9. 计算:
(1)$-\frac{5}{6}×(12-2\frac{2}{5}-0.6)$;
(2)$2×\frac{3}{5}-(-5)×\frac{3}{5}-3×\frac{3}{5}$.
答案:$(1)-\frac{15}{2} (2)\frac{12}{5}$
解析:
(1)
$\begin{aligned}-\frac{5}{6}×(12 - 2\frac{2}{5} - 0.6)&=-\frac{5}{6}×\left(12 - \frac{12}{5} - \frac{3}{5}\right)\\&=-\frac{5}{6}×\left(12 - \frac{15}{5}\right)\\&=-\frac{5}{6}×(12 - 3)\\&=-\frac{5}{6}×9\\&=-\frac{45}{6}\\&=-\frac{15}{2}\end{aligned}$
(2)
$\begin{aligned}2×\frac{3}{5} - (-5)×\frac{3}{5} - 3×\frac{3}{5}&=\frac{3}{5}×(2 + 5 - 3)\\&=\frac{3}{5}×4\\&=\frac{12}{5}\end{aligned}$
10. 用简便方法计算:
(1)$9\frac{18}{19}×15$;
(2)$-99\frac{71}{72}×36$.
答案:$(1)149\frac{4}{19} (2)-3599\frac{1}{2}$
解析:
(1) $9\frac{18}{19} × 15$
$=(10 - \frac{1}{19}) × 15$
$=10×15 - \frac{1}{19}×15$
$=150 - \frac{15}{19}$
$=149\frac{4}{19}$
(2) $-99\frac{71}{72} × 36$
$=-(100 - \frac{1}{72}) × 36$
$=-(100×36 - \frac{1}{72}×36)$
$=-(3600 - \frac{1}{2})$
$=-3599\frac{1}{2}$
11. 定义一种新运算“※”,其规则为$x※y= x× y - x + y$. 例如:$6※5= 6×5 - 6 + 5= 29$.
(1)求$5※6$的值.
(2)有理数的加法和乘法运算满足交换律,即$a + b = b + a$,$a× b = b× a$. “※”运算是否满足交换律?若满足,请说明理由;若不满足,请举例说明.
答案:
(1)31.5※6=5×6-5+6=31
(2)不满足.先理解交换律的含义:a※b=b※a,即a×b-a+b=b×a-b+a,再通过举例子判断,如6※5=29,5※6=31,29≠31