三年级奥数乘法简便运算及答案

2018 秋季数学集训三队 A 教材每周习题 (6) 参
考答案
星期一
简便计算。

125 X 4X 8X 25 X 5 X 2
1200
=(125 X 8) X (4 X 25) X (5 X 2)
=1000 X 100X 10 =600000 - (125 X 8) - (25 X 4) =600000 - 1000 - 100
8- 7+ 9 - 7 + 11-7
125
X 401
21
X 73＋26X 21 ＋21 =(8 + 9 + 11) - 7
=125X (400 + 1)
=21 X (73 + 26 + 1) =28 - 7
=125X 400 + 125
=21X 100 =4
=50000+125
=2100
=50125
=1000000
=48
=6
或：原式=12 X (100 - 25)
=12 X 4
=48
600000
=(1200 X 4) - (25 X 4)
=4800 - 100 372- 162X 54
=372 - (162 - 54) =372 - 3 =124
2222
X 9998
981
＋5X 9810＋49X 981 =2222 X (10000 — 2) =981 + 50X 981 + 49X 981
=2222X 10000—2222 X 2 =981 X (1 + 50 + 49)
=22220000—4444 =981X 100
=22215556
=98100
简便计算。

222X 444＋222X 556
=222 X (444 + 556) =222X 1000
=222000
1440
X 976 - 488
=1440 X (976 - 488) =1440X 2 =2880
28 - 3 X 54 X 15 -54 - 14
(48
=(28 - 14) X (54 - 54) X (15 - 3) =2X 1X 5 X 75 X 81) - (25 X 24 X 27) =(48 - 24) X (75 - 25) X (81 - 27) =2 X 3 X 3 =10
=18
(720 — 180-450) - 9
72
=720 - 9— 180 - 9 — 450 - 9 =80 — 20 —
50
=10
X 108＋108X 46— 118X 142＋118X 134 =108 X (72 + 46) — 118 X (142 — 134) =108X 118 — 118X 8 =118 X (108 — 8) =11800
星期二
星期三
简便计算。

450000 - (25 X 45)
3333
X 2222 - 6666
=45 X 10000 - 25 - 45
=1111 X (3 X 2222 - 6666) =(45 - 45) X (10000 - 25)
=1111X 1 =1X 400
=1111
=400
13-9 + 5-9+ 21 - 5— 6 - 5
25
X 77+ 55X 14+ 15X 77 =(13 + 5) - 9 + (21 — 6) - 5 = 25X 77+ 10X 77+ 15X 77 =18-9 + 15- 5
=77X (25+10+15) =2+ 3
= 77X 50 =5
= 3850
999 X 999+ 1999
125
=999 X 999+ 999 + 1000 =999 X (999 + 1) + 1000 =1000 X (999 + 1) =1000000
333X 666+ 999X 778
234
=333 X 3X 222 + 999X 778 =999 X (222 + 778) =999X 1000 =999000
星期四
189+188+187X 98
3
-(5 - 7) - (7 - 9) - (9 - 11) + •••十(2013 - 2015) = 187X 2+2+ 1+ 187X 98
=3-5X 7- 7X 9- 9X 11+ …十 2013X 2015
=187X (2+98)+3
=3X (2015 - 5) = 18700+ 3
= 3X 403 = 18703
= 1209
54 X 36 X 56 - 36
(123456
+234561+ 345612+456123+ 561234+612345) - 7
=(54 X 56) X (36 - 36) =(111111 + 222222 + 333333 + 444444 + 555555 + 666666) - 7 = 5X (5 + 1) X 100+ 4X 6
=(111111 + 666666) X 3 - 7 = 3000+ 24
=777777- 7X 3 = 3024
= 333333
X 36 - (18 - 8) =125 X 36十 18X 8 =(125 X 8) X (36 - 18) =1000 X 2 =2000
X 566－233X 567
=(233 + 1) X 566- 233 X (566 + 1) =233 X 566 + 566- 233 X 566 — 233 =566—233 =333
1. 简便计算。

12345X 99+12345X 999—98X 12345
=12345 X (99 + 999— 98) =12345X 1000 =12345000
209209209
X 803— 803803803X 209
=209X 1001001 X 803— 803X 1001001 X 209
2.1234567654321 X (1 + 2+ 3 + 4 + 5+ 6+ 7 + 6 + 5+ 4 + 3 + 2+ 1)是什么平方数?
解：原式=1111111 X 1111111 X 7X 7
=100 — 1 + 100 — 1 =198
=(1111111 X 7) X (1111111 X 7)
=77777772
答：该平方数是 7777777：
1.简便计算。

5432X 9090 + 5432X 909
9
=5432 X (9090 + 909) =5432 X (10000 — 1) =5432X 10000—5432
=54320000— 5432
=54314568
星期五
X 17+ 91 - 17— 5 X 17 + 45 - 17 =(9 — 5) X 17+ (91 + 45) - 17 =4 X 17+ 136 - 17 =68 + 8 =76
2997 X 729 - (81 X 81)
3861 =(2997 - 81) X (729 - 81) =37 X 3 X 3 -39 + 8613- 87
=(3900 — 39) - 39+ (8700 — 87) - 87 =3900 - 39 — 39 - 39 + 8700 -87 — 87- 87 =111 X 3
=333
1997X 1999—1996X 2000
1 =1997 X (2000 — 1) — 1996 X 2000 =1997X 2000—1997—1996X 2000 =2000 X (1997 — 1996) — 1997 =2000—1997
-(3 - 5) - (5 - 7) - (7 -9)十…十(998 - 999) =1十3X 5十5X 7十7X 9十…十998X 999
=1 X 999 - 3
=333
2.计算：36X 34= 1224 ; 27 X 23= 621 ; 69X 61 = 4209 ; 52 X 58= 3016
(1)根据上面的计算，请总结出这类“头同尾合十”的简便算法。

先将两个因数的个位数相乘，并把积写在末尾，如果积不满 的十位数乘它本身加 1的和，积写在两个个位数积的前面。

10,十位上要补写0;然后再将两个因数
(2)利用上面的结论计算:
18X 12=
216
; 72 X 78= 5616 ; 91 X 99=
9009
3.计算：63X 43= 2709 ; 72 X 32= 2304 ; 96X 16 = 1536 ; 25 X 85= 2125
(1)根据上面的计算，请总结出这类“尾同头合十”的简便算法。

先将两个因数的个位数相乘，并把积写在末尾，如果积不满
10,十位上要补写0;然后再将两个因数
的十位数相乘后再加上个位数，和写在两个个位数积的前面。

(2)利用上面的结论计算：81 X 21= 1701 ; 27 X 87= 2349 ; 19X 99= 1881。