1-5 / 6 + 7 / 12-9 / 20 + 11 / 30-13 / 42 = 15 / 56-17 / 72

1-5 / 6 + 7 / 12-9 / 20 + 11 / 30-13 / 42 = 15 / 56-17 / 72

1-5/6+7/12-9/20+11/30-13/42+15/56-17/72
=1-(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)
=1-1/2-1/3+1/3+1/4-1/4-1/5+1/5+1/6-1/6-1/7+1/7+1/8-1/8-1/9
=1-1/2-1/9
=7/18

One and a half - five sixths + seven twelfth - nine twentieth + eleven thirtieth - forty-two thirteenth

1 and half - 5 / 6 + 7 / 12 - 9 / 20 + 11 / 30 - 13 / 42 = 1 + 1 / 2-5 / 6 + 7 / 12-9 / 20 + 11 / 30-13 / 42 = 1 + 1 / 2-2 / 6-3 / 6 + 3 / 12 + 4 / 12-4 / 20-5 / 20 + 5 / 30 + 6 / 30-6 / 42-7 / 42 = 1 + 1 / 2-1 / 3-1 / 3 / 2 + 1 / 4 + 1 / 6 + 1 / 5-1 / 7-1

1.2-5 / 6 + 7 / 12-9 / 20 + 11 / 30-13 / 42 + 15 / 56
Seek the master's solution (simple calculation)

1 / 2-5 / 6 + 7 / 12-9 / 20 + 11 / 30-13 / 42
=1+1/2-5/6+7/12-9/20+11/30-13/42
=1+1/2-2/6-3/6+3/12+4/12-4/20-5/20+5/30+6/30-6/42-7/42
=1+1/2-1/3-1/2+1/4+1/3-1/5+1/4+1/6+1/5-1/7-1/6
=1-1/7
=6/7

How to reduce one by half, one by three, one by four, and finally one by two?

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