Question

计算题：

（1） 1又1/4+2又1/28+3又1/70+4又1/130

（2）26+25×27/26×27-1

（3）7/12-9/20+11/30-13/42+15/56-17/72

（4）7×8/15-7×12/35+7×16/63-20/99×7

Answer 1

1又1/4+2又1/28+3又1/70+4又1/130
=1+1/4+2+1/28+3+1/70+4+1/130
=(1+2+3+4)+(1/4+1/28+1/70+1/130)
=10+1/3×(3/4+3/28+3/70+3/130)
=10+1/3×[(1-1/4)+(1/4-1/7)+(1/7-1/10)+(1/10-1/13)]
=10+1/3×(1-1/4+1/4-1/7+1/7-1/10+1/10-1/13)
=10+1/3×(1-1/13)
=10+1/3×12/13
=10+4/13
=10又4/13

(26+25×27)/(26×27-1)
=(27+25×27-1)/(26×27-1)
=[27×(1+25)-1]/(26×27-1)
=(26×27-1)/(26×27-1)
=1

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

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