Dạng 2: Tính các tổng đại số

$\begin{array}{l}\left(756-217\right)-\left(183-44\right)\\ =756-217-183+44\\ =\left(756+44\right)+\left(-217-183\right)\\ =800+\left(-400\right)\\ =400.\end{array}$

$\begin{array}{l}13-18-\left(-42\right)-15\\ =13-18+42-15\\ =\left(13+42\right)+\left(-18-15\right)\\ =55+\left(-33\right)\\ =22.\end{array}$

$$\begin{gathered} -2018+\left(-21+75+2018\right) \\ \begin{array}{l}=-2018+-21+75+2018\\ =\left(-2018+2018\right)+\left(-21+75\right)\\ =0+54\\ =54.\end{array} \end{gathered}$$

$\begin{array}{l}-2012+\left(-596\right)+\left(-201\right)+496+301\\ =-2012+\left(-596+496\right)+\left(-201+301\right)\\ =-2012+\left(-100\right)+100\\ =-2012+0\\ =-2012.\end{array}$

$\begin{array}{l}210+\left[46+\left(–210\right)+\left(–26\right)\right]\\ =210+46+\left(–210\right)+\left(–26\right)\\ =\left[210+\left(–210\right)\right]+\left[46+\left(-26\right)\right]\\ =0+20\\ =20.\end{array}$

$\begin{array}{l}\left(-123\right)+77+\left(-257\right)+23-43\\ =\left(-123+23\right)+\left[\left(-43\right)+\left(-257\right)\right]+77\\ =-100+\left(-300\right)+77\\ =-400+77\\ =-323.\end{array}$

Ta có:

$\begin{array}{l}\mathrm{A}=52-\left(37+43\right)\\ =52-80\\ =-28.\\ \begin{array}{l}\mathrm{B}=512-1024+256\\ =-512+256\\ =-256.\end{array}\\ \begin{array}{l}\mathrm{C}=1128-\left(27-69\right)\\ =1128-\left(-42\right)\\ =1128+42\\ =1170.\end{array}\\ \begin{array}{l}\mathrm{D}=-128-64-\left(32+16+16\right)\\ =-128-64-64\\ =-192-64\\ =-256.\end{array}\\ \begin{array}{l}\mathrm{E}=584+\left(969-383\right)\\ =584+586\\ =1170.\end{array}\\ \begin{array}{l}\mathrm{F}=1-\left(2+27\right)\\ =1-29\\ =-28.\end{array}\\ \Rightarrow \mathrm{A}=\mathrm{F};\mathrm{B}=\mathrm{D};\mathrm{C}=\mathrm{E}.\end{array}$

$$\begin{gathered} \mathrm{A}=31–\left[26–\left(209+35\right)\right] \\ \begin{array}{l}=31–\left[26–\left(209+35\right)\right]\\ =31-\left[26-244\right]\\ =31-\left(-218\right)\\ =31+218\\ =249.\end{array} \end{gathered}$$

$$\begin{gathered} B=-418-\left\{-218-\left[-118-\left(-318\right)+2012\right]\right\} \\ \begin{array}{l}=-418-\left\{-218-\left[-118+318+2012\right]\right\}\\ =-418-\left\{-218-\left[200+2012\right]\right\}\\ =-418-\left\{-218-2212\right\}\\ =-418-\left(-2430\right)\\ =-418+2430\\ =2012.\end{array} \end{gathered}$$

$$\begin{gathered} C=1-2+3-4+\mathrm{...}+97-98+99-100 \\ \begin{array}{l}=\left(1-2\right)+\left(3-4\right)+\mathrm{...}+\left(97-98\right)+\left(99-100\right)\\ =-1+\left(-1\right)+\mathrm{...}+\left(-1\right)+\left(-1\right)\\ =-1.50\\ =-50.\end{array} \end{gathered}$$

$$\begin{gathered} D=1-2-3+4+5-6-7+\mathrm{...}+97-98-99+100 \\ \begin{array}{l}=\left(1-2\right)+\left(-3+4\right)+\left(5-6\right)+\mathrm{...}+\left(97-98\right)+\left(-99+100\right)\\ =-1+1+\left(-1\right)+\mathrm{...}+\left(-1\right)+1\\ =\left(-1+1\right)+\left[\left(-1\right)+1\right]+\mathrm{...}+\left[\left(-1\right)+1\right]-1\\ =0+0+\mathrm{...}+0-1\\ =-1.\end{array} \end{gathered}$$

$$\begin{gathered} E=2-5+8-11+14-17+\mathrm{...}+98-101 \\ \begin{array}{l}=\left(2-5\right)+\left(8-11\right)+\left(14-17\right)+\mathrm{...}+\left(98-101\right)\\ =-3+\left(-3\right)+\left(-3\right)+\mathrm{...}+\left(-3\right)\\ =-3.17\\ =-51.\end{array} \end{gathered}$$