Tính nhanh a) 13/23 . 7/11 + 10/23 . 7/11 b) 5/9 . 23/11 - 1/11 . 5/9 + 5/9

* Hướng dẫn giải

a) $\frac{13}{23}.\frac{7}{11}+\frac{10}{23}.\frac{7}{11}$

$=\frac{7}{11}.\left(\frac{13}{23}+\frac{10}{23}\right)$

$=\frac{7}{11}.\frac{23}{23}=\frac{7}{11}.1=\frac{7}{11}$

b) $\frac{5}{9}.\frac{23}{11}-\frac{1}{11}.\frac{5}{9}+\frac{5}{9}$

$=\frac{5}{9}.\left(\frac{23}{11}-\frac{1}{11}+1\right)$

$=\frac{5}{9}.\left(\frac{22}{11}+1\right)$

$=\frac{5}{9}.\left(2+1\right)$

$=\frac{5}{9}.3=\frac{5}{3}$

c) $\left[\left(-\frac{4}{9}\right)+\frac{3}{5}\right]:\frac{13}{17}+\left(\frac{2}{5}-\frac{5}{9}\right):\frac{13}{17}$

$=\left[\left(-\frac{4}{9}\right)+\frac{3}{5}\right].\frac{17}{13}+\left(\frac{2}{5}-\frac{5}{9}\right).\frac{17}{13}$

$=\left(-\frac{4}{9}+\frac{3}{5}+\frac{2}{5}-\frac{5}{9}\right).\frac{17}{13}$

$=\left(\frac{-4-5}{9}+\frac{3+2}{5}\right).\frac{17}{13}$

$=\left(\frac{-9}{9}+\frac{5}{5}\right).\frac{17}{13}$

$=\left(-1+1\right).\frac{17}{13}$

$=0.\frac{17}{13}=0$

d) $\frac{3}{16}:\left(\frac{3}{22}-\frac{3}{11}\right)+\frac{3}{16}:\left(\frac{1}{10}-\frac{2}{5}\right)$

$=\frac{3}{16}:\left(\frac{3}{22}-\frac{6}{22}\right)+\frac{3}{16}:\left(\frac{1}{10}-\frac{4}{10}\right)$

$=\frac{3}{16}:\frac{-3}{22}+\frac{3}{16}:\frac{-3}{10}$

$=\frac{3}{16}.\frac{22}{-3}+\frac{3}{16}.\frac{10}{-3}$

$=\frac{3}{16}.\left(\frac{22}{-3}+\frac{10}{-3}\right)$

$=\frac{3}{16}.\frac{32}{-3}$

$=\frac{\mathrm{3.16.2}}{\mathrm{16.3.}(-1)}=-2$