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\(\frac{1}{5}+\frac{1}{45}+\frac{1}{117}+\frac{1}{221}+...+\frac{1}{9021}+\frac{1}{9797}\)
\(=\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+\frac{1}{13.17}+...+\frac{1}{93.97}+\frac{1}{97.101}\)
\(=\frac{1}{4}.\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+\frac{4}{13.17}+...+\frac{4}{93.97}+\frac{4}{97.101}\right)\)
\(=\frac{1}{4}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{101}\right)\)
\(=\frac{1}{4}.\left(1-\frac{1}{101}\right)\)
\(=\frac{1}{4}.\left(\frac{101}{101}-\frac{1}{101}\right)\)
\(=\frac{1}{4}.\frac{100}{101}\)
\(=\frac{25}{101}\)
1/5+1/45+1/117+1/221+...+1/9021+1/9797
=1/1.5+1/5.9+1/9.13+1/13.17+...+1/93.97+1/97.101
=1-1/5+1/5-1/9+1/9-1/13+1/13-1/17+...+1/93-1/97+1/97-1/101
=1-1/101
=100/101
e)10:(x-2)=2
x-2=10:2
x=5+2
x=7
g)(70-x):8=9
70-x=8*9
x=72-70
x=2
h)(x-10)-30=47
x-10=47+30
x=77+10
x-87
420 + 65x4 = ( x + 175) : 5 + 30
420 + 260 = x : 5 + 175 : 5 + 30
680 = x : 5 + 35 + 30
680 - 30 = x : 5 + 35
650 = x : 5 + 35
650 - 35 = x : 5
615 = x : 5
615 x 5 = x
3075 = x
b) ( 32 x 15) : 2 = ( x + 70):14 - 40
480 : 2 = x : 14 + 70 : 14 - 40
240 = x : 14 + 5 - 40
240 + 40 = x : 14 + 5
280 = x: 14 + 5
280 - 5 = x : 14
275 = x : 14
275 x 14 = x
3850 = x
c) x - 4867 = ( 175 x 2050 x 70) : 25 + 23
x - 4867 = 25 112 500 : 25 + 23
x - 4867 = 1004500 + 23
x - 4867 = 1004523
x = 1004523 + 4867
x = 1008390
263779
-9021+30x9091+70
=9091x30-8951
=272730-8951
=263779