第一章计算题训练基础篇.docx

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(a÷b)+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=a÷c+b÷c(a-b)÷c=a÷c-b÷ca-b-c=a-(b+c)a-(b-c)=a-b+ca÷b÷c=a÷(bc)3 平方差公式：(a+b)(a-b)=a2b24 熟记100以内质数:2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,975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17×1999×9279×12102×2761×371997×999二用结合律凑整25×48125×368375×56124÷0.12524÷0.3757992×253125÷25三化多位数为一位数2722824.2×4548×4537×814.2x45四凑整意识之分配律【例1】计算：200.9X20.08-200.8X20.07【巩固】计算:20.09×31.5÷2,009×317+200.9×3.68=【巩固】计算:2.009x43+20.09x2.9+200.9x0.28=【巩固】计算:1999×3.14÷199.9×31.4+19.99×314.【巩固】计算:199.9×19.98-199.8×19.97【巩固】计算:10.37×3.4÷1.7×19.26=【例2】计算：6.25×8.27×16÷3.75×0.827×8【巩固】计算:20.09×62+200.9×3.9-7x2.87=【巩固】计算:2.89x47+1.53-1.4x1.1+24x0.11+288x0.53-0.1=【巩固】计算:223×7.5+22.3×12.5+230÷4-0.7×2.5+1=【巩固】计算：19.98×37+199.8×2.3+9.99×80【巩固】计算：379×0.038+159×0.00621+3.79x0.121【巩固】计算78.16x1.45+3.14x21.84+169x0.7816【巩固】计算:7.8I6×1.45+3.14×2.184+1.69×7.816=【巩固】计算：147.75×8.4+4.792+409×2.1+0.9521×479【例3】计算：125÷3.6-7÷9+83÷3.6【例4】计算8.1×1.3-8÷1.3+1.9×1.3+11.9÷1.3【例5】(2)2003×2001÷111÷2003×73÷37【例6】计算：5L2×8.1+11×9.25+537×0.19【例7计算：223×7.5+22.3×12.5+230÷4-0.7×2.5+l【巩固】1.25×17.6+36÷0.8÷264×125=【例8】计算：2007-(8.5×8,5-1.5×1.5)÷10÷160-03.【巩固】计算(980X65320)÷(66+98X64)【巩固】2004.05×1997.05-2001.05×1999.05【巩固】(873x477-198)+(476x874+199)【例9】计算：1.23452+0.76552÷2.469×0.7655.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+0.99-0.98-0.97÷0.96+0.95-0.94-0.93+÷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)9.996÷29.98÷169.9+3999.5(2)89+899+8999+89999+899999模块三、位值原理例6(123456789.987654321+234567891.198765432+912345678.876543219)÷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11÷÷÷÷±kfa+2+2+23420JU45÷AYf2+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-55彳列2、2005×97.75+4010×l.12537×llll+7777×9巩固练习：4.7×2.8+3.6×9.4999×778+333×666例3、199×208-198×209巩固练习：35×67-34×681324、-×39+-×25+-×35551119巩固练习：17X至+llJoJO例5、12×3434-34×1212巩固练习：20182018×1998-19981998X2018例 6、 123÷12312312415731巩固练习：1573÷1573-÷15741575例7、159×-105×535353104巩固练习:169×Illlll131313+2004×20022003例8、1477×101+100x103巩固练习:13×55×7HF7x9299x1011-5-+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)2320102320123201<232010；1317.6×2011.4÷(2011.4÷12.5)×2.45-÷(0.13×l÷400)×9992+19998×llll+9999×8573+697×57236361573×697-12472722010×0.31.2I2012×0.520129799X499842114×23+lo×-+×71377132Q3-×(7.75÷3.375÷9.25×3-)927816.25÷1.7+0.75÷1.71,4l-×17.6+36÷-+2.64×12.5452009 2010)×2009×2010×1÷22÷7×427 7 277121(19.2 + 13)× 6.25 + (40.8 + 26)×6-3 15 U 30 29 -× + 0.375× + 3÷8× 8 37373739 空+ 148x 也+ 48 卫1491491492 5 .3 7 n 4 951÷-÷71-÷-+ 91÷-3 34 45 52011÷2011201120121001×5-+ 198÷198- + 1131992001-328÷(328×2.5)÷1.20.75×2.5÷0.085×75-7.5×0.1(6-×5.43+4.57÷-)-(1-)×1.4442524694×56.87÷94×43.48+60×l0.0357.15x2.5x18-1.25x28x7.154213”124×22+lo×-+×915991522012)×2011×2012331Q(15×-÷17.7÷l一一0.75)×104323C2K45、-73一×(3I)+3.4X511171151.4Ur,八r1414/Cr1×5.760.213×1×6.37191919190911.56×6.8+2.4×1.56+9.2×0.44×67.8÷54.3÷1221×9%1095”6“11159179 9 17×79+50×-+×76×(-)+23×(-+)-53×(-)235353762376._161_16._6._1164.75×+15×F4.75×+15×1141111411W÷2J2+LZ132251356313+86×0.25+0.625×86-+0.125×8