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Dạng 1: Thực hiện phép tính Bài 1: Tính: 1) $-12:(\frac34-\frac56)^2 = -12:(\frac{15}{60})^2 = -12:(\frac{1}{4})^2 = -12: \frac{1}{16} = -192$ 2) $(\frac13-2\frac16)^2:(-3\frac{13}{36}) = (\frac{1}{3} - \frac{13}{6})^2 : (-\frac{121}{36}) = (\frac{-23}{6})^2 : (-\frac{121}{36}) = \frac{529}{36} : \frac{-121}{36} = -\frac{529}{121} = -\frac{23}{11}$ 3) $2^3+3.(\frac19)^0-\frac1{2^2}.4+[(-2)^2:\frac12].8 = 8 + 3*1 - \frac{1}{4}*4 + [4:\frac{1}{2}]*8 = 8 + 3 - 1 + 16 = 26$ 4) $|\frac{-1}2|+(\frac{-1}3)^2:|-2|-(\frac{-2}3)^0 = \frac{1}{2} + (\frac{1}{9}):\frac{1}{2} - 1 = \frac{1}{2} + \frac{2}{9} - 1 = \frac{1}{18}$ 5) $-\sqrt{64}+2\sqrt{(-5)^2}-7\sqrt{0,01}+8\sqrt{\frac{25}{16}} = -8 + 2*5 - 7*0.1 + 8* \frac{5}{4} = -8 + 10 - 0.7 + 10 = 11.3$ 6) $[3\sqrt{225}-5\sqrt{(-12)^2}-12|\frac{-7}6|]\sqrt{2\frac14} = [3*15 - 5*12 - 12*\frac{7}{6}]*\frac{3}{2} = [45 - 60 - 14]*\frac{3}{2} = [-29]*\frac{3}{2} = -43.5$ 7) $\frac{2^7.9^3}{6^3.8^2} = \frac{128*729}{216*64} = \frac{93312}{13824} = 6.75$ 8) $\frac{15^8.27^2.2^{24}}{6^{14}.10^9} = \frac{2562890625*729*16777216}{7529536*1000000000} = \frac{312500000000000000000000000}{75295360000000000} = 414720$ 9) $|\frac1{-5}|-\frac{(-2)^2}{|-5|}-\frac{|-2|}5 = \frac{1}{5} - \frac{4}{5} - \frac{2}{5} = -\frac{1}{5}$ 10) $(\frac{-2}3)^3:(\frac{-2}3)^2+\frac{2^{40}.3^{29}}{8^{13}.9^{15}} = (\frac{-8}{27}):\frac{4}{9} + \frac{1099511627776*205891132094649}{35184372088832*205891132094649} = -\frac{2}{3} + 31.5 = 31.167$ 11) $[(\frac13)^2.\frac{27}7+\sqrt{\frac{16}{49}}-3]:\frac47 = [(\frac{1}{9}*\frac{27}{7}) + \frac{4}{7} - 3] : \frac{4}{7} = [\frac{1}{3} + \frac{4}{7} - 3] : \frac{4}{7} = -\frac{11}{21} : \frac{4}{7} = -\frac{77}{28}$ 12) $\sqrt{16}.\sqrt4-\sqrt{25}+2\sqrt{49} = 4*2 - 5 + 2*7 = 8 - 5 + 14 = 17$ Bài 2: Tính bằng cách hợp lý nếu có thể: 1) $-\frac{11}8-1\frac4{11}+1\frac38+0,5-\frac5{41} = -\frac{11}{8} - \frac{15}{11} + \frac{11}{8} + \frac{1}{2} - \frac{5}{41} = -\frac{15}{11} + \frac{1}{2} - \frac{5}{41} = -\frac{45}{66} + \frac{33}{66} - \frac{10}{66} = -\frac{22}{66} = -\frac{1}{3}$ 2) $-(\frac37+\frac38)-(-\frac38+\frac47) = -(\frac{15}{56}) - (\frac{1}{56}) = -\frac{16}{56} = -\frac{2}{7}$ 3) $\frac{-5}{17}.\frac{31}{33}+\frac{-5}{17}.\frac2{33}+2\frac5{17} = \frac{-155}{561} + \frac{-10}{561} + \frac{170}{561} = \frac{5}{561}$ 4) $\frac{12}{17}.\frac57-\frac{-12}7.\frac2{17}-\frac4{17} = \frac{60}{85} + \frac{24}{119} - \frac{4}{17} = \frac{12}{17} + \frac{24}{119} - \frac{4}{17} = \frac{8}{17} + \frac{24}{119} = \frac{104}{289}$ 5) $\frac38.\frac{23}{14}-\frac38.\frac9{14}+(\frac38)^0 = \frac{69}{112} - \frac{27}{112} + 1 = \frac{42}{112} + 1 = \frac{3}{8} + 1 = 1.375$ 6) $\frac{-3}{11}.\frac57+\frac57.\frac{-8}{11}+2\frac57 = \frac{-15}{77} + \frac{-40}{77} + \frac{70}{35} = \frac{-55}{77} + 2 = 1.286$ 7) $35\frac16:(-\frac45)-45\frac16:(\frac{-4}5) = -\frac{211}{6} + \frac{271}{6} = \frac{60}{6} = 10$ 8) $\frac{\frac{-6}7+\frac6{19}-\frac6{31}}{\frac97-\frac9{19}+\frac9{31}} = \frac{-\frac{6}{7} + \frac{6}{19} - \frac{6}{31}}{\frac{9}{7} - \frac{9}{19} + \frac{9}{31}} = \frac{-\frac{114}{1333} + \frac{70}{1333} - \frac{42}{1333}}{\frac{171}{1333} - \frac{63}{1333} + \frac{39}{1333}} = \frac{-86}{147}$ 9) $(0,125)^{100}.8^{101} = (2^{-3})^{100} * 2^{303} = 2^{-300} * 2^{303} = 2^3 = 8$ 10) $-3,75.(-7,2)+2,8.3,75 = 27 + 10.5 = 37.5$ 11) $A=\frac{155-\frac{10}7-\frac5{11}+\frac5{23}}{403-\frac{26}7-\frac{13}{11}+\frac{13}{23}}+\frac{\frac35+\frac3{13}-0,9}{\frac7{91}+0,2-\frac3{10}} = \frac{21.857 - 0.455 + 0.217}{57.571 - 1.182 + 0.565} + \frac{0.6 + 0.231 - 0.9}{0.077 + 0.2 - 0.3} = \frac{21.619}{56.954} + \frac{-0.069}{-0.023} = 0.379 + 3 = 3.379$ Dạng 2. Tìm x: Bài 1: Tìm x, biết: 1) $\frac35x+\frac23=2\frac23$ => $\frac{3}{5}x = 2\frac{2}{3} - \frac{2}{3}$ => $x = \frac{5}{3} * 2 = \frac{10}{3} = 3\frac{1}{3}$ 2) $\frac{-5}8-x=\frac{-3}{20}-(\frac{-1}6)$ => $-\frac{5}{8} - x = -\frac{3}{20} + \frac{1}{6}$ => $x = -\frac{5}{8} + \frac{3}{20} - \frac{1}{6} = -\frac{11}{24}$ 3) $\frac{-1}4-\frac34:x=-\frac{11}{36}$ => $-\frac{1}{4} - \frac{3}{4x} = -\frac{11}{36}$ => $\frac{3}{4x} = \frac{1}{4} + \frac{11}{36} = \frac{19}{72}$ => $x = \frac{3}{4} * \frac{72}{19} = \frac{54}{19}$ 4) $-\frac25x+\frac12=|-\frac25+\frac12|$ => $-\frac{2}{5}x + \frac{1}{2} = \frac{3}{10}$ => $-\frac{2}{5}x = \frac{3}{10} - \frac{1}{2} = -\frac{2}{10}$ => $x = \frac{2}{5} * \frac{10}{2} = 2$ 5) $\frac25x+\frac23=-\frac15x-\frac13$ => $\frac{2}{5}x + \frac{1}{5}x = -\frac{2}{3} + \frac{1}{3}$ => $\frac{3}{5}x = -\frac{1}{3}$ => $x = \frac{5}{3} * -\frac{1}{3} = -\frac{5}{9}$ 6) $(2x+1,4)(-1,5+3x)=0$ => $2x + 1.4 = 0$ hoặc $-1.5 + 3x = 0$ => $x = -\frac{1.4}{2} = -0.7$ hoặc $x = \frac{1.5}{3} = 0.5$ 7) $(4x-1)(5x-\frac12)=0$ => $4x - 1 = 0$ hoặc $5x - \frac{1}{2} = 0$ => $x = \frac{1}{4}$ hoặc $x = \frac{1}{10}$ 8) $\frac1{1.4}+\frac1{4.7}+\frac1{7.10}+...+\frac1{x(x+3)}=\frac{125}{376},(x\in N^*)$ => Đây là dạng bài toán tổng quan về dãy số, không thể giải được chỉ bằng cách sử dụng các phép tính cơ bản.