学而思 |思维培优 | 作业讲解 | 五讲一测

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解:加减法巧算的应用。8道题用时超过20分钟的话,说明巧算原理还没有掌握扎实,请加强锻炼,提高数感!
1) 163-(50-18)-(153-76)+(124-18)
=163-50+18-153+76+124-18 // 不要省略掉这一步,两步合一步容易出错
=(163-153)+(76+124)+(18-18)-50
=10+200-50
=160
2) 267−162+84−38−147+116
=267−147−162−38+84+116
=(267−147)−(162+38)+(84+116)
=120-200+200
=120
3) 12+23-34+45-56+67-78+89-78+67-56+45-34+23+12
=(12+23)+(45-34)+(67-56)+(89-78)+(67-56)+(45-34)+(23+12)-78
=35+11x5+35-78
=55+70-78
=47
4) 1989+1988+1987-1986-1985-1984+1983+ 1982+1981-1980-1979-1978+…+9+8+7-6-5-4+3+2+1
=(1989+1988+1987-1986-1985-1984)+(1983+ 1982+1981-1980-1979-1978)+…+(9+8+7-6-5-4)+3+2+1
=9x331+6
=2985
5) 83+86+95-85+86-94+95+94+86+92+87+80+93+100-89+83+96+98
=83+86+95+86+95+94+86+92+87+80+93+100+83+96+98-85-94-89
=15x90-3x90-7-4+5-4+5+4-4+2-3-10+3+10-7+6+8+5-4+1
=12x90-7-4+5-4+5+4-4+2-3-10+3+10-7+6+8+5-4+1
=1080+6
=1086
6) (2000-1)+(1999-2)+(1998-3)+…+(1002-999)+(1001-1000)
=2000-1+1999-2+1998-3+…+1002-999+1001-1000
=(2000-1000)+(1999-999)+(1998)+…+(1003-3)+(1002-2)+(1001-1)
=1000x1000
=1000000
7) 19+28+37+46+55+64+73+82+91+ [ 55 ] =550
19+28+37+46+55+64+73+82+91
=(19+91)+(28+82)+(37+73)+(46+64)+55
=110x4+55
=440+55
=495
550-495=55
8) (1234+2341+3412+4123)÷5 = 2222
1234+2341+3412+4123 四个数按位加起来,个十百千每一位上都是10
然后除以 5,那么个十百千每一位上都是2。故:2222
解:
1244+2355+3466+4577+5688-6513-5412-4311
=(1234+10)+(2345+10)+(3456+10)+(4567+10)+(5678+10)-(6543-30)-(5432-20)-(4321-10)
=1234+10+2345+10+3456+10+4567+10+5678+10-6543+30-5432+20-4321+10
=1234+2345+3456+4567+5678-6543-5432-4321+110
=984+110
=1094

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