Bài 1:
a: \(1\dfrac{2}{5}+3\dfrac{3}{5}=1+\dfrac{2}{5}+3+\dfrac{3}{5}=4+1=5\)
b: \(\left(-\dfrac{5}{9}\right)\cdot\dfrac{3}{11}+\left(-\dfrac{4}{9}\right)\cdot\dfrac{3}{11}\)
\(=\dfrac{3}{11}\left(-\dfrac{5}{9}-\dfrac{4}{9}\right)=\dfrac{3}{11}\cdot\left(-1\right)=-\dfrac{3}{11}\)
c: \(2023-\left(\dfrac{1}{3}\right)^2\cdot3^2\)
\(=2023-\left(\dfrac{1}{3}\cdot3\right)^2\)
=2023-1=2022
d: \(\dfrac{5^{16}\cdot27^7}{125^5\cdot9^{11}}=\dfrac{5^{16}\cdot3^{21}}{\left(5^3\right)^5\cdot\left(3^2\right)^{11}}=\dfrac{5^{16}}{5^{15}}\cdot\dfrac{3^{21}}{3^{22}}=\dfrac{5}{3}\)
e: \(\dfrac{5}{2}-\dfrac{2}{11}\left(\dfrac{4}{3}+\dfrac{1}{2}\right)=\dfrac{5}{2}-\dfrac{2}{11}\cdot\left(\dfrac{8}{6}+\dfrac{3}{6}\right)=\dfrac{5}{2}-\dfrac{2}{11}\cdot\dfrac{11}{6}\)
\(=\dfrac{5}{2}-\dfrac{2}{6}=\dfrac{15}{6}-\dfrac{2}{6}=\dfrac{13}{6}\)
g: \(\left(\dfrac{8}{27}\right)^{20}:\left(\dfrac{2}{3}\right)^{58}=\left(\dfrac{2}{3}\right)^{60}:\left(\dfrac{2}{3}\right)^{58}=\left(\dfrac{2}{3}\right)^2=\dfrac{4}{9}\)
Bài 4: Số tiền chi tiêu là \(8\cdot\dfrac{3}{5}=4,8\)(triệu đồng)
200 nghìn=0,2 triệu đồng
Số tiền mẹ còn lại trong 1 tháng là:
8-4,8-0,2=3(triệu đồng)
Bài 3:
a: \(1\dfrac{1}{5}+\dfrac{4}{5}:x=0,75\)
=>\(\dfrac{4}{5}:x=\dfrac{3}{4}-\dfrac{6}{5}=\dfrac{15}{20}-\dfrac{24}{20}=-\dfrac{9}{20}\)
=>\(x=-\dfrac{4}{5}:\dfrac{9}{20}=-\dfrac{4}{5}\cdot\dfrac{20}{9}=\dfrac{-80}{45}=-\dfrac{16}{9}\)
b: \(\dfrac{1}{9}\cdot3^4\cdot3^x=3^7\)
=>\(3^x\cdot3^2=3^7\)
=>x+2=7
=>x=5
c: \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)
=>\(\left[{}\begin{matrix}x+\dfrac{1}{2}=\dfrac{1}{4}\\x+\dfrac{1}{2}=-\dfrac{1}{4}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{4}-\dfrac{1}{2}=-\dfrac{1}{4}\\x=-\dfrac{1}{4}-\dfrac{1}{2}=-\dfrac{3}{4}\end{matrix}\right.\)
d: \(\dfrac{1}{2}x-\dfrac{2}{3}=\dfrac{5}{4}\)
=>\(\dfrac{1}{2}x=\dfrac{2}{3}+\dfrac{5}{4}=\dfrac{8}{12}+\dfrac{15}{12}=\dfrac{23}{12}\)
=>\(x=\dfrac{23}{12}\cdot2=\dfrac{23}{6}\)
e: \(3-\dfrac{1}{2}x=1\)
=>\(\dfrac{1}{2}x=3-1=2\)
=>\(x=2\cdot2=4\)
g: \(\dfrac{1}{3}x+\sqrt{16}=5\)
=>\(\dfrac{x}{3}=5-4=1\)
=>x=3