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a) 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11
= (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + (9 - 10) + 11
= -1 + (-1) + (-1) + (-1) + (-1) + 11
= -1 x 5 + 11
= -5 + 11
= 6
b) 98 + 87 + 76 + ... + 21 - 12 - 23 - 34 - ... - 89
= (98 89) + (87 - 78) + ... + (21 - 12) (có 8 nhóm)
= 9 + 9 + ... + 9 (có 8 số 9)
= 9 x 8
= 72
\(1-2+3-4+.....-10+11\)
\(=\left(1-2\right)+\left(3-4\right)+...\left(9-10\right)+11\)
\(=1+\left(-1\right)+\left(-1\right)+\left(-1\right)+\left(-1\right)+11\)
\(=-1\times5+11\)
\(=6\)

Bài 1:
a; \(\dfrac{5}{18}\) + \(\dfrac{8}{19}\) - \(\dfrac{7}{21}\) + (- \(\dfrac{10}{36}\) + \(\dfrac{11}{19}\) + \(\dfrac{1}{3}\)) - \(\dfrac{5}{8}\)
= \(\dfrac{5}{18}\) + \(\dfrac{8}{19}\) - \(\dfrac{1}{3}\) -\(\dfrac{10}{36}\) + \(\dfrac{11}{19}\) + \(\dfrac{1}{3}\) - \(\dfrac{5}{8}\)
= (\(\dfrac{5}{18}\) - \(\dfrac{10}{36}\)) + (\(\dfrac{8}{19}\) + \(\dfrac{11}{19}\)) - (\(\dfrac{1}{3}\) - \(\dfrac{1}{3}\)) - \(\dfrac{5}{8}\)
= (\(\dfrac{5}{18}\) - \(\dfrac{5}{18}\)) + \(\dfrac{19}{19}\) - 0 - \(\dfrac{5}{8}\)
= 0 + 1 - \(\dfrac{5}{8}\)
= \(\dfrac{3}{8}\)
b; \(\dfrac{1}{13}\) + (\(\dfrac{-5}{18}\) - \(\dfrac{1}{13}\) + \(\dfrac{12}{17}\)) - (\(\dfrac{12}{17}\) - \(\dfrac{5}{18}\) + \(\dfrac{7}{5}\))
= \(\dfrac{1}{13}\) - \(\dfrac{5}{18}\) - \(\dfrac{1}{13}\) + \(\dfrac{12}{17}\) - \(\dfrac{12}{17}\) + \(\dfrac{5}{18}\) - \(\dfrac{7}{5}\)
= (\(\dfrac{1}{13}\) - \(\dfrac{1}{13}\)) + (\(\dfrac{12}{17}\) - \(\dfrac{12}{17}\)) + (-\(\dfrac{5}{18}\) + \(\dfrac{5}{18}\)) - \(\dfrac{7}{5}\)
= 0 + 0 + 0 - \(\dfrac{7}{5}\)
= - \(\dfrac{7}{5}\)
Bài 1 c;
\(\dfrac{15}{14}\) - (\(\dfrac{17}{23}\) - \(\dfrac{80}{87}\) + \(\dfrac{5}{4}\)) + (\(\dfrac{17}{23}\) - \(\dfrac{15}{14}\) + \(\dfrac{1}{4}\))
= \(\dfrac{15}{14}\) - \(\dfrac{17}{23}\) + \(\dfrac{80}{87}\) - \(\dfrac{5}{4}\) + \(\dfrac{17}{23}\) - \(\dfrac{15}{14}\) + \(\dfrac{1}{4}\)
= (\(\dfrac{15}{14}-\dfrac{15}{14}\)) + (\(-\dfrac{17}{23}+\dfrac{17}{23}\)) - (\(\dfrac{5}{4}\) - \(\dfrac{1}{4}\)) + \(\dfrac{80}{87}\)
= 0 + 0 - 1 + \(\dfrac{80}{87}\)
= - \(\dfrac{7}{87}\)

Gọi tổng là X, ta có :
X = 1+2+3+4+5+6+7+8+9+10+11+12+1+1345+6+544+435+22+00+34+567+13+7+6+9+8+0+6+5+4+3+4+5+6+66+6+2+3+8888+666+1000+87+98 !
Đây là bài toán hay đấy !

\(A=\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{8}+\dfrac{1}{8}-\dfrac{1}{19}+...+\dfrac{1}{57}-\dfrac{1}{87}=\dfrac{1}{3}-\dfrac{1}{87}=\dfrac{28}{87}\)

\(=\left(7-8\right)+\left(9-10\right)+...+\left(87-88\right)+89\)
\(=\left(-1\right)+\left(-1\right)+...+\left(-1\right)+89\)
Số các số hạng từ 7 đến 88 là: \(88-7+1=82\) (số hạng)
\(=\left(-1\right)\cdot\left(82\div2\right)+89\)
\(=\left(-1\right)\cdot41+89\)
\(=\left(-41\right)+89\)
\(=48\)
\(\text{|-5| . (-11) + 5 . (-87) - 10}\)
=\(5.\left(-11\right)+5.\left(-87\right)-10\)
\(=5.\left[\left(-11\right)+\left(-87\right)\right]-10\)
\(=5.\left(-98\right)-10\)
\(=-490-10\)
\(=-500\)
học tốt
|-5| . (-11) + 5 . (-87) - 10
= 5 . (-11) + 5 . (-87) - 5 . 2
= 5 . [-11+(-87)-2]
= 5 . (-100)
= -500