Tính 1 cách hợp lí
\(A=\dfrac{-1}{9}+\dfrac{3}{7}+\dfrac{3}{9}+\dfrac{6}{7}\)
Thực hiện phép tính (hợp lí nếu có thể):
a) \(13\dfrac{2}{7}\) : (\(\dfrac{-8}{9}\)) + \(2\dfrac{5}{7}\) : (\(\dfrac{-8}{9}\))
b) (\(\dfrac{-6}{11}\)) . \(\dfrac{7}{10}\) . (\(\dfrac{11}{-6}\)) . (-20)
c) (\(-1\dfrac{1}{2}\)) : \(\dfrac{3}{4}\) . (\(-4\dfrac{1}{2}\))
a) \(=\left(13\dfrac{2}{7}+2\dfrac{5}{7}\right):\left(-\dfrac{8}{9}\right)\)
\(=16:\dfrac{-8}{9}=\dfrac{-8\cdot\left(-2\right)\cdot9}{-8}=-18\)
b)
\(=\left(\dfrac{-6}{11}\cdot\dfrac{11}{-6}\right)\cdot\dfrac{7\cdot10\cdot\left(-2\right)}{10}\)
\(=-14\)
c) \(=\dfrac{-1}{2}\cdot\dfrac{4}{3}\cdot\dfrac{-7}{2}\)
\(=\dfrac{-1\cdot2\cdot2\cdot\left(-7\right)}{2\cdot3\cdot2}=\dfrac{7}{3}\)
Tính hợp lí :
A = \(\dfrac{-2}{9}\) + \(\dfrac{-3}{4}\) + \(\dfrac{3}{5}\) + \(\dfrac{1}{15}\) + \(\dfrac{1}{57}\) + \(\dfrac{1}{3}\) + \(\dfrac{-1}{36}\)
B = \(\dfrac{1}{2}\) + \(\dfrac{-1}{5}\) + \(\dfrac{-5}{7}\) + \(\dfrac{1}{6}\) + \(\dfrac{-3}{35}\) + \(\dfrac{1}{3}\) + \(\dfrac{1}{41}\)
C = \(\dfrac{-1}{2}\) + \(\dfrac{3}{5}\) + \(\dfrac{-1}{9}\) + \(\dfrac{1}{127}\) + \(\dfrac{-7}{18}\) + \(\dfrac{4}{35}\) + \(\dfrac{2}{7}\)
Thực hiện phép tính ( tính hợ lí nếu được)
a, \(\dfrac{3}{4}+\dfrac{9}{5}:\dfrac{3}{2}-1\) b, \(\dfrac{6}{7}.\dfrac{8}{13}+\dfrac{6}{13}.\dfrac{9}{7}-\dfrac{4}{13}.\dfrac{6}{7}\)
a: \(=\dfrac{3}{4}+\dfrac{9}{5}\cdot\dfrac{2}{3}-1=\dfrac{3}{4}+\dfrac{6}{5}-1=\dfrac{19}{20}\)
b: \(=\dfrac{6}{7}\left(\dfrac{8}{13}+\dfrac{9}{13}-\dfrac{4}{13}\right)=\dfrac{6}{7}\cdot\dfrac{13}{13}=\dfrac{6}{7}\)
Thực hiện phép tính ( tính hợ lí nếu được)
a, \(\dfrac{3}{4}+\dfrac{9}{5}:\dfrac{3}{2}-1\) b, \(\dfrac{6}{7}.\dfrac{8}{13}+\dfrac{6}{13}.\dfrac{9}{7}-\dfrac{4}{13}.\dfrac{6}{7}\)
= \(\dfrac{3}{4}+\dfrac{6}{5}-1\) = \(\dfrac{6}{7}.\left(\dfrac{8}{13}+\dfrac{9}{13}-\dfrac{4}{13}\right)\)
= \(\dfrac{15}{20}+\dfrac{24}{20}-\dfrac{20}{20}\) = \(\dfrac{6}{7}.\left(\dfrac{17}{13}-\dfrac{4}{13}\right)\)
= \(\dfrac{39}{20}-\dfrac{20}{20}\) = \(\dfrac{6}{7}.1\)
= \(\dfrac{19}{20}\) = \(\dfrac{6}{7}\)
Thực hiện phép tính (hợp lí nếu có thể):
a) (\(\dfrac{-6}{11}\)) . \(\dfrac{7}{10}\) . \(\dfrac{11}{-6}\) . (-20)
b) (\(-1\dfrac{1}{2}\)) : \(\dfrac{3}{4}\) . \(-4\dfrac{1}{2}\))
c) \(13\dfrac{2}{7}\) : (\(\dfrac{-8}{9}\)) + \(2\dfrac{5}{7}\) : (\(\dfrac{-8}{9}\))
\(a.\left[-\dfrac{6}{11}.\dfrac{11}{-6}\right].\dfrac{7}{10}.\left(-20\right)=1.7.\left(-2\right)=-14\)
\(b.\dfrac{-1}{2}:\dfrac{3}{4}.\dfrac{-7}{2}=\dfrac{7}{4}:\dfrac{3}{4}=\dfrac{7}{3}\)
\(c.\dfrac{93}{7}:-\dfrac{8}{9}+\dfrac{19}{7}:\dfrac{-8}{9}=\left(\dfrac{93}{7}+\dfrac{19}{7}\right):-\dfrac{8}{9}=\dfrac{-9}{8}.\dfrac{112}{7}=-18\)
Tính một cách hợp lí: \(B = \dfrac{{ - 1}}{9} + \dfrac{8}{7} + \dfrac{{10}}{9} + \dfrac{{ - 29}}{7}\)
\(\begin{array}{l}B = \dfrac{{ - 1}}{9} + \dfrac{8}{7} + \dfrac{{10}}{9} + \dfrac{{ - 29}}{7}\\ = \left( {\dfrac{{ - 1}}{9} + \dfrac{{10}}{9}} \right) + \left( {\dfrac{8}{7} + \dfrac{{ - 29}}{7}} \right)\\ = \dfrac{9}{9} + \dfrac{{ - 21}}{7} = 1 - 3 = - 2\end{array}\)
Tính (hợp lí nếu có thể)
\(\dfrac{1}{3}\) - \(\dfrac{3}{5}\) + \(\dfrac{5}{7}\) - \(\dfrac{7}{9}\) + \(\dfrac{9}{11}\) - \(\dfrac{11}{13}\) + \(\dfrac{13}{15}\) + \(\dfrac{11}{13}\) - \(\dfrac{9}{11}\) + \(\dfrac{7}{9}\) - \(\dfrac{5}{7}\) + \(\dfrac{3}{5}\) - \(\dfrac{1}{3}\)
\(\dfrac{1}{3}-\dfrac{3}{5}+\dfrac{5}{7}-\dfrac{7}{9}+\dfrac{9}{11}-\dfrac{11}{13}+\dfrac{13}{15}+\dfrac{11}{13}-\dfrac{9}{11}+\dfrac{7}{9}-\dfrac{5}{7}+\dfrac{3}{5}-\dfrac{1}{3}\)
\(=\left(\dfrac{1}{3}-\dfrac{1}{3}\right)-\left(\dfrac{3}{5}-\dfrac{3}{5}\right)+\left(\dfrac{5}{7}-\dfrac{5}{7}\right)-\left(\dfrac{7}{9}-\dfrac{7}{9}\right)+\left(\dfrac{9}{11}-\dfrac{9}{11}\right)-\left(\dfrac{11}{13}-\dfrac{11}{13}\right)+\dfrac{13}{15}\)
\(=\dfrac{13}{15}\)
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.
Tính (Tính hợp lí nếu có thể)
a) \(\dfrac{-7}{12}\)-\(\dfrac{3}{36}\)
b) (4-\(\dfrac{5}{12}\)):2+\(\dfrac{5}{24}\)
c) \(\dfrac{8}{9}\)+\(\dfrac{1}{9}\).\(\dfrac{2}{13}\)+\(\dfrac{1}{9}\).\(\dfrac{11}{13}\)
d) \(\dfrac{3}{4}\).\(\dfrac{8}{9}\).\(\dfrac{15}{16}\). ... .\(\dfrac{9999}{10000}\)
e) \(\dfrac{3}{1.4}\)+\(\dfrac{3}{4.7}\)+\(\dfrac{3}{7.10}\)+...+\(\dfrac{3}{97.100}\)
*Lưu ý: Mong các anh chị trình bày chi tiết để em có thể hiểu bài, em xin các anh chị đừng viết mỗi kết quả xong em chả biết một cái gì ;-;
a: =-21/36-3/36=-24/36=-2/3
b: =43/12*1/2+5/24=43/24+5/24=2
c: =8/9+1/9=1
e: =1-1/4+1/4-1/7+...+1/97-1/100
=1-1/100=99/100
Tính bằng cách hợp lí giá trị của biểu thức.
A = \(\left(3-\dfrac{1}{4} +\dfrac{3}{2}\right)\)- \(\left(5+\dfrac{1}{3}-\dfrac{5}{6}\right)\)-\(\left(6-\dfrac{7}{4}+\dfrac{3}{2}\right)\)
B =\(0,5+\dfrac{1}{3}+0,4+\dfrac{5}{7}+\dfrac{1}{6}-\dfrac{4}{35}+\dfrac{1}{41}\)
\(A=\left(3-\dfrac{1}{4}+\dfrac{3}{2}\right)-\left(5+\dfrac{1}{3}-\dfrac{5}{6}\right)-\left(6-\dfrac{7}{4}+\dfrac{2}{3}\right)\\ \Rightarrow A=3-\dfrac{1}{4}+\dfrac{3}{2}-5-\dfrac{1}{3}+\dfrac{5}{6}-6+\dfrac{7}{4}-\dfrac{2}{3}\\ \Rightarrow A=\left(3-5-6\right)-\left(\dfrac{1}{4}+\dfrac{7}{4}\right)+\left(\dfrac{3}{2}+\dfrac{5}{6}-\dfrac{2}{3}\right)\\ \Rightarrow A=-8-\dfrac{3}{2}+\dfrac{5}{3}\\ =-\dfrac{47}{6}.\\ B=0,5+\dfrac{1}{3}+0,4+\dfrac{5}{7}+\dfrac{1}{6}-\dfrac{4}{35}+\dfrac{1}{41}\)
\(\Rightarrow B=\left(0,5+0,4\right)+\left(\dfrac{1}{3}+\dfrac{1}{6}\right)+\left(\dfrac{5}{7}-\dfrac{4}{35}\right)+\dfrac{1}{41}\\ \Rightarrow B=\dfrac{9}{10}+\dfrac{1}{2}+\dfrac{3}{5}+\dfrac{1}{41}\\ \Rightarrow B=2+\dfrac{1}{41}\\ \Rightarrow B=\dfrac{83}{41}.\)