Thực hiện phép tính ( bằng cách hợp lí nếu có thể):

a, \(5\frac{4}{13}.15\frac{3}{41}-5\frac{4}{13}.2\frac{3}{41}\)

\(=5\frac{4}{13}\left(15\frac{3}{41}-2\frac{3}{41}\right)\)

\(=15\frac{4}{13}\left(\frac{618}{41}-\frac{85}{41}\right)\)

\(=\frac{69}{13}.13\)

\(=69\)

b, \(6.\left(-\frac{1}{3}\right)^2-\left(\frac{1}{4}:2-\frac{7}{16}.\frac{-4}{21}\right)\)

\(=6.\frac{1}{9}-\left(\frac{1}{8}-\frac{-1}{12}\right)\)

\(=\frac{2}{3}-\left(\frac{3}{24}-\frac{-2}{24}\right)\)

\(=\frac{2}{3}-\frac{5}{24}\)

\(=\frac{16}{24}-\frac{5}{24}\)

\(=\frac{11}{24}\)

Chúc bạn hok tốt!!! lưu khánh huyền

bài này đề bài là :thực hiện phép tính(bằng cách hợp lí nếu có thể):

a)\(5\frac{4}{3}.15\frac{3}{41}-5\frac{4}{13}.2\frac{3}{41}\)

=\(5\frac{4}{13}.\left(15\frac{3}{41}-2\frac{3}{41}\right)\)

=\(5\frac{4}{13}.13\)

=69

HD: Vũ Phương Vy  em chỉ cần đặt ts c rồi rút gọn

ko chép lại đề nha

=\(A=\frac{2\left(1-\frac{2}{19}+\frac{2}{23}\right)-\frac{1}{1010}}{3\left(1-\frac{1}{19}+\frac{1}{23}-\frac{1}{2020}\right)}\)\(.\frac{4\left(1-\frac{1}{29}+\frac{1}{41}\right)-\frac{1}{505}}{5\left(1-\frac{1}{29}+\frac{1}{41}\right)-\frac{1}{404}}\)

rồi em chỉ cần rút gọn tiếp 

p/s đến đây thấy đề kì kì sao đó 

em chek lại đề đc k

đề đúng rồi đó ạ

đề đúng mà ko sai đâu nếu bạn ko tin thì xem bài 5 của đề này nhé : https://online-learning-izteach-aws-source-bucket.s3-ap-southeast-1.amazonaws.com/resource/49714800-4b02-11ea-a775-01bd84d6799a/4baf4091-c5ae-4d0f-819c-e9ee9eedd6a8/de-so-13-on-tap-va-cung-co-toan-6-pdf

\(\frac{\left(2n+1\right)^3+n^3}{\left(n+1\right)^3-n^3}=\frac{\left(3n+1\right)\left(3n^2+3n+1\right)}{3n^2+3n+1}=3n+1\)

\(\Rightarrow A=\left(3.1+1\right)+\left(3.2+1\right)+...+\left(3.20+1\right)\)

\(=3\left(1+2+...+20\right)+20\)

\(=\frac{3.20.21}{2}+20=...\)

a: \(=\dfrac{3\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}{4\left(\dfrac{1}{41}-\dfrac{4}{47}+\dfrac{9}{53}\right)}+\dfrac{-\dfrac{1}{4}\cdot\dfrac{-2}{3}-\dfrac{3}{4}:\dfrac{1}{6}}{\dfrac{3}{2}\cdot\left(\dfrac{-2}{3}-\dfrac{3}{4}\cdot\dfrac{-2}{3}\right)}\)

\(=\dfrac{3}{4}+\dfrac{\dfrac{2}{12}-\dfrac{9}{2}}{\dfrac{3}{2}\cdot\dfrac{-1}{6}}=\dfrac{3}{4}+\dfrac{-13}{3}:\dfrac{-3}{12}\)

\(=\dfrac{3}{4}+\dfrac{13}{3}\cdot\dfrac{12}{3}=\dfrac{3}{4}+\dfrac{156}{9}=\dfrac{217}{12}\)

b: \(A=158\left(\dfrac{12\left(1-\dfrac{1}{7}-\dfrac{1}{289}-\dfrac{1}{85}\right)}{4\left(1-\dfrac{1}{7}-\dfrac{1}{289}-\dfrac{1}{85}\right)}:\dfrac{5\left(1+\dfrac{1}{13}+\dfrac{1}{169}+\dfrac{1}{91}\right)}{6\left(1+\dfrac{1}{13}+\dfrac{1}{169}+\dfrac{1}{91}\right)}\right)\cdot\dfrac{50550505}{711711711}\)

\(=158\cdot\left(3\cdot\dfrac{6}{5}\right)\cdot\dfrac{50550505}{711711711}\)

\(\simeq40.39\)

\(A=17\frac{2}{31}-\left(\frac{15}{17}+6\frac{2}{31}\right)=\left(17\frac{2}{31}-6\frac{2}{31}\right)-\frac{15}{17}=11-\frac{15}{17}=10+\left(1-\frac{15}{17}\right)=10\frac{2}{17}\)

\(B=\left(31\frac{6}{13}-36\frac{6}{13}\right)+5\frac{9}{41}=-5+5\frac{9}{41}=\frac{9}{41}\)

C=\(\left(27\frac{51}{59}-7\frac{51}{59}\right)+\frac{1}{3}=20+\frac{1}{3}=20\frac{1}{3}\)

\(D=\left(13\frac{29}{31}-2\frac{28}{31}\right)+\left(4-3\frac{7}{8}\right)=11\frac{1}{31}+\frac{1}{8}=11\frac{8+31}{31.8}=11\frac{39}{248}\)

\(A=\frac{-5}{12}+\frac{4}{37}+\frac{17}{12}-\frac{41}{37}=(\frac{-5}{12}+\frac{17}{12})+(\frac{4}{37}-\frac{41}{37})=\frac{12}{12}+\frac{-37}{37}=1+(-1)=0\)

\(B=\frac{1}{2}-\frac{43}{101}+\frac{-1}{3}-\frac{1}{6}=\frac{-43}{101}+(\frac{1}{2}+\frac{-1}{3}-\frac{1}{6})=\frac{-43}{101}+(\frac{3}{6}+\frac{-2}{6}-\frac{1}{6})=\frac{-43}{101}+0=\frac{-43}{101}\)

\(A=\frac{-5}{12}+\frac{4}{37}+\frac{17}{12}-\frac{41}{37}.\)

\(A=\left(\frac{-5}{12}+\frac{17}{12}\right)-\left(\frac{41}{37}-\frac{4}{37}\right)\)

\(A=1-1=0\)

\(B=\frac{1}{2}-\frac{43}{101}+\left(\frac{-1}{3}\right)-\frac{1}{6}\)

\(B=\left(\frac{1}{2}+\left(\frac{-1}{3}\right)-\frac{1}{6}\right)-\frac{43}{101}\)

\(A=0-\frac{43}{101}=\frac{-43}{101}\)

\(C=\frac{-5}{6}\cdot\frac{12}{-7}\cdot-\frac{21}{15}\)

\(C=\frac{-5}{2.3}\cdot\frac{3.2.2}{-7}\cdot\frac{3.\left(-7\right)}{3.5}\)

\(C=\frac{-2}{1}=-2\)

Tiếp:

\(C=\frac{-5}{6}.\frac{12}{-7}.\frac{-21}{15}=\frac{(-5).12.(-21)}{6.(-7).15}=\frac{1.2.3}{1.1.(-3)}=\frac{2}{-1}=-2\)

_Học tốt_