Tính: a) (3/4 + 1 1/2) - (5/6 : 1/3); b) [(-1/5) : 1/10] - 5/7 . (2/3 - 1/5);

* Hướng dẫn giải

a) $\left(\frac{3}{4}:1\frac{1}{2}\right)-\left(\frac{5}{6}:\frac{1}{3}\right)=\left(\frac{3}{4}:\frac{3}{2}\right)-\left(\frac{5}{6}.\frac{3}{1}\right)$

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

b) $\left[\left(\frac{-1}{5}\right):\frac{1}{10}\right]-\frac{5}{7}.\left(\frac{2}{3}-\frac{1}{5}\right)$

$=\frac{-1}{5}.\frac{10}{1}-\frac{5}{7}.\left(\frac{10}{15}-\frac{3}{15}\right)$

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

$=\frac{-6}{3}-\frac{1}{3}=\frac{-7}{3}$

c) $\left(-0,4\right)+2\frac{2}{5}.{\left[\left(\frac{-2}{3}\right)+\frac{1}{2}\right]}^2$

$=\frac{-2}{5}+\frac{12}{5}.{\left[\frac{-4}{6}+\frac{3}{6}\right]}^2$

$=\frac{-2}{5}+\frac{12}{5}.{\left[\frac{1}{6}\right]}^2=\frac{-2}{4}+\frac{12}{5}.\frac{1}{36}$

$=\frac{-2}{5}+\frac{1}{15}=\frac{-6}{15}+\frac{1}{15}=\frac{-5}{15}=\frac{-1}{3}$

d) $\left\{\left[{\left(\frac{1}{25}-0,6\right)}^2:\frac{49}{125}\right].\frac{5}{6}\right\}-\left[\left(\frac{-1}{3}\right)+\frac{1}{2}\right]$

$=\left\{\left[{\left(\frac{1}{25}-\frac{3}{5}\right)}^2:\frac{49}{125}\right].\frac{5}{6}\right\}-\left[\frac{-2}{6}+\frac{3}{6}\right]$

$=\left\{\left[{\left(\frac{1}{25}-\frac{3}{5}\right)}^2:\frac{49}{125}\right].\frac{5}{6}\right\}-\left[\frac{-2}{6}+\frac{3}{6}\right]$

$=\left\{\left[{\left(\frac{1}{25}-\frac{15}{25}\right)}^2:\frac{49}{125}\right].\frac{5}{6}\right\}-\frac{1}{6}$

$=\left\{\left[{\left(\frac{-14}{25}\right)}^2:\frac{49}{125}\right].\frac{5}{6}\right\}-\frac{1}{6}$

$=\left\{\left[\frac{{\left(-2\right)}^2{.7}^2}{{\left(5^2\right)}^2}:\frac{7^2}{5^3}\right].\frac{5}{6}\right\}-\frac{1}{6}$

$=\left\{\left[\frac{{\left(-2\right)}^2{.7}^2}{5^4}.\frac{5^3}{7^2}\right].\frac{5}{6}\right\}-\frac{1}{6}$

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

$=\frac{4}{6}-\frac{1}{6}$

$=\frac{3}{6}=\frac{1}{2}$