Question

小学奥数简便运算

1. 2007×20082008—2008×20072007

2. 4.2÷0.25÷4

3. 2+4+6+8+、、、+96+98+100

4. 1/4×3÷1/4×3

5. 1/1×3+1/3×5+1/5×7+、、、+1/19×21

6. 9999×7＋1111×37

Answer 1

1. 2007×20082008—2008×20072007
=2007×2008×10001-2008×1007×10001
=0

2. 4.2÷0.25÷4
=4.2÷(0.25×4)
=4.2÷1
=4.2

3. 2+4+6+8+、、、+96+98+100
=(2+100)×50÷2
=2550

4. 1/4×3÷1/4×3
=1/4÷1/4×3×3
=9

5. 1/1×3+1/3×5+1/5×7+、、、+1/19×21
=(1/2)×(1-1/3+1/3-1/5+1/5-1/7+....+1/19-1/21)
=1/2×(1-1/21)
=10/21

6. 9999×7＋1111×37
=1111×9×7+1111×37
=1111×(63+37)
=1111×100
=111100

Answer 2

2007x20082008-2008x20072007
=2007x2008x10001-2007x2008x10001
=0

Answer 3

1.=4/3x2/3x5/4x3/4x……x101/100x99/100
=(4/3x5/4x6/5x……x100/99x101/100)x(2/3x3/4x4/5x……x98/99x99/100)
=101/3x2/100
=101/150
2.请问是否忘了加括号？（1999+2000x1998）/（1999x2000-1）
=[(2000-1)+2000x(2000-2)]/[2000x(2000-1)-1]
=(2000x2000+2000-2000x2-1)/(2000x2000-2000-1)
=(2000x2000-2000-1)/(2000x2000-2000-1)
=1
3.(2002x1999-1957)/(42+1999x2001)
=(2002x1999-1999+42)/(2001x1999+42)
=[(2002-1)x1999+42]/(2001x1999+42)
=1
4.1/(2x4)+1/(4x6)+1/(6x8)1+/(8x10)+1/(10x12)
=1/4x(1/2+1/6+1/12+1/20+1/30)
=1/4x(1x1/2+1/2x1/3+1/3x1/4+1/4x1/5+1/5x1/6)
=1/4x(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6)
=1/4x(1-1/6)
=5/24

Answer 4

2000+1999-1998-1997+1996+1995-1994-1993+……+1108+1107-1106-1105+1104+1103-1102-1101
=(2000+1999-1998-1997)+(1996+1995-1994-1993)+……+(1108+1107-1106-1105)+(1104+1103-1102-1101)
很明显每一括号里的4个数的和都是4，而且一共有(2000-1108)/4+1=893个括号。
所以总和是4*893=3572.

Answer 5

你有没抄错题？