18-1.25x28x7.154213”12422+lo-+915991522012)20112012331Q(15-17.7l一一0.75)104323C2K45、-73一(3I)+3.4X511171151.4Ur,八r1414/Cr15.760.21316.37191919190911.566.8+2.41.56+9.20.4467.854.312219%1095”6“11159179 9 1779+50-+76(-)+23(-+)-53(-)23535
13、3762376._161_16._6._1164.75+15F4.75+151141111411W2J2+LZ132251356313+860.25+0.62586-+0.12586-19191919171717、171717(1)99999997979737-0.378.28-3.70.17212+24+36+48+510+10202346+69+812+1015+2030+-一+一+612201一90151119+-一+一+261220109+IlO2+7x13213x192+1451512007282008-28200720071143200898一一22510-+200-28-4255
14、4592-+3-5.22910527.2-6-+5.2295020060.41.6、1)2008x0.52008(1112 3(-)x3322 33-)(ll-L)-(ill+-L)x(l+1+-L)20072320082320082320071+3+5+7+100510071009+1011+2011(257)(-+-)25712(+)23+257169712009120072008)2007200820081237+237237-200.718-270.823923855453-0.25+0.353-+5-3-0.440,82,512.59999(11788x99x10)1789(46-)
15、-+(43-)-+(41-)-+(l-)-78787878(l-L-L)(-L)-(-L-L-L)(-Ll)112131213141112131412131H1F111F1447710101313161619192222x25612203042567290l3-+5-+7+9+1113-+15+17133201.2-+201220.12-520010l32+5+Z+l+H+123457820212435一十FF+HH+F24816326412825651220092-20082502x49899992222+33333334901x8992001x199912502-750220112-200
16、92第二章计算题训练中档题知识要点：1较为复杂的裂项和原理2换元法一换元法z11lxJ11Lzl111Ix11L(1+-+)(-+-+-)-(1+-+-+-)(-+-+)23423452345234(1-18%)5x+9(66-x)=85%5x+80%9(66-x)lx-ll(x-l)-22=ll(x-l)(x+100):(-100)=(3x+300):(x+300)二计算量较大的问题32152(32)(3.375+4)2683101213(1075-4)2(1.125+)(2.2510制199819981998.1I9992三平方差的应用18541X18541 - 12709x1270913
17、500+4?+6?+.+loo?)-#+3?+.+992)1+2+3+10+9+8+1四等比定理的应用7224248(96-+36-)(32-+12)77557755x39t26x2Q+3x915+4xl22p5xl5x2512x3+24x6+369+48J25xl0xl5(ll-l.-)(.)2344950262750五逆向思维的应用141-(378-0-1)l32.4l37_1而二二1-8+-X六从简单情况入手找规律1 1 1111. H123 234891011351H1-. +35711113151111131H11FH1+21+2+31+2+3+41+2+3+4+.+101+2+3+
18、4+5+6+5+4+3+2+16666666623W1(12)(l+2)(l+2+3),(l+2+3+.+9)(l+2+3+.+10)61/2+1/4+1/8+1/16+1/32+1/647I/2+3/4+7/8+15/16+31/32+63/641- + 2- + 4- + 8+ 16+ 32248163216412 2011 13一+30 4215 17156 7210 1 22 33 4.+30 3111 l3+23+33 + .+243七较难的凑整13.631.4+43.96.4(Iq)(i-l).(i-2r)601 602625八估计与放缩A=IllIll110/222222221=
19、444444443888888887比较A与B的大小九循环小数必须化分数再计算:(1)0.29i+0.1钺+0.375+0.5262.829-求S的整数部分8888888888888888-292+0.i29(3)0.330X0.186巩固练习IJ_J_J_J_3-i535-6399-1-i-_1r+.+j.吟l+(l+)(l+)(1+)(1+)(1+)(1+)(1+)(1)(1jqqq)Illl 1I1H2513 8 15 24360169 6FF.H1234234578910135QQ7比较上xxx.N与1/10大小2461001+2+3+4+5+6+7+8+7+6+5+4+3+2+19l
20、2-I6-l12-l20-l30-I42IO3.657.4+69.96.41的整数部分11-.H198119821998121+(1+2)+(1+2+3)+ooo(l+2+3+ooo+50)131+4!-+7+.100114133557676920043-2003(20042+2005)15(0.7542.7-0.57325+57.3)37992161+x%=(l-6.4%)(1+x%+8%)3.计算：238238翁18111011II13Ui可3+60.25+0.6256+60.125=191717171720(16-1.6875+2-)-85612i9920042 - 2004 2003
21、+ 2003230(1) 2.45+3.13；(2) 2.609-1.32；-982972-962+32-22f221998x343x559+37231 53241 239.7xl3169251+1.-L)(ill.232002232001)-(1+l-L)(ll.-L)2200223200126(240.918+2410.8)1827(9772-60100)121993x1994-11993 + 1992199420042-2004lJbL丑.A-第二早兄赛扁643161-5315919971997上空1999199719971+1998 19992199719973997199719971
22、199839971277(4-3)1-(1.75+-)1.651211178(1996199719971996-1996199619971997)199.71.996499请用3, 3, 8, 8算24点4480 21934 1185567i18333 25909 , 3525574137117475-l-+-(3l.1+0.12x2)14773710512599321124724610732132116810041007s.62091069333337例6计算210013228691060222977 1463 3263，,，- XX46189 5957 2793 57911+ +134 3
23、6 144 400 900 178412349I1+-+2232342345234109998971l4+24+.100412+22.1OO2+1232343459910010111FH1212312341234.9第四章有理数计算第一节基础训练知识要点：找片段，定符号，代数和一基础训练一、有理数加法(T) +1Tl(-9)+(-13)(-12)+27(-28)+(-34)67+(-92)(-27.8)+43.9(-23)+7+(-152)+6538+(-22)+(+62)+(-78)(-8)+(-10)+2+(-1)(-1)+0+)+-)+(-f)(-8)+47+18+(-27)(-5)+2
24、1+(-95)+29(-8.25)+8.25+(-0.25)+(-5.75)+(-7.5)6+(-7)+(9)+272+65+(-105)+(-28)(-23)+-63+-37+(-77)19+ (-195) +47(+18)+(-32)+(-16)+(+26)(0.8)+(1.2)+0.6)+(-2.4)(-8)+(-3)+2+(-)+125+(-51)+4+(T)-637)+(-3J)+6.37+2.75二、有理数减法7-9-7-90-(-9)(-25)-(-13)8.2-(-6.3)(一34)5十(-12.5)-(-7.5)(-26)-(-12)-12-18-1-(-)-(+(-20)-
25、(+5)-(-5)-(-12)(-23)-(-59)-(-3.5)-32-(-2)-72-(-5)(-4)-8(+10-(-jf)-3-(-3.2)-74 +6+(-3)-20.5+ (T)- (-2.75) +f+4.3) - (-4) + (-2.3) - (+4)(-0.5) - (-3 ) +6.75-5 三、有理数乘法（-9） (- ) (-0.26)(-2) 3l -0.5) (-5) + -13)(-4) (-10) 0.5 (-3)(- ) 4 (-1.8)n ，(-0.25) X364(-96)X(-0.25)(I-+)56(66) (1 ,22 - )+ ( -)(-36)
26、I+I-j(-)(8-f-0.4)25I-(-25)X=+25-J-c+4-6+9)X72(2-f)(-f)(-)四、有理数除法18(-3)(-24)6(-57)-3)(-42)(-6)90.25-36(-1)-f)-l)-4)3(-)(-)O(-3j)X(-7)3(-j)(-241)(-6)2(5-18)1j(3)()i(-1)+(一*)4-)-6(I-+4)(-)-3.5(-OJ)7,-,716.y/1-L)二f工二(_)2)-工X工二a5入32j-47k5712340.8+4.8(-)-2.2I+0.8五、有理数混合运匏6-+5-(-154)(-)7(-2.4)2(T)I(-5)15-l
27、f+3(-)fX(-5)(-)5(-LL4.-22二/一-L321+147J，42,-13I-0.34+(-13)-0.348-25)(-5)-13)(-134)-)178-87.21+43+53-12.79(-6)(-4)+(-32)(-8)-3(-9)(-4)+(-60)l2l(-)-+J(-)-310-(-15)Xv-1(-7)4o11(-2)2-2(-i)2-3(-6)29(-69)236(-i)2-(-3)3-3+0.4-1-j(-2)-14(1-0.5)-2(-3)2I2J3-33-4(l-7)(-5)3-3(-2)3-(-2-1+(-3)2(-2)3巩固练习-3211535111
28、2347471.2+3J+（）(-5.3)+3.27- (-25)-4.8391511414 3 1443.2-+S-+-+-+(-7-)-5-0.182+3.105-(0.318-6.065)-15-3-+5.5 -2.754-4-6(+3.6)-(-3-)- (1-)6-+24+4.4-16-6.8-3.25-3F 0.5 1-2 6672-Ll(-1-)(-3-)237-3X 2r (-1一)352346-+24+(-18)4-16+18-6.8+(-32)5523 155-156164114 8552510510987987 (-987 )988338929-12-7-(-2-)(1-
29、)(l-)(-2-)238(-238-)239启斗/)425842533241512212-2-2-(1-1-)4-33-2.57(-l-)(-5)725117251135514133-0.124(-)(-100)17.894-75-l-1-61054105-2-55(-4-)(-l-)(-3-)-32-(-3)2+(-2)2-23325131o1332-2.50.75(-)(-l)(-1.4)-I232(6.8752)0.25(31)42.5O.320.52(-2)2.41-4.125-(18-13.42)-3-(-l-)21-31375517216(-2)2+(-2)97+(l-5)(-2
30、)12-25.229-ll-3-171410 10(1-+0.75+)22+0.5z497u4949、ro14J4、G(X+1.65)2(4-2)1.359020909015153Z+43+5x+6241-+51-+61-137137344556123I271+(-+-)(2-3-)126.3(1)小2 2、/5 5(9- + 7-)(-+ -797 923411311第二节提高篇3、仔L(-3。 J J4、2-f-8-1 f-2-1+ 25-15-2.75 04 I 2； I 4j6、 - 3 1 7、10.81；8、176.2580.75；566429、1 113 41 11O5 62/一
31、2 斗色 X，闫一 0.75； 5 1 5)21 I 4；11、-1- 1-(1-0. 63) X 2-(-3) (-4)；12、5 2耳(3Q (+4) X(0.2)；14、(-253(-)X .4(7j2/ (YoOO+(T)。15、(-3+4-2216、(_3计4+(_3)卜(一5)。17、0(-4)-42-(-8)(-D3:18、-32-(-3)2-(-3)3+(-l)6:21、3X(-2)2+(-2X3)2+(-2+3)2;22、-5-l-0.2(-3j0.2(1V(1V、26、-l(-2j1-1+-1-l-2-2JI2J27、8.12-(-16)-4-55K-2(-l)J28、-2
32、EX(-2)29.jW-4)-0.25(-5)(-4j;30、:卜(-24)5(-1)；31、-25(-4)-12-15+24;32、-6-G22)+02+23-9215,5735、-37-3(-9)+-(-8)o36、-2Q(3 + 4.375)19-(-2+(-0.28)O37、(1)x4(-4)+-1；卜（-。4）r52c5223940(-2) (-3) (-6) + (-1)20 6383144134-+(-22)-227242(-3.75)4.23(-36)+125(-2.8)0.423巩固练习1、7-(l-l-+3-)(-2-)928442、-34-2-(-4)(14-16)4J13133、21(5?+5x3+3?)4、5(2)3(10.8-)-1-1|5、(5)(16)(2)36、-4+2(-3)-60.2537、(5)1.85(21-)X748、18l-0.4+(1-0.4)X0.411、(3. 5-7. 75-4. 25)1. 113.323-5322+632i10、-3-4-(4-3.5-)X-2+(-3)
