ĐỀ 1:
Bài 1:
a) \(\dfrac{2}{3}-\dfrac{5}{7}\cdot\dfrac{14}{25}=\dfrac{2}{3}-\dfrac{2}{5}=\dfrac{4}{15}\)
b) \(\dfrac{-2}{5}\cdot\dfrac{5}{8}+\dfrac{5}{8}\cdot\dfrac{3}{5}=\dfrac{5}{8}\cdot\left(\dfrac{-2+3}{5}\right)=\dfrac{5}{8}\cdot\dfrac{1}{5}=\dfrac{1}{8}\)
c) \(25\%-1\dfrac{1}{2}+0,5\cdot\dfrac{12}{5}=\dfrac{1}{4}-\dfrac{3}{2}+\dfrac{6}{5}=\dfrac{-1}{20}\)
Bài 2:
a) \(x+\dfrac{1}{2}=\dfrac{3}{4}\Leftrightarrow x=\dfrac{3}{4}-\dfrac{1}{2}\Leftrightarrow x=\dfrac{1}{4}\)
b) \(\dfrac{4}{5}\cdot x=\dfrac{4}{7}\Leftrightarrow x=\dfrac{4}{7}:\dfrac{4}{5}\Leftrightarrow x=\dfrac{4}{7}\cdot\dfrac{5}{4}\Leftrightarrow x=\dfrac{5}{7}\)
c) \(8x=7,8\cdot x+25\)
\(\Leftrightarrow8x-7,8x=25\)
\(\Leftrightarrow0,2x=25\)
\(\Leftrightarrow x=125\)
ĐỀ 2:
Bài 1:
a) \(\dfrac{7\cdot9-14}{3-17}=\dfrac{63-14}{-14}=\dfrac{49}{-14}=-\dfrac{7}{2}\)
b) \(0,25\cdot2\dfrac{1}{3}\cdot30\cdot0,5\cdot\dfrac{8}{45}=\dfrac{14}{9}\)
c) \(\dfrac{9}{23}\cdot\dfrac{5}{8}+\dfrac{9}{23}\cdot\dfrac{3}{8}-\dfrac{9}{23}=\dfrac{9}{23}\cdot\left(\dfrac{5+3-1}{8}\right)=\dfrac{9}{23}\cdot\dfrac{7}{8}=\dfrac{63}{184}\)
Bài 2:
a) \(\dfrac{1}{2}-\left(\dfrac{2}{3}\cdot x-\dfrac{1}{3}\right)=\dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{2}{3}.x-\dfrac{1}{3}=-\dfrac{1}{6}\)
\(\Leftrightarrow\dfrac{2}{3}.x=\dfrac{1}{6}\)
\(\Leftrightarrow x=\dfrac{1}{4}\)
b) \(\dfrac{3}{x+5}=15\%\)
\(\Leftrightarrow\dfrac{3}{x+5}=\dfrac{3}{20}\Leftrightarrow x+5=20\Leftrightarrow x=15\)
Bài 3:
\(A=\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}+...+\dfrac{1}{49\cdot50}\)
\(A=\dfrac{2-1}{1\cdot2}+\dfrac{3-2}{2\cdot3}+\dfrac{4-3}{3\cdot4}+...+\dfrac{50-49}{49\cdot50}\)
\(A=\dfrac{2}{1\cdot2}-\dfrac{1}{1\cdot2}+\dfrac{3}{2\cdot3}-\dfrac{2}{2\cdot3}+\dfrac{1}{3\cdot4}-\dfrac{3}{3\cdot4}+...+\dfrac{50}{49\cdot50}-\dfrac{49}{49\cdot50}\)
\(A=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{49}-\dfrac{1}{50}\)
\(A=1-\dfrac{1}{50}=\dfrac{49}{50}\)
Đề 1
Bài 1:
a, \(\dfrac{2}{3}-\dfrac{5}{7}.\dfrac{14}{25}\)
\(=\dfrac{2}{3}-\dfrac{5}{15}.\dfrac{14}{7}\)
\(=\dfrac{2}{3}-\dfrac{1.2}{3}\)
\(=0\)
b, \(\dfrac{-2}{5}.\dfrac{5}{8}+\dfrac{5}{8}.\dfrac{3}{5}\)
\(=\dfrac{5}{3}.\left(-\dfrac{2}{3}+\dfrac{3}{5}\right)\)
\(=\dfrac{5}{8}.\dfrac{1}{5}=\dfrac{1}{8}\)
c, \(25\%-1\dfrac{1}{2}+0,5.\dfrac{12}{5}\)
\(=0,25-2,5+1,2\)
\(=-1,05\)
Bài 2:
a, \(x+\dfrac{1}{2}=\dfrac{3}{4}\)
\(x=\dfrac{3}{4}-\dfrac{1}{2}\)
\(x=\dfrac{1}{4}\)
b, \(\dfrac{4}{5}x=\dfrac{4}{7}\)
\(x=\dfrac{4}{7}:\dfrac{4}{5}\)
\(x=\dfrac{5}{7}\)
c, \(8x=7,8x+25\)
\(\Leftrightarrow8x-7,8=25\)
\(\Leftrightarrow0,2x=25\)
\(\Leftrightarrow x=25:0,2\)
\(\Leftrightarrow x=125\)
Đề 2
Bài 1:
a, \(\dfrac{7.9-14}{3-17}\)\(=\dfrac{63-14}{-14}=-\dfrac{7}{2}\)
b,\(0,25.2\dfrac{1}{3}30.0,5.\dfrac{8}{45}\)
\(=\dfrac{1}{4}.\dfrac{7}{3}.30.\dfrac{1}{2}.\dfrac{8}{45}\)
\(=\dfrac{1.7.15.2.1.8}{4.2.3.15.3}\)
\(=\dfrac{7.2}{3.3}\)
\(=\dfrac{14}{9}\)
c, \(\dfrac{9}{23}.\dfrac{5}{8}+\dfrac{9}{23}.\dfrac{3}{8}-\dfrac{9}{23}\)
\(=\dfrac{9}{23}.\left(\dfrac{5}{8}+\dfrac{3}{8}\right)-\dfrac{9}{23}\)
\(=\dfrac{9}{23}.1-\dfrac{9}{23}=0\)
Bài 2:
a, \(\dfrac{1}{2}-\left(\dfrac{2}{3}x-\dfrac{1}{3}\right)=\dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{2}{3}x-\dfrac{1}{3}=\dfrac{1}{2}-\dfrac{2}{3}\)
\(\Leftrightarrow\dfrac{2}{3}x-\dfrac{1}{3}=-\dfrac{1}{6}\)
\(\Leftrightarrow\dfrac{2}{3}x=-\dfrac{1}{6}+\dfrac{1}{3}\)
\(\Leftrightarrow\dfrac{2}{3}x=\dfrac{1}{6}\)
\(x=\dfrac{1}{4}\)
b, \(\dfrac{3}{x+5}=15\%\)
\(\Leftrightarrow\dfrac{3}{x+5}=\dfrac{3}{20}\)
\(\Leftrightarrow x+5=20\)
\(\Leftrightarrow x=20-5\)
\(\Rightarrow x=15\)
Bài 3:
\(A=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{49.50}\)
\(=\left(1-\dfrac{1}{2}\right)+\left(\dfrac{1}{2}-\dfrac{1}{3}\right)+\left(\dfrac{1}{3}-\dfrac{1}{4}\right)+...+\left(\dfrac{1}{49}-\dfrac{1}{50}\right)\)
\(\Rightarrow\) Do \(-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}+...+\dfrac{1}{49}=0\)
\(\Rightarrow A=1-\dfrac{1}{50}=\dfrac{49}{50}\)
-Chúc bạn học tốt-
