有理數(中學奧數)

(1) 89 + 899 + 8999 + 89999
= 90 - 1 + 900 - 1 + 9000 - 1 + 90000 - 1
= 99990 - 4
= 99986
(2) 32*75*125
= 4*75*8*125
= 300*1000
= 300000
(3) 88*1.25 - 7 25
=11*8*1.25 - 7*4/100
= 11*10 - 28/100
= 110 - 0.28
= 109.72
(4) 9999 * 2222 + 3333 * 3334
= 3333 * 3 * 2222 + 3333 * 3334
= 3333 * 6666 + 3333 * 3334
= 3333 *(6666 + 3334)
= 33330000
(5) 1999 * 20002000 - 2000 * 19991999
= 1999 * 2000 * 10001 - 2000 * 1999 - 10001
= 0
(6){3_ 33份之5+9_11份之5+11_9份之5}{3_33份之1+9_11份之1+11_9份之1
= (104/33 + 104/11 + 104/9) / (100/33 + 100/11 + 100/9)
= [104(1/33 + 1/11 + 1/9)] / [100(1/33 + 1/11 + 1/9)]
= 104/100
= 1.04
(7) S = 1+2+3+.....+100
S = 100 + 99 + 98 + ... + 1
S+S = 101 + 101 + 101 + ... + 101 共100項
2S = 101 * 100
S = 5050
(8) S = 1+3+5+.....+99
S = 99 + 97 + 95 + ... + 1
S + S = 100 + 100 + 100 + ... + 100共50項
2S = 100 * 50 /2 = 2500
(9)1-2+3-.....100
= (1 - 2) + (3 - 4) + (5 - 6) + ... + (99 - 100)
= -1 - 1 - 1 - ... - 1共50項
= -50
(10) 99^2
= (100 - 1) * 99
= 9900 - 99
= 9801
(11) 9876543211^2 - 9876543210*9876543212
= 9876543211^2 - (9876543211 - 1)(9876543211 + 1)
= 9876543211^2 - (9876543211^2 - 987654211 + 9876543211 - 1)
= 1

2009-10-10 12:36:03 補充：
更正:
5) 1999 * 20002000 - 2000 * 19991999

= 1999 * 2000 * 10001 - 2000 * 1999 * 10001

= 0

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