Question

分数的简便计算，急急急，明天要交！

7 13 21 31 43 57 73 91
— +— +— +— +—+ —+ — +—
6 12 20 30 42 56 72 90

要求写出算的过程~~~~

Answer 1

原式=7/(2x3)+13/(3x4)+21/(4x5)+31/(5x6)+43/(6x7)+57/(7x8)+73/(8x9)
+91/(9x10)
=7(1/2-1/3)+13(1/3-1/4)+21(1/4-1/5)+31(1/5-1/6)+.....+73(1/8-
1/9)+91(1/9-1/10)
=7x(1/2)+6x(1/3)+8x(1/4)+10x(1/5)+12x(1/6)+14x(1/7)+16x(1/8)+
18x(1/9)-91x(1/10)
=7/2+2+2+2+2+2+2+2-91/10
=35/10-91/10+14
=14+5.6=19.6

Answer 2

1+1/6+1+1/12+1+1/20+...+1+1/90
1+1/2*3+1+1/3*4+...+1+1/9*10
=1+(1/2-1/3)+1+(1/3-1/4)+...+1+(1/9-1/10)
=8+(1/2-1/3+1/3-1/4+...+1/9-1/10）
=8+(1/2-1/10)
=8+2/5
=42/5

Answer 3

1+1/6+1+1/12+1+1/20+1+1/42+1+1/56+1+1/72+1+1/90
=8+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=8+1/2-1/10
=8.4

Answer 4

7/6+13/12+21/20+31/30+43/42+57/56+73/72+91/90
=(1+1/6)+(1+1/12)+(1+1/20)+(1+1/30)+(1+1/42)+(1+1/56)+(1+1/72)+(1+1/90)
=8+1/6+1/12+1/20+1/30+1/42+1/56+1/72+1/90
=8+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=8+1/2-1/10
=42/5