Bài 1: (4 điểm) Thực hiện phép tính: a) $\left( 9\frac{4}{9}+5\frac{2}{3} \right)-5\frac{1}{9}$ b) $\frac{13}{9}.\frac{15}{4}-\frac{13}{9}.\frac{7}{4}-\frac{13}{9}.\frac{5}{4}$ c) $\frac{2}{3}+\frac{5}{8}-\frac{-1}{3}+0,375$ d) $75-3\frac{1}{2}+1,5:\frac{10}{7}$ Bài 2: (3,5 điểm) Tìm x, biết: a) $-\frac{5}{6}-x=\frac{7}{12}+\frac{-1}{3}$ b) $2\left( x-\frac{1}{3} \right)={{\left( \frac{1}{3} \right)}^{2}}+\frac{5}{9}$ c) $\left| 2x-\frac{3}{4} \right|-\frac{3}{8}=\frac{1}{8}$ d) $\frac{2}{3}x+\frac{1}{6}x=-3\frac{5}{8}$ Bài 3: (1,5 điểm) Cho $\frac{-4}{8}=\frac{x}{-10}=\frac{-7}{y}=\frac{z}{-3}$. Tìm các số nguyên x, y, z. Bài 4: (1 điểm) Tính tổng: $A=\frac{6}{5.8}+\frac{22}{8.19}+\frac{24}{19.31}+\frac{140}{31.101}+\frac{198}{101.200}$ Bài làm: Bài 1: a) Ta có: $\left( 9\frac{4}{9}+5\frac{2}{3} \right)-5\frac{1}{9}=$$\left( 9+\frac{4}{9}+5+\frac{2}{3} \right)-\left( 5+\frac{1}{9} \right)$ $=9+\frac{4}{9}+5+\frac{6}{9}-5-\frac{1}{9}=\left( 9+5-5 \right)+\left( \frac{4}{9}+\frac{6}{9}-\frac{1}{9} \right)$ $=9+1=10$ b) Ta có: $\frac{13}{9}.\frac{15}{4}-\frac{13}{9}.\frac{7}{4}-\frac{13}{9}.\frac{5}{4}=\frac{13}{9}.\left( \frac{15}{4}-\frac{7}{4}-\frac{5}{4} \right)=\frac{13}{9}.\frac{3}{4}=\frac{13}{12}$ c) Ta có: $\frac{2}{3}+\frac{5}{8}-\frac{-1}{3}+0,375=\frac{2}{3}+\frac{5}{8}+\frac{1}{3}+\frac{3}{8}=\left( \frac{2}{3}+\frac{1}{3} \right)+\left( \frac{5}{8}+\frac{3}{8} \right)=1+1=2$ d) $75-3\frac{1}{2}+1,5:\frac{10}{7}=\frac{3}{4}-\frac{7}{2}+\frac{3}{2}.\frac{7}{10}=\frac{3}{4}-\frac{7}{2}+\frac{21}{20}=\frac{15}{20}-\frac{70}{20}+\frac{21}{20}=\frac{-34}{20}=\frac{-17}{10}$ Bài 2: a) Ta có: $-\frac{5}{6}-x=\frac{7}{12}+\frac{-1}{3}$ $x=\frac{-5}{6}-\frac{7}{12}-\left( \frac{-1}{3} \right)$ $x=\frac{-10}{12}-\frac{7}{12}+\frac{4}{12}$ $x=\frac{-13}{12}$ b) Ta có: $2\left( x-\frac{1}{3} \right)={{\left( \frac{1}{3} \right)}^{2}}+\frac{5}{9}$ $2\left( x-\frac{1}{3} \right)=\frac{1}{9}+\frac{5}{9}$ $2\left( x-\frac{1}{3} \right)=\frac{2}{3}$ $x-\frac{1}{3}=\frac{2}{3}:2$ $x-\frac{1}{3}=\frac{2}{3}.\frac{1}{2}$ $x-\frac{1}{3}=\frac{1}{3}$ $x=\frac{1}{3}+\frac{1}{3}$ $x=\frac{2}{3}$ c) Ta có: $\left| 2x-\frac{3}{4} \right|-\frac{3}{8}=\frac{1}{8}$ $\begin{align} & \left| 2x-\frac{3}{4} \right|=\frac{1}{8}+\frac{3}{8} \\ & \left| 2x-\frac{3}{4} \right|=\frac{1}{2} \\ \end{align}$ $2x-\frac{3}{4}=\frac{1}{2}$ hoặc $2x-\frac{3}{4}=\frac{-1}{2}$ $2x=\frac{1}{2}+\frac{3}{4}$ hoặc $2x=\frac{-1}{2}+\frac{3}{4}$ $2x=\frac{2}{4}+\frac{3}{4}$ hoặc $2x=\frac{-2}{4}+\frac{3}{4}$ $2x=\frac{5}{4}$ hoặc $2x=\frac{1}{4}$ $x=\frac{5}{4}:2$ hoặc $x=\frac{1}{4}:2$ $x=\frac{5}{4}.\frac{1}{2}$ hoặc $x=\frac{1}{4}.\frac{1}{2}$ $x=\frac{5}{8}$hoặc $x=\frac{1}{8}$ d) Ta có: $\frac{2}{3}x+\frac{1}{6}x=-3\frac{5}{8}$ $\left( \frac{2}{3}+\frac{1}{6} \right)x=\frac{-29}{8}$ $\left( \frac{4}{6}+\frac{1}{6} \right)x=\frac{-29}{8}$ $\frac{5}{6}x=\frac{-29}{8}$ $x=\frac{-29}{8}:\frac{5}{6}$ $x=\frac{-29}{8}.\frac{6}{5}$ $x=\frac{-87}{20}$ Bài 3: Ta có: $\frac{-4}{8}=\frac{x}{-10}=\frac{-7}{y}=\frac{z}{-3}$ Do đó: $\frac{x}{-10}=\frac{-4}{8}\Rightarrow x=\frac{-4}{8}.\left( -10 \right)=5$ $\frac{-7}{y}=\frac{-4}{8}\Rightarrow \frac{y}{-7}=\frac{-8}{4}\Rightarrow y=\frac{-8}{4}.\left( -7 \right)=14$ $\frac{z}{-3}=\frac{-4}{8}\Rightarrow z=\frac{-4}{8}.\left( -3 \right)=\frac{3}{2}$ Vậy: $x=5;\,y=14;\,z=\frac{3}{2}$ Bài 4: Ta có: $A=\frac{6}{5.8}+\frac{22}{8.19}+\frac{24}{19.31}+\frac{140}{31.101}+\frac{198}{101.200}$ $A=2.\frac{3}{5.8}+2.\frac{11}{8.19}+2.\frac{12}{19.31}+2.\frac{70}{31.101}+2.\frac{99}{101.200}$ $A=2.\left( \frac{3}{5.8}+\frac{11}{8.19}+\frac{12}{19.31}+\frac{70}{31.101}+\frac{99}{101.200} \right)$ $A=2.\left( \frac{8-5}{5.8}+\frac{19-8}{8.19}+\frac{31-19}{19.31}+\frac{101-31}{31.101}+\frac{200-101}{101.200} \right)$ $A=2.\left( \frac{1}{5}-\frac{1}{8}+\frac{1}{8}-\frac{1}{19}+\frac{1}{19}-\frac{1}{31}+\frac{1}{31}-\frac{1}{101}+\frac{1}{101}-\frac{1}{200} \right)$ $A=2.\left( \frac{1}{5}-\frac{1}{200} \right)$ $A=2.\left( \frac{40}{200}-\frac{1}{200} \right)$ $A=2.\frac{39}{200}$ $A=\frac{39}{100}$ Theo LTTK Education tổng hợp
