Question

七年级计算题

1-3+5-7+9-11+......+4997-4999=?

1/3-7/12+9/20-11/30+13/42-15/56=?

Answer 1

1-3+5-7+9-11+......+4997-4999
=(1-3)+(5-7)+(9-11)+...+(4997-4999)
=-2+(-2)+(-2)+...+(-2)
=-2×[(4997-1)÷4+1]
=-2×1250
=-2500;

1/3-7/12+9/20-11/30+13/42-15/56
=1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)
=1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8
=-1/8;

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Answer 2

（1）1-3+5-7+9-11+......+4997-4999=?
前后2位结合，即1-3=-2，5-7=-2......
共有(4999-1)/2+1=2500个数，即有2500/2=1250组-2，
所以结果为-2*1250=-2500
（2）1/3-7/12+9/20-11/30+13/42-15/56
1/3-7/12+9/20-11/30+13/42-15/56
=1/3-(1/3+1/4)+(1/4+1/5)-(1/5+1/6)+(1/6+1/7)-(1/7+1/8)
=1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8
=-1/8

Answer 3

1-3+5-7+9-11+......+4997-4999=-2*2500=-5000
1/3-7/12+9/20-11/30+13/42-15/56=1/3-1/3-1/4+1/4+1/5-1/5-1/6+1/6+1/7-1/7-1/8=-1/8

Answer 4

-2*1250=-2500

-1/8