Dạng 5. Bài toán tổng hợp có đáp án

a) $3.\frac{-5}{11}=\frac{3.(-5)}{11}=\frac{-15}{11}$

$b)\frac{3}{5}+\frac{4}{7}.\frac{14}{6}=\frac{3}{5}+\frac{4.14}{7.6}=\frac{3}{5}+\frac{4}{3}$

$c)\frac{10}{21}-\frac{3}{8}.\frac{4}{15}=\frac{10}{21}-\frac{3.4}{8.15}=\frac{10}{21}-\frac{1}{10}$

$d)\left(\frac{2}{3}+\frac{3}{4}\right).\left(\frac{5}{7}+\frac{5}{14}\right)=\left(\frac{8}{12}+\frac{9}{12}\right).\left(\frac{10}{14}+\frac{5}{14}\right)$

$a)A=\frac{5}{11}.\frac{5}{7}+\frac{5}{11}.\frac{2}{7}+\frac{6}{11}=\frac{5}{11}.\left(\frac{5}{7}+\frac{2}{7}\right)+\frac{6}{11}=\frac{5}{11}+\frac{6}{11}=1$

$b)B=\frac{3}{13}.\frac{6}{11}+\frac{3}{13}.\frac{9}{11}-\frac{3}{13}.\frac{4}{11}=\frac{3}{13}.\left(\frac{6}{11}+\frac{9}{11}-\frac{4}{11}\right)=\frac{3}{13}.\frac{11}{11}.$

$c)C=\left(\frac{12}{61}-\frac{31}{22}+\frac{14}{91}\right)\left(\frac{3}{6}-\frac{2}{6}-\frac{1}{6}\right)=\left(\frac{12}{61}-\frac{31}{22}+\frac{14}{91}\right).0=0$

$a)\frac{3}{5}:\left(\frac{1}{2}.\frac{3}{5}\right)=\frac{3}{5}:\frac{3}{10}=\frac{3}{5}.\frac{10}{3}=2$

$b)\frac{4}{5}+\frac{3}{5}:3-\frac{7}{8}=\frac{4}{5}+\frac{1}{5}-\frac{7}{8}=1-\frac{7}{8}=\frac{1}{8}$

$c)\left(\frac{3}{4}:\frac{2}{3}\right):\frac{3}{5}=\frac{1}{8}:\frac{3}{5}=\frac{1}{8}.\frac{5}{3}=\frac{15}{8}$

$d)\left(\frac{5}{12}.\frac{21}{15}\right):\frac{1}{4}=\frac{7}{12}.4=\frac{7}{3}$

$M=\frac{3.\left(\frac{1}{4}+\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}{6.\left(\frac{1}{4}+\frac{1}{5}+\frac{1}{7}-\frac{1}{11}\right)}=\frac{3}{6}=\frac{1}{2}$

$N=\frac{\frac{2}{3}+\frac{2}{5}-\frac{2}{7}-\frac{2}{11}}{2+\frac{6}{5}-\frac{6}{7}-\frac{6}{11}}=\frac{2.\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{7}-\frac{1}{11}\right)}{6\left(\frac{1}{3}+\frac{1}{5}-\frac{1}{7}-\frac{1}{11}\right)}=\frac{2}{6}=\frac{1}{3}$

$a)x-\frac{1}{5}=\frac{7}{11}.\frac{3}{21}$

$x-\frac{1}{5}=\frac{1}{11}$

$x=\frac{1}{11}+\frac{1}{5}$

$x=\frac{16}{55}$

$b)\frac{x}{25}=\frac{-3}{15}.\frac{7}{6}$

$\frac{x}{25}=\frac{-7}{45}$

$x=\frac{25.(-7)}{45}$

$x=\frac{-35}{9}$

$c)x+\frac{7}{5}=\frac{9}{8}.\frac{4}{27}$

$x+\frac{7}{5}=\frac{1}{6}$

$x=\frac{1}{6}-\frac{7}{5}$

$x=\frac{-37}{30}$

$d)x:\frac{5}{11}=\frac{-4}{12}.6$

$x:\frac{5}{11}=-2$

$x=-2.\frac{5}{11}$

$x=\frac{-10}{11}$

$a)x-\frac{1}{2}=\frac{3}{10}.\frac{5}{6}$

$x-\frac{1}{2}=\frac{1}{4}$

$x=\frac{1}{4}+\frac{1}{2}$

$x=\frac{3}{4}$

$b)\frac{x}{5}=\frac{-3}{14}.\frac{7}{3}$

$\frac{x}{5}=\frac{-1}{2}$

$x=\frac{-1.5}{2}=\frac{-5}{2}$

$c)x+\frac{2}{3}=\frac{9}{15}.\frac{5}{27}$

$x+\frac{2}{3}=\frac{1}{9}$

$x=\frac{1}{9}-\frac{2}{3}$

$x=\frac{-5}{9}$

$d)x:\frac{4}{11}=\frac{11}{4}.2$

$x:\frac{4}{11}=\frac{11}{2}$

$x=\frac{11}{2}.\frac{4}{11}=2$

$a)\frac{4}{7}.x+\frac{2}{3}=\frac{-1}{5}$

$\frac{4}{7}.x=\frac{-1}{5}-\frac{2}{3}=\frac{-13}{15}$

$x=\frac{-13}{15}:\frac{4}{7}$

$x=\frac{-91}{60}.$

$b)\frac{2}{9}-\frac{7}{8}.x=1$

$\frac{7}{8}.x=\frac{2}{9}-1=\frac{-7}{9};$

$x=\frac{-7}{9}:\frac{7}{8}$

$x=\frac{-8}{9}$

$c)\frac{4}{5}+\frac{7}{6}:x=\frac{1}{6}$

$\frac{7}{6}:x=\frac{1}{6}-\frac{4}{5}=\frac{-19}{30}$

$x=\frac{7}{6}:\frac{-19}{30}$

$x=\frac{-35}{19}$

$d)\frac{5}{7}:x-1=\frac{2}{3}$

$\frac{5}{7}:x=\frac{2}{3}+1=\frac{5}{3}$

$x=\frac{5}{7}:\frac{5}{3}$

$x=\frac{3}{7}.$