1+2+3+34+5+7+.....+1996
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a) A=1-2-3+4+5-6-7+.....+1996+1997-1998-1999+2000
=(1-2-3+4)+(5-6-7+8)+...+(1997-1998-1999+2000)
=0
b) B=1-3+5-7+....+2001-2003+2005
=(1-3)+(5-7)+...+(2001-2003)+2005
=-2.501+2005
=-1002+2005
=1003
c) C=1-2-3+4+5-6-7+8+.....+1993-1994-1995+1996+1997
=(1-2-3+4)+(5-6-7+8)+...+(1993-1994-1995+1996)+1997
=1997
d) D=1000+998+996+......+10-999-997-995-...-11
=(1000-999)+(998-997)+(996-995)+....+(12-11)+10
=1.495+10
=595

\(a,\dfrac{2}{7}+\dfrac{5}{7}.\dfrac{7}{10}-\dfrac{1}{14}\)
\(=\dfrac{1}{7}.2+\dfrac{1}{7}.5.\dfrac{7}{10}-\dfrac{1}{7}.\dfrac{1}{2}\)
\(=\dfrac{1}{7}.\left(2+\dfrac{35}{10}-\dfrac{1}{2}\right)\)
\(=\dfrac{1}{7}.\left(\dfrac{4}{2}+\dfrac{7}{2}-\dfrac{1}{2}\right)\)
\(=\dfrac{1}{7}.5=\dfrac{5}{7}\)
\(b,\left(3\dfrac{1}{2}-\dfrac{2}{3}\right).\dfrac{7}{34}-\dfrac{5}{34}\)
\(=\left(\dfrac{7}{2}-\dfrac{2}{3}\right).\dfrac{7}{34}-\dfrac{7}{34}.\dfrac{5}{7}\)
\(=\dfrac{7}{34}.\left(\dfrac{17}{6}-\dfrac{5}{7}\right)\)
\(=\dfrac{7}{34}.\dfrac{89}{42}=\dfrac{89}{204}\)
a: =2/7-1/14+5/10
=2/7-1/14+1/2
=4/14-1/14+7/14
=10/14=5/7
b: =(7/2-2/3)*7/34-5/34
\(=\dfrac{21-4}{6}\cdot\dfrac{7}{34}-\dfrac{5}{34}\)
\(=\dfrac{7}{6}\cdot\dfrac{1}{2}-\dfrac{5}{34}=\dfrac{7}{12}-\dfrac{5}{34}=\dfrac{89}{204}\)


a) 4/5 x 3/7 + 4/5 x 4/7
= 4/5 x ( 3/7 + 4/7 )
= 4/5 x 1
= 4/5

[1-2-3+4]+........+[1997-1998-1999+2000]+2001
=0+0+....+0+2001
=2001
[1-2-3+4]+........+[1997-1998-1999+2000]+2001
=0+0+....+0+2001
=2001

b) \(\frac{1}{5}:\frac{1}{3}\cdot\frac{\frac{1}{3}}{\frac{1}{5}}+1996\)
\(=\frac{3}{5}\cdot\left(\frac{1}{3}:\frac{1}{5}\right)+1996\)
\(=\frac{3}{5}\cdot\frac{5}{3}+1996\)
\(=1+1996=1997\)
a) \(\frac{2}{3}:\frac{5}{7}\cdot\frac{5}{7}\cdot\frac{2}{3}+1934\)
\(=\frac{2\cdot7}{5\cdot3}\cdot\frac{5\cdot2}{7\cdot3}+1934\)
\(=\frac{2\cdot7\cdot5\cdot2}{5\cdot3\cdot7\cdot3}+1996=\frac{4}{9}+1996\)
