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速算的方法与技巧

(2013-10-08 13:46:16)

  速算的方法与技巧

  一. 十几乘十几的速算方法是:将这个数加上一个数的个位数,得数作前积,然后两个个位数乘得数作后积,满十左进。 口诀:先加后乘

                     14+2=16

 (1) 14X12=                      [连写]=168

                     4X2=8

   

                     13+3=16

2 13X13=                      [连写]=169

                     3X3=9

                    15+2=17

315X12=                        [连写]=180

                     5X2=10

              

                     17+8=25

 (4) 17X18=                        [连写]=306

                      7X8=56

­

练习题:

16X18=                               17X19=                             15X14=

13X17=                               18X15=                             12X19=

­

    .一百零几乘一百零几(一百一十几)的速算方法:被乘数加上乘数的个位,得数作前积,两个尾数(包括十位和个位)相乘得数作后积(没有十位用零补)

     口诀:先加后乘

                     108+4=112

(1) 108X104=                            (连写)=11232

                         8X4=32

                       107+9=116

(2) 107X109=                             (连写)=11663

                         7X9=63

­

                      102+3=105

(3) 102X103=                             (连写)=10506

                        2X3=06

­

                      112+4=116

(4) 112X104=                            (连写)=11648

                       12X4=48

­

练习题:

 108X105=              106X107=                104X109=             119X108=

 102X107=               109X103=               105X106=             115X106=              

­    .个位是1的两位数相乘的速算方法是:十位数与十位数相乘得数作前积,十位数与十位数相加,得数作后积,得数接写,最后再添1.(满十位左进). 口诀:先乘后加再添1

                  5X2=10

       (1)51X21=                   (连写)=1071

                     5+2=7  

­

                    6X8=48

      (2)61X81=                    (连写)=4941

                    6+8=14                  

     ­

练习题:

    31X51=                    61X71=                        81X31=

    51X41=                    81X61=                        21X91=

­

­    .十几乘几十几的速算方法是:被乘数的个位乘以乘数的十位所得的积与乘数相加得数放作积前,个位相乘得数作积后(满十左进)

                        4X7+72=100

(1) 14X72=                                  (连写)=1008

                          4X2=8

­

                          5X6+64=94

(2)15X64=                                       (连写)=960

                          5X4=20

­

 练习题:

     13X39=                       16X78=                      15X96=

     12X34=                       17X82=                      19X48=

­

    .十位数相同的两位数相乘的速算法:一个数加上另一个数的个位得数乘以十位得出的积作前积,两个位相乘得数作后积,满十位左进.

                      42+3)X4=180

:(1)42X43=                                 (连写)=1806

                      2X3=6

­

­                      (65+3)X6=408

(2)65X63=                                     (连写)=4095

                       2X3=6

­

 练习题:

   37X36=                    29X28=                        43X46=

   87X88=                    67X62=                        74X78=

­

­    .十位数相同,个位之和等于10的两位数相乘的速算方法是:十位加1乘十位,个位乘积接着写(没有十位用零补)

                (6+1)X6=42

63X67=                               (连写)=4221

                3X7 =21

­

                (8+1)X8=72

82X88=                                (连写)=7216

                 2X8=16

­

                 (7+1)X7=56

71X79=                                 (连写)=5609

                  1X9=9

­

练习题:

          31X39=                      42X48=                         53X57=

          64X66=                      82X88=                         96X94=

­

­

    .被乘数首尾之和是10,乘数首尾相同的两位数相乘的速算方法是:被乘数十位加1得数再乘以乘数的十位,得出的积作积前,两个位相乘得出的积作积后,没有十位用零补.

                           (4+1)X5=25

(1)  46X55=                                   (连写)=2530

                           6X5=30

­

                           (3+1)X8=32

(2)   37X88=                                     (连写)=3256

                           7X8=56

­

­练习题:

    28X33=                       19X66=                            46X88=

    37X22=                       55X44=                            64X77=

   

    .两首位和是10,两尾数相同的两位数相乘的速算方法:两首位相乘之积加上一个尾数,得数放积前,两尾数相乘(尾平方),得数放积后,(没有十位用零补)

                            2X8+6=22

:26X86=                                      (连写)=2236

                            6X6=36

­

                           2X8+1=17

21X81=                                          (连写)=1701

                            1X1=01

­

                                没有十位用零补

练习题:

   85X25=                             47X64=                    38X78=

  94X14                               53X53=                    69X49=

­

    .两首位差是1,两尾数和是10的两位数相乘的速算方法是: A2-B8=(A+B)·(A-B)

­

:(1)38X22=(30+8)X(30-8) =900-64=836

   (2)46X34=(40+6)X(40-6) =1600-36=1564

­

练习题:

    85X75=              64X56=               78X62=

    96X84=              38X22=               73X67=

­

  . 30以下的倍数乘以37的速算方法是:看被乘数是3的几倍,积就是3个几.

­

 (1)24X37=24÷3=8        连写38=888

     (2)15X37=15÷3=5         连写35=555

­

练习题:

   12X37=                        18X37=                    27X37=

­

    十一. 3的两位倍数乘以34的速算方法是:将这个数除以3,得出的数作积前,然后将积前乘以2得出的数作积后.

­

 (1)42X34=?

                     42÷3=14    

42X34=                             (连写)=1428

                     14X2=28

­

(2) 84X34=?

                     84÷3

84X34=                              (连写)=2856

                    28X2=56

­

练习题:

   39X34=                       63X34=                            87X34=

   99X34=                       84X34=                            57X34=

­

­    十二.3的两位倍数乘以67的速算方法是:将这个数除以3,所得的积作后积.后积乘以2得出的积作前积.

                       42÷3=14           积后

  :(1)42X67=                                              (连写)=2814

                       14X2=28            积前

­

                       81÷3=27           积后

     (2)81X67=                                              (连写)=5427

                       27X2=54            积前

­

练习题:

  66X67=                        39X67=                             87X67=

  84X67=                        54X67=                             69X67=

­

­    十三.任何多位数乘以11的速算方法:将这个数的头尾两位数写在积的头尾,然后将这个数从右到左挨位相加的和,依次放中间,满十左进.

(1).32152 X 11 =?

              23  12  51  52 从右至左换位相加

32152X11= 3        2

                             

练习题

     67X11=                      369X11=                     357X11=

  13456X11=                    37865X11=                     38X11=

­

­    十四.几百零几乘以两位数的速算方法是:将几百零几的百位乘以这个两位数得出的数作积前;几百零几的个位数乘这个两位数得数作积后.满百位左进.

­

                          6X38=228

: 602X38=                                       连写=22876

                          2X38=76

­

                          3X26=78

304X26=                                         连写=7904

                         4X26=104

­

练习题:

  405X29=                      607X58=                          903X36=

  709X82=                     605X37=                             806X47=

­

­

    十五.四位数与两位数相乘的速算: 千百乘两数积前,个十乘两放积后,满百位左进

­

                      63X23=1449

6324X23=                                      连写=145452

                     24X23=552

­

                                         ­

练习题:

1024X34=                2136X42=                 3725X63=            4382X46=

­

    十六.几百零几乘以几百零几的速算方法是::百位是头,个位是尾

口诀:X=    X=    X+X=   没有十位用零补

                  5X6=  30

:504X608=   5X8+4X6=  64            连写=306432

                  4X8=  32

­

                  2X8=16

207X802=      2X2+7X8=60            连写=166014

                  7X2=14

练习题:

307X608=                    503X706=                      309X708=

403X504=                    602X702=                      905X906=

    十七.任何数乘以25的速算方法是:将这个数除以4,所得的商乘以100,得数便是准确答案.

­

                                 3248÷4=812

:3248X25=                                                =81200

                               812X100=81200

­

    十八.任何数乘以125的速算方法是:将这个数除以8,所得的商乘以1000得数便是答案.

­

                               843÷8=105.375

:843X125=                                                  =105375

                               105.375X1000

­

    十九.任何数乘以625的速算方法是:将这个数除以16,所得的数乘以10000,得数便是答案.

­

                                   963216=602

:9632X625=                                                    =6020000

                                   602X10000=6020000

­

任何数乘以25.  125 .  625  的练习题

387X25=                        429X25=                      372X25=

5832X125=                     376X125=                    4963X125=

6498X625=                    3754X625=                     982X625=

­

   .任何两位数与101相乘的速算方法是:将这个两位数连写两次便是答案.

  

:82X101=8282           96X101=9696

­

    二十一.任何三位数与101相乘的速算方法是:将这个数的前两位(百位和十位)放在前,后两位(即个位与十位)放在后,首尾相加放中间,(逢十位左进)

                   32

:324X101=        3+4=7       连写=32724

                   24

                   53

:536X101=        5+6=11        连写=54136

                   36

    二十二.任何四位数与101相乘的速算方法是:将这个数的前两位,(即百位和千位)放在前,后两位(即个位和十位)放在后,相间相加放中间(逢十位左进)

­

                      32

                        3+4=7  

  :3243X101=       2+3=5      连写=327543

                     43                                                                         ­

­                               

                  52

   5264X101=      5+6=11     连写=531664

                    2+4=6

                    36

练习题:

  35X101=             72X101=               48X101=      

 326X101=            738X101=              841X101= 

1204X101=            3248101=             5362X101=

   

    二十三.任何两位数与111相乘的速算方法是:将两位数的头尾分别作积的头尾,两位数头尾相加的和连写两次放在中间,(逢十在进)

                 2

24X111=        2+4=6连写两次=66             =2664

                 4

­

                 3

38X111=          3+8=11连写两次 (满十左进         =4218

                 8

练习题:

36X111=                  48X111=                       53X111=

84X111=                  38X111=                       96X111=

    二十四.几百零几与三位数相乘的速算方法是:百位乘以乘数,得数作积前,个位乘以乘数得数作积后.(逢百左进)

                  3X321=963 (前积)

:302X321=                                     连写=96942

                  2X321=642 (后积)

­

­

        逢百左进

:几百零几的数,须放在被乘数的位轩上进行速算

­

练习题:

305X218=                  406X272=                    307X123=

508X632=                  704X346=                    603X278=

­

    二十五. 二至四位数平方的速算法:

1.求个位是5的平方速算法:

               (3+1)X3=12

(1) 35X35=     再写25 :5X5=25            连写=1225

                       

­

                (41)X4=20

(2)452=         再写25 :5X5=25          连写=2025

                        

­

2. 25——75之间的平方速算法:

将这个数和25比较:得出差数作积前,50比较差的平方放作积后.(差平方没有十位用零补)

                  46-25=21

:46X46=                             连写=2116

               (50-46)2=16  

­

                  43-25=18

   43X43=                             连写=1849

               (50-43)2=49

­

                  56-25=31

   56X56=                             连写=3136

               (56-50)2=36

­

                  58-25=33

   58X58=                             连写=3364

               (58-50)2=64

­

(3)75----99之间的两位数平方:

首先我们应掌握:19的补数,28的补数,37的补数,46的补数,55的补数.

1+9=10      2+8=10      3+7=10         4+6=10        5+5=10

什么叫补数,将这个数凑它成整十,整百.整千.整万.十万.百万……的另一个数就是它的补数,速算方法:将这个数减去自己的补数得数作积前,补数平方得数作积后,(满百左进,没有十位用零补).

                  97-3=94

:97X97=                                   连写=9409

                   3X3=9 (没有十位用零补)

­

                  96-4=92

   96X96=                             连写=9216

                   4X4=16

­

                 88-12=76

   88X88=                            连写=7744

                 12X12=144

­

­两位数平方练习题:

252              352                652                752=

552              952                472                382=

532              622                492                372=

862              942                782           722=

3. 求三位数,四位数的平方速算:

    将这个数分成左右两段,(三位数右段包含两位)先算左段平方(a2)得数作积前,再算左加两段积的2(a.bx2)得数作积中,然后再算右段平方(b2)得数作积后.满百左进.

公式    a2=    a .bx2=    b2=

             3       先算3X3=9

:3072               3X07X2=42             连写=94249  

            右边 07       07X07=49

­

                    先算4X4=16

 4122                  4X12X2=96             连写= 169744   a2  b2    3072

              右边12      12X12=144  (满百左进)

­

                12, 先算12X12=144

12042                  12X04X2=96        连写=1449616

            右边12        04X04=16

练习题:

3082                              4132                      5262=

17032                             12632                     32142=

­

  二十六.任何多个9乘以不大于它的数的速算方法是:乘数减去1作积前,被乘数再减去积前作积后.

  

                    86-1=85

:99X86=                              连写=8514

                   99-85=14

­

                        374-1=856373

999999X856374=                          连写=856373143626

                999999-856373=143626

­

  二十七.任何多个9乘以大于它的数的速算方法是:看这个数被乘数是多少个9组成,就在乘数后面添上多少个零.然后减去这个乘数.

­

                被乘数是由两个9个组成

:99X123=                                 =12300-123=12177

                123的后面添两个0

­

9999X53768=537680000-53768=537626232

                                      

  二十八.两个接近100100010000 ……的数相乘的速算方法是:将一个数减去另一个数的补数,得数作积前,两补数相乘得数作积后,(注两位数没有十位用0,三位数没有百位用0,四位没有千位以上以此类推.

­

               97的补数是  95-3=92

:97X95=                                    连写=9215

                95的补数是  5X3=15

­

           89的补数是11  98-11=87

   89X98=                               连写=8722

            98的补数是   11X2=22

­

                 988的补数是12  987-12=975

  987X988=                                        连写=975156

                 987的补数是13   12X13=156

­

                                          四位数没有千位用0              0168

                 995的补数是   1046-5=1041

995X1046=

                1046的补数是-46   5X(-46)=-230

因为9951046都接近1000,所以在前积后面先添30,1041000,再加上补数相乘的积,-230 =1041000-230=1040770    995X1046=1040770

­

练习题:

86X94=                  73X95=                       103X97=

987X996=                1032X998=                   9986X9988=

10023X9997=             9899X9789=                   10048X9996=

­

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