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\(42+\frac{93}{6}+\frac{87}{12}+\frac{79}{20}+\frac{69}{30}+\frac{57}{42}\)
\(=37+\left(1+\frac{93}{6}\right)+\left(1+\frac{87}{12}\right)+\left(\frac{79}{20}+1\right)+\left(1+\frac{69}{30}\right)+\left(1+\frac{57}{42}\right)\)
\(=37+\frac{99}{6}+\frac{99}{12}+\frac{99}{20}+\frac{99}{30}+\frac{99}{42}\)
\(=37+99\left(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(=37+99\left(\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(=37+99\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(=37+99\left(\frac{1}{2}-\frac{1}{7}\right)\)
\(=37+99.\frac{5}{14}\)
\(=37+35\frac{5}{14}\)
\(=72\frac{5}{14}\)
\(=\frac{3.\left(\frac{1}{51}-\frac{4}{57}+\frac{11}{59}\right)}{5.\left(\frac{1}{51}-\frac{4}{57}+\frac{11}{59}\right)}=\frac{3.1}{5.1}=\frac{3}{5}\)
a) 320 x 63 - 16 x 20 + 32 x 370
= 320 x 63 - 320 x + 320 x 37
= 320 x ( 63 - 1 + 37 )
= 320 x 99
= 320 x ( 100 - 1 )
= 320 x 100 - 320
= 32000 - 320 = 31 680
b) 35 x 61 + 215 x 5 + 35 x 39 + 57 x 25
= 5 x 427 + 5 x 215 + 5 x 273 + 5 x 285
= 5 x ( 427 + 215 + 273 + 285 )
= 5 x 1200 = 6000
c) 34 x 24 - 94 x 6 + 83 x 48 - 47 x 88
= 204 x 4 - 4 x 141 + 996 x 4 - 1034 x 4
= 4 x ( 204 - 141 + 996 - 1034 )
= 4 x 25 = 100
a) (-30) + 17 + (-70) + 33
=[-30+(-70)]+(17+33)
=-100+50
=-50
b) 56 - 15 - 6 + (-75)
=(56-6)-[15+(-75)]
=50-(-60)
=110
c) (157 - 56) - (44 + 57)
=157-56-44+57
=(-157-57)-(56+44)
=-100-100
=-200
d) (-24 + 174) - (174 - 24)
=-24+174-174+24
=(-24+24)+(174-174)
=0+0
=0
e) (35 - 47) - (-123 + 35) + [20 - (123 - 57)]
=35-47+123-35+[20-123+57]
=35-47+123-35+20-123+57
=(35-35)+(123-123)+(-47+57)
=0+0+(-10)
=-10
\(57\cdot25+57:\frac{1}{35}+114\cdot20\)
\(=57\cdot25+57\cdot35+2\cdot57\cdot20\)
\(=57\cdot\left(25+35+2\cdot20\right)\)
\(=57\cdot\left(25+35+40\right)\)
\(=57\cdot100\)
\(=5700\)
\(=57.25+57.35+57.2.20\)
\(=57.\left(25+35+60\right)\)
\(=57.100=5700\)