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17. (16分)计算.
(1)$\frac{1}{2}+(-\frac{2}{3})+\frac{4}{7}+(-\frac{1}{2})+(-\frac{1}{3})$;
(2)$-\frac{4}{7}×3.59+\frac{4}{7}×(-2.41)-\frac{4}{7}$;
(3)$(-\frac{1}{4}+\frac{1}{3}-\frac{5}{12})×(-24)$;
(4)$-3^{2}-(2 - 5)+7+(-2)^{2}×|-\frac{1}{4}|$.
(1)$\frac{1}{2}+(-\frac{2}{3})+\frac{4}{7}+(-\frac{1}{2})+(-\frac{1}{3})$;
(2)$-\frac{4}{7}×3.59+\frac{4}{7}×(-2.41)-\frac{4}{7}$;
(3)$(-\frac{1}{4}+\frac{1}{3}-\frac{5}{12})×(-24)$;
(4)$-3^{2}-(2 - 5)+7+(-2)^{2}×|-\frac{1}{4}|$.
答案
(1)
$\begin{aligned}\frac{1}{2}+(-\frac{2}{3})+\frac{4}{7}+(-\frac{1}{2})+(-\frac{1}{3})\\= \frac{1}{2} - \frac{1}{2} - \frac{2}{3} - \frac{1}{3} + \frac{4}{7} \\= 0 - 1 + \frac{4}{7} \\= - \frac{3}{7}\end{aligned}$
(2)
$\begin{aligned}-\frac{4}{7} × 3.59 + \frac{4}{7} × (-2.41) - \frac{4}{7} \\= \frac{4}{7} × (-3.59 - 2.41 - 1) \\= \frac{4}{7} × (-7) \\= -4\end{aligned}$
(3)
$\begin{aligned}(-\frac{1}{4} + \frac{1}{3} - \frac{5}{12}) × (-24) \\= (-\frac{3}{12} + \frac{4}{12} - \frac{5}{12}) × (-24) \\= (-\frac{4}{12}) × (-24) \\= 8\end{aligned}$
(4)
$\begin{aligned}-3^{2} - (2 - 5) + 7 + (-2)^{2} × |-\frac{1}{4}| \\= -9 + 3 + 7 + 4 × \frac{1}{4} \\= -9 + 3 + 7 + 1 \\= 2\end{aligned}$
$\begin{aligned}\frac{1}{2}+(-\frac{2}{3})+\frac{4}{7}+(-\frac{1}{2})+(-\frac{1}{3})\\= \frac{1}{2} - \frac{1}{2} - \frac{2}{3} - \frac{1}{3} + \frac{4}{7} \\= 0 - 1 + \frac{4}{7} \\= - \frac{3}{7}\end{aligned}$
(2)
$\begin{aligned}-\frac{4}{7} × 3.59 + \frac{4}{7} × (-2.41) - \frac{4}{7} \\= \frac{4}{7} × (-3.59 - 2.41 - 1) \\= \frac{4}{7} × (-7) \\= -4\end{aligned}$
(3)
$\begin{aligned}(-\frac{1}{4} + \frac{1}{3} - \frac{5}{12}) × (-24) \\= (-\frac{3}{12} + \frac{4}{12} - \frac{5}{12}) × (-24) \\= (-\frac{4}{12}) × (-24) \\= 8\end{aligned}$
(4)
$\begin{aligned}-3^{2} - (2 - 5) + 7 + (-2)^{2} × |-\frac{1}{4}| \\= -9 + 3 + 7 + 4 × \frac{1}{4} \\= -9 + 3 + 7 + 1 \\= 2\end{aligned}$
