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7*15分之8-35分之12+63分之16-99分之20简便计算

解:依题意得算式, 7×15分之8-7×35分之12+7×63分之16-99分之20×7 =(15分之8-35分之12+63分之16-99分之20)×7 =【(3分之1+5分之1)-(5分之1+7分之1)+(7分之1+9分之1)-(9分之1+11分之1)】×7 =(3分之1+5分之1-5分之1-7分之1+7分之1+9分之...

7*8/15-7*12/35+7*16/63-20/99*7 = 7*[1/3+1/5-(1/5+1/7)+1/7+1/9-(1/9+1/11)] =7*(1/3-1/11)=7*8/33 =56/33

7×8/15-7×12/35+7×16/63-7×20/99 =7×(8/15-12/35+16/63-20/99) =7×(1/3+1/5-1/5-1/7+1/7+1/9-1/9-1/11) =7×(1/3-1/11) =7×8/33 =56/33 =1又23/33

4/3-8/15+12/35-16/63+20/99 =(4/3-16/63)+(12/35-8/15)+20/99 =(81/63-16/63)+(36/105-56/105)+20/99 =65/63-20/105+20/99 =65/63-12/63+20/99 =53/63+20/99 =583/693+140/693 =723/693

裂项法: 7×8╱15-7×12╱35+7×16╱63-7×20╱99 =7×(8╱15-12╱35+16╱63-20╱99) =7×1/2×(1/3+1/5-1/5-1/7+1/7+1/9-1/9-1/11) =7/2×(1/3-1/11) =7/2×8/33 =28/33

这个还真的不想去算的啊

1/2+3/4+7/8+15/16+31/32+63/64 =6-(1/2+1/4+1/8+1/16+1/32+1/64) =6-(1-1/64) =6-1+1/64 =5又1/64

裂项法: 8×8/15-8×12/35+8×16/63-8×20/99 =8×(8/15-12/35+16/63-20/99) =8×(1/3+1/5-1/5-1/7+1/7+1/9-1/9-1/11) =8×(1/3-1/11) =8×8/33 =64/33 =1又31/33

1又1/3-8/15+12/35-16/63+20/99 =1+1/3-(1/3+1/5)+(1/5+1/7)-(1/7+1/9)+(1/9+1/11) =1+1/3-1/3-1/5+1/5+1/7-1/7-1/9+1/9+1/11 =1+1/11 =1又1/11

9×(1-4/3+8/15-12/35+16/63) =9x【1-(1+1/3)+(1/3+1/5)-(1/5+1/7)+(1/7+1/9)】 =9x(1-1-1/3+1/3+1/5-1/5-1/7+1/7+1/9) =9x1/9 =1

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