Tính giá trị các biểu thức:
A=(-1)+(-5)+(-9)+...+(-101)
B=\(\dfrac{-5}{17}\).\(\dfrac{8}{19}\)+\(\dfrac{-12}{17}\). \(\dfrac{8}{19}\) - \(\dfrac{11}{19}\)
C=\(\dfrac{10}{1.6}\)+\(\dfrac{10}{6.11}\)+\(\dfrac{10}{11.16}\)+...+\(\dfrac{10}{2016.2021}\)
C = \(\dfrac{4}{9}\)\(\times\)\(\dfrac{13}{17}\)+\(\dfrac{4}{17}\)\(\times\)\(\dfrac{4}{9}\)+\(\dfrac{2}{9}\)
D = \(\dfrac{8}{19}\)\(\times\)\(\dfrac{5}{11}\)+\(\dfrac{7}{11}\)\(\times\dfrac{8}{19}+\dfrac{12}{11}\times\dfrac{11}{19}\)
\(C=\dfrac{4}{9}\times\dfrac{13}{17}+\dfrac{4}{17}\times\dfrac{4}{9}+\dfrac{2}{9}\\ =\dfrac{4}{9}\times\left(\dfrac{13}{17}+\dfrac{4}{17}\right)+\dfrac{2}{9}\\ =\dfrac{4}{9}\times1+\dfrac{2}{9}\\ =\dfrac{4}{9}+\dfrac{2}{9}\\ =\dfrac{6}{9}=\dfrac{2}{3}\)
\(D=\dfrac{8}{19}\times\dfrac{5}{11}+\dfrac{7}{11}\times\dfrac{8}{19}+\dfrac{12}{11}\times\dfrac{11}{19}\\ =\dfrac{8}{19}\times\left(\dfrac{5}{11}+\dfrac{7}{11}\right)+\dfrac{12}{11}\times\dfrac{11}{19}\\ =\dfrac{8}{19}\times\dfrac{12}{11}+\dfrac{12}{11}\times\dfrac{11}{19}\\ =\dfrac{12}{11}\times\left(\dfrac{8}{19}+\dfrac{11}{19}\right)\\ =\dfrac{12}{11}\times19\\ =\dfrac{12}{11}\)
\(C=\dfrac{4}{9}\cdot\dfrac{13}{17}+\dfrac{4}{17}\cdot\dfrac{4}{9}+\dfrac{2}{9}\)
\(C=\dfrac{4}{9}\cdot\left(\dfrac{13}{17}+\dfrac{4}{17}\right)+\dfrac{2}{9}\)
\(C=\dfrac{4}{9}\cdot\dfrac{13+4}{17}+\dfrac{2}{9}\)
\(C=\dfrac{4}{9}\cdot\dfrac{17}{17}+\dfrac{9}{2}\)
\(C=\dfrac{4}{9}\cdot1+\dfrac{2}{9}\)
\(C=\dfrac{4}{9}+\dfrac{2}{9}\)
\(C=\dfrac{4+2}{9}\)
\(C=\dfrac{6}{9}\)
\(C=\dfrac{2}{3}\)
\(D=\dfrac{8}{19}\cdot\dfrac{5}{11}+\dfrac{7}{11}\cdot\dfrac{8}{19}+\dfrac{12}{11}\cdot\dfrac{11}{19}\)
\(D=\dfrac{8}{19}\cdot\left(\dfrac{5}{11}+\dfrac{7}{11}\right)+\dfrac{12}{11}\cdot\dfrac{11}{19}\)
\(D=\dfrac{8}{19}\cdot\dfrac{12}{11}+\dfrac{12}{11}\cdot\dfrac{11}{19}\)
\(D=\dfrac{12}{11}\cdot\left(\dfrac{8}{19}+\dfrac{11}{19}\right)\)
\(D=\dfrac{12}{11}\cdot\dfrac{19}{19}\)
\(D=\dfrac{12}{11}\cdot1\)
\(D=\dfrac{12}{11}\)
Tính giá trị các biểu thức sau một cách hợp lí :
\(A=\dfrac{7}{19}.\dfrac{8}{11}+\dfrac{7}{19}.\dfrac{3}{11}+\dfrac{12}{19}\)
\(B=\dfrac{5}{9}.\dfrac{7}{13}+\dfrac{5}{9}.\dfrac{9}{13}-\dfrac{5}{9}.\dfrac{3}{13}\)
\(C=\left(\dfrac{67}{111}+\dfrac{2}{33}-\dfrac{15}{117}\right).\left(\dfrac{1}{3}-\dfrac{1}{4}-\dfrac{1}{12}\right)\)
Gợi ý: Sử dụng tính chất phân phối của phép nhân đối với phép cộng để nhóm thừa số chung ra ngoài.
bài 1 tính :
\(\dfrac{-8}{9}\) . \(\dfrac{12}{19}\) . \(\dfrac{9}{-4}\) . \(\dfrac{19}{24}\) \(\dfrac{-5}{16}\) . \(\dfrac{17}{15}\) : \(\dfrac{-17}{8}\)
\(\dfrac{4}{13}\) . \(\dfrac{2}{7}\) + \(\dfrac{-3}{26}\) + \(\dfrac{4}{13}\) . \(\dfrac{5}{7}\) \(\dfrac{6}{11}\) . \(\dfrac{3}{4}\) + \(\dfrac{-12}{60}\) +\(\dfrac{-3}{4}\) .\(\dfrac{-5}{11}\)
giúp mk vs mn ơi , mai cô giáo ktra mk r
a: \(=\dfrac{8}{9}\cdot\dfrac{9}{4}\cdot\dfrac{12}{19}\cdot\dfrac{19}{24}=\dfrac{1}{2}\cdot2=1\)
b: \(=\dfrac{5}{16}\cdot\dfrac{17}{15}\cdot\dfrac{8}{17}=\dfrac{5}{16}\cdot\dfrac{8}{15}=\dfrac{40}{240}=\dfrac{1}{6}\)
c: \(=\dfrac{4}{13}\left(\dfrac{2}{7}+\dfrac{5}{7}\right)-\dfrac{3}{26}=\dfrac{4}{13}-\dfrac{3}{26}=\dfrac{5}{26}\)
c: \(=\dfrac{3}{4}\left(\dfrac{6}{11}+\dfrac{5}{11}\right)-\dfrac{1}{5}=\dfrac{3}{4}-\dfrac{1}{5}=\dfrac{11}{20}\)
Tính giá trị biểu thức.
a) \(\dfrac{4}{9}+\dfrac{2}{9}-\dfrac{5}{18}\) b) \(2-\dfrac{3}{5}+\dfrac{8}{15}\) c) \(\dfrac{9}{8}-\left(\dfrac{11}{8}-\dfrac{19}{32}\right)\)
a)
\(\dfrac{4}{9}+\dfrac{2}{9}-\dfrac{5}{18}\\ =\dfrac{6}{9}-\dfrac{5}{18}\\ =\dfrac{6\times2}{9\times2}-\dfrac{5}{18}\\ =\dfrac{12}{18}-\dfrac{5}{18}\\ =\dfrac{7}{18}\)
b)
\(2-\dfrac{3}{5}+\dfrac{8}{15}\\ =\dfrac{2\times15}{15}-\dfrac{3\times3}{5\times3}+\dfrac{8}{15}\\ =\dfrac{30-9+8}{15}\\ =\dfrac{29}{15}\)
c)
\(\dfrac{9}{8}-\left(\dfrac{11}{8}-\dfrac{19}{32}\right)\\ =\dfrac{9}{8}-\left(\dfrac{11\times4}{8\times4}-\dfrac{19}{32}\right)\\ =\dfrac{9}{8}-\left(\dfrac{44}{32}-\dfrac{19}{32}\right)\\ =\dfrac{9}{8}-\dfrac{25}{32}\\ =\dfrac{9\times4}{8\times4}-\dfrac{25}{32}\\ =\dfrac{36-25}{32}\\ =\dfrac{11}{32}\)
a) \(\dfrac{4}{9}+\dfrac{2}{9}-\dfrac{5}{18}=\dfrac{8}{18}+\dfrac{4}{18}-\dfrac{5}{18}=\dfrac{8+4-5}{18}=\dfrac{7}{18}\)
b) \(2-\dfrac{3}{5}+\dfrac{8}{15}=\dfrac{30}{15}-\dfrac{9}{15}+\dfrac{8}{15}=\dfrac{30-9+8}{15}=\dfrac{29}{15}\)
c) \(\dfrac{9}{8}-\left(\dfrac{11}{8}-\dfrac{19}{32}\right)=9-\left(\dfrac{44}{32}-\dfrac{19}{32}\right)=9-\dfrac{25}{32}=\dfrac{288}{32}-\dfrac{25}{32}=\dfrac{288-25}{32}=\dfrac{263}{32}\)
Tính hợp lí:
d) \(\dfrac{-7}{9}.\dfrac{3}{11}+\dfrac{-7}{9}.\dfrac{8}{11}+1\dfrac{7}{9}\)
e) \(\dfrac{7}{35}.\dfrac{10}{19}+\dfrac{7}{35}.\dfrac{9}{19}-\dfrac{2}{35}\)
f) \(\left(-25\right).125.4.\left(-8\right).\left(-17\right)\)
d: \(=\dfrac{-7}{9}\left(\dfrac{3}{11}+\dfrac{8}{11}\right)+1+\dfrac{7}{9}=1\)
e: \(=\dfrac{1}{5}\left(\dfrac{10}{19}+\dfrac{9}{19}\right)-\dfrac{2}{35}=\dfrac{1}{5}-\dfrac{2}{35}=\dfrac{5}{35}=\dfrac{1}{7}\)
f: \(=\left(-25\cdot4\right)\cdot\left(-8\cdot125\right)\cdot\left(-17\right)=-1700000\)
Tính một cách hợp lí:
a) \(\dfrac{27}{13}-\dfrac{106}{111}+\dfrac{-5}{111};\)
b) \(\dfrac{12}{11}-\dfrac{-7}{19}+\dfrac{12}{19};\)
c) \(\dfrac{5}{17}-\dfrac{25}{31}+\dfrac{12}{17}+\dfrac{-6}{31}.\)
\(a.\)
\(\dfrac{27}{13}-\dfrac{106}{111}+-\dfrac{5}{111}=\dfrac{27}{13}-\dfrac{106}{111}-\dfrac{5}{111}=\dfrac{27}{13}-\left(\dfrac{106+6}{111}\right)=\dfrac{27}{13}-1=\dfrac{14}{13}\)
\(b.\)
\(\dfrac{12}{11}-\dfrac{-7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+\dfrac{7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+1=\dfrac{23}{11}\)
\(c.\)
\(\dfrac{5}{17}-\dfrac{25}{31}+\dfrac{12}{17}+-\dfrac{6}{31}=\left(\dfrac{5}{17}+\dfrac{12}{17}\right)-\left(\dfrac{25}{31}+\dfrac{6}{31}\right)=1-1=0\)
a) \(\dfrac{27}{13}-\dfrac{106}{111}+\dfrac{-5}{111}=\dfrac{27}{13}+\left(\dfrac{-106}{111}+\dfrac{-5}{111}\right)=\dfrac{27}{13}+-1=\dfrac{14}{13}\)
b) \(\dfrac{12}{11}-\dfrac{-7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+\left(\dfrac{7}{19}+\dfrac{12}{19}\right)=\dfrac{12}{11}+1=\dfrac{23}{11}\)
c)\(\dfrac{5}{17}-\dfrac{25}{31}+\dfrac{12}{17}+\dfrac{-6}{31}=\left(\dfrac{5}{17}+\dfrac{12}{17}\right)+\left(\dfrac{-25}{31}+\dfrac{-6}{31}\right)=1+-1=0\)
a) \(\dfrac{5}{7}\)+\(\dfrac{3}{4}\).\(\dfrac{-11}{2}\)
b) (\(\dfrac{12}{17}\)+\(\dfrac{19}{7}\)) - (\(\dfrac{-5}{17}\)-\(\dfrac{3}{7}\))
c) (0,125)\(^{12}\).(-8)\(^{12}\)-\(\dfrac{45^3}{15^3}\)
d) \(5\dfrac{2}{7}\).(\(-\dfrac{1}{3}\))-\(2\dfrac{2}{7}\).(\(-\dfrac{1}{3}\))
e) \(\dfrac{9^2.9^3}{3^9}\)
\(a,=\dfrac{5}{7}-\dfrac{33}{8}=-\dfrac{191}{56}\\ b,=\left(\dfrac{12}{17}+\dfrac{5}{17}\right)+\left(\dfrac{19}{7}+\dfrac{3}{7}\right)=1+3=4\\ c,=\left(0,125\cdot8\right)^{12}-\left(\dfrac{45}{15}\right)^3=1-3^3=-26\\ d,=\left(-\dfrac{1}{3}\right)\left(5\dfrac{2}{7}-2\dfrac{2}{7}\right)=-\dfrac{1}{3}\cdot3=-1\\ e,=\dfrac{3^4\cdot3^6}{3^9}=3\)
Tính hợp lý nếu có thể:
a) \(\dfrac{2}{9}+\dfrac{-3}{10}+\dfrac{-7}{10}\)
b) \(\dfrac{-11}{6}+\dfrac{2}{5}+\dfrac{-1}{6}\)
c) \(\dfrac{27}{13}-\dfrac{106}{111}+\dfrac{-5}{111}\)
d) \(\dfrac{12}{11}-\dfrac{-7}{19}+\dfrac{12}{19}\)
a, \(=\dfrac{2}{9}-\dfrac{10}{10}=\dfrac{2}{9}-1=-\dfrac{7}{9}\)
b, \(=-\dfrac{12}{6}+\dfrac{2}{5}=-2+\dfrac{2}{5}=-\dfrac{8}{5}\)
c, \(=\dfrac{27}{13}-1=\dfrac{14}{13}\)
d, \(=\dfrac{12}{11}+\dfrac{7}{19}+\dfrac{12}{19}=\dfrac{12}{11}+1=\dfrac{23}{11}\)
a) \(\dfrac{2}{9}+\dfrac{-3}{10}+\dfrac{-7}{10}\)
\(=\dfrac{2}{9}+\dfrac{-10}{10}=\dfrac{2}{9}-1=-\dfrac{7}{9}\)
b) \(\dfrac{-11}{6}+\dfrac{2}{5}+\dfrac{-1}{6}\)
\(=-2+\dfrac{2}{5}=-\dfrac{8}{5}\)
a,\(=\dfrac{2}{9}+\left(\dfrac{-3}{10}+\dfrac{-7}{10}\right)=\dfrac{2}{9}+\left(-1\right)=\dfrac{-7}{9}\)
b,\(=\left(\dfrac{-11}{6}+\dfrac{-1}{6}\right)+\dfrac{2}{5}=-2+\dfrac{2}{5}=\dfrac{-8}{5}\)
c,\(=\dfrac{27}{13}-\left(\dfrac{106}{111}+\dfrac{-5}{111}\right)=\dfrac{27}{13}-1=\dfrac{14}{13}\)
C= 2-\(\dfrac{5}{3}\)+\(\dfrac{7}{6}\)-\(\dfrac{9}{10}\)+\(\dfrac{11}{15}\)-\(\dfrac{13}{21}\)+\(\dfrac{15}{28}\)-\(\dfrac{17}{36}\)+\(\dfrac{19}{45}\)
tính C
\(=2-\left(\dfrac{5}{3}-\dfrac{7}{6}+\dfrac{9}{10}-...-\dfrac{19}{45}\right)\)
\(=2-2\left(\dfrac{5}{6}-\dfrac{7}{12}+\dfrac{9}{20}-...-\dfrac{19}{90}\right)\)
\(=2-2\left(\dfrac{1}{2}+\dfrac{1}{3}-\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}+\dfrac{1}{5}-...-\dfrac{1}{9}-\dfrac{1}{10}\right)\)
\(=2-2\cdot\dfrac{4}{10}=2-\dfrac{8}{10}=2-\dfrac{4}{5}=\dfrac{6}{5}\)