Thực hiện phép tính (bằng cách hợp lí nếu có thể) a) 5/23 + 7/17 + 0,25

Thực hiện phép tính (bằng cách hợp lí nếu có thể)

$a) \frac{5}{23}+\frac{7}{17}+0,25-\frac{5}{23}+\frac{10}{17}$

b) $\frac{3}{7}.2\frac{2}{3}-\frac{3}{7}.1\frac{1}{2}$

c) $13\frac{1}{4}:\left(-\frac{4}{7}\right)-17\frac{1}{4}:\left(-\frac{4}{7}\right)$

d) $\frac{100}{123}:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)$

b) $\frac{3}{7}.2\frac{2}{3}-\frac{3}{7}.1\frac{1}{2}$

$=\frac{3}{7}.\frac{8}{3}-\frac{3}{7}.\frac{3}{2}$$=\frac{3}{7}.\left(\frac{8}{3}-\frac{3}{2}\right)$

$=\frac{3}{7}.\left(\frac{16}{6}-\frac{9}{6}\right)$$=\frac{3}{7}.\frac{7}{6}=\frac{1}{2}$

c) $13\frac{1}{4}:\left(-\frac{4}{7}\right)-17\frac{1}{4}:\left(-\frac{4}{7}\right)$

$=\left(13+\frac{1}{4}\right).\left(\frac{-7}{4}\right)-\left(17+\frac{1}{4}\right)\left(\frac{-7}{4}\right)$

$$\begin{gathered} =\left(\frac{-7}{4}\right).\left(13+\frac{1}{4}-17-\frac{1}{4}\right) \\ =\left(\frac{-7}{4}\right).\left[\left(13-17\right)+\left(\frac{1}{4}-\frac{1}{4}\right)\right] \\ =\left(\frac{-7}{4}\right).\left(-4\right)=7. \end{gathered}$$

d) $\frac{100}{123}:\left(\frac{3}{4}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{9}{5}-\frac{7}{15}\right)$

$=\frac{100}{123}:\left(\frac{9}{12}+\frac{7}{12}\right)+\frac{23}{123}:\left(\frac{27}{15}-\frac{7}{15}\right)$

$=\frac{100}{123}:\frac{16}{12}+\frac{23}{123}:\frac{20}{15}$

$=\frac{100}{123}:\frac{4}{3}+\frac{23}{123}:\frac{4}{3}$

$=\frac{100}{123}.\frac{3}{4}+\frac{23}{123}.\frac{3}{4}$

$=\frac{3}{4}.\left(\frac{100}{123}+\frac{23}{123}\right)$

$=\frac{3}{4}.\frac{123}{123}=\frac{3}{4}$