3. 如图,两摞规格完全相同的课本整齐地叠放在桌子上,请根据图中所给出的数据信息,回答下列问题:
(1)求每本课本的厚度;
(2)若有一摞上述规格的课本$x$本,整齐地叠放在桌子上,用含$x$的代数式表示出这一摞课本的顶部距离地面的高度;
(3)在(2)的条件下,当$x = 35$时,求课本的顶部距离地面的高度.

(1)求每本课本的厚度;
(2)若有一摞上述规格的课本$x$本,整齐地叠放在桌子上,用含$x$的代数式表示出这一摞课本的顶部距离地面的高度;
(3)在(2)的条件下,当$x = 35$时,求课本的顶部距离地面的高度.
答案
(1)设每本课本的厚度为$d$cm,桌子高度为$h$cm。根据题意可得:$\begin{cases}h + 3d = 86.5 \\ h + 6d = 88\end{cases}$,两式相减得$3d = 1.5$,解得$d = 0.5$。
(2)由(1)知$h = 86.5 - 3×0.5 = 85$,所以高度为$h + xd = 85 + 0.5x$。
(3)当$x = 35$时,$85 + 0.5×35 = 85 + 17.5 = 102.5$(cm)。
(1)0.5cm;(2)$85 + 0.5x$;(3)102.5cm
(2)由(1)知$h = 86.5 - 3×0.5 = 85$,所以高度为$h + xd = 85 + 0.5x$。
(3)当$x = 35$时,$85 + 0.5×35 = 85 + 17.5 = 102.5$(cm)。
(1)0.5cm;(2)$85 + 0.5x$;(3)102.5cm
4. 阅读下列材料,计算:$50÷(\frac{1}{3} - \frac{1}{4} + \frac{1}{12})$.
解法1思路:原式$= 50÷\frac{1}{3} - 50÷\frac{1}{4} + 50÷\frac{1}{12} = 50×3 - 50×4 + 50×12$;对吗?
解法2提示:先计算原式的倒数,$(\frac{1}{3} - \frac{1}{4} + \frac{1}{12})÷50 = \frac{1}{3}×\frac{1}{50} - \frac{1}{4}×\frac{1}{50} + \frac{1}{12}×\frac{1}{50} = \frac{1}{300}$,故原式$= 300$.
(1)请你用解法2的方法计算:$( - \frac{1}{30})÷(\frac{2}{3} - \frac{1}{10} + \frac{1}{6} - \frac{2}{5})$.
(2)计算:$(1\frac{3}{4} - \frac{7}{8} - \frac{7}{12})÷( - \frac{7}{8}) - \frac{7}{8}÷(1\frac{3}{4} - \frac{7}{8} - \frac{7}{12})$.现在这个题简单了吧?来吧,试试吧!
解法1思路:原式$= 50÷\frac{1}{3} - 50÷\frac{1}{4} + 50÷\frac{1}{12} = 50×3 - 50×4 + 50×12$;对吗?
解法2提示:先计算原式的倒数,$(\frac{1}{3} - \frac{1}{4} + \frac{1}{12})÷50 = \frac{1}{3}×\frac{1}{50} - \frac{1}{4}×\frac{1}{50} + \frac{1}{12}×\frac{1}{50} = \frac{1}{300}$,故原式$= 300$.
(1)请你用解法2的方法计算:$( - \frac{1}{30})÷(\frac{2}{3} - \frac{1}{10} + \frac{1}{6} - \frac{2}{5})$.
(2)计算:$(1\frac{3}{4} - \frac{7}{8} - \frac{7}{12})÷( - \frac{7}{8}) - \frac{7}{8}÷(1\frac{3}{4} - \frac{7}{8} - \frac{7}{12})$.现在这个题简单了吧?来吧,试试吧!
答案
(1)$-\frac{1}{10}$;(2)$-\frac{10}{3}$
解析
(1)先求原式的倒数:$(\frac{2}{3} - \frac{1}{10} + \frac{1}{6} - \frac{2}{5})÷(-\frac{1}{30})$
通分计算括号内:$\frac{20}{30} - \frac{3}{30} + \frac{5}{30} - \frac{12}{30} = \frac{10}{30} = \frac{1}{3}$
则倒数为:$\frac{1}{3}×(-30) = -10$,故原式$= -\frac{1}{10}$
(2)设$A = 1\frac{3}{4} - \frac{7}{8} - \frac{7}{12}$,$1\frac{3}{4} = \frac{7}{4}$
通分计算$A$:$\frac{42}{24} - \frac{21}{24} - \frac{14}{24} = \frac{7}{24}$
$A÷(-\frac{7}{8}) = \frac{7}{24}×(-\frac{8}{7}) = -\frac{1}{3}$
$\frac{7}{8}÷A = \frac{7}{8}×\frac{24}{7} = 3$
原式$= -\frac{1}{3} - 3 = -\frac{10}{3}$
通分计算括号内:$\frac{20}{30} - \frac{3}{30} + \frac{5}{30} - \frac{12}{30} = \frac{10}{30} = \frac{1}{3}$
则倒数为:$\frac{1}{3}×(-30) = -10$,故原式$= -\frac{1}{10}$
(2)设$A = 1\frac{3}{4} - \frac{7}{8} - \frac{7}{12}$,$1\frac{3}{4} = \frac{7}{4}$
通分计算$A$:$\frac{42}{24} - \frac{21}{24} - \frac{14}{24} = \frac{7}{24}$
$A÷(-\frac{7}{8}) = \frac{7}{24}×(-\frac{8}{7}) = -\frac{1}{3}$
$\frac{7}{8}÷A = \frac{7}{8}×\frac{24}{7} = 3$
原式$= -\frac{1}{3} - 3 = -\frac{10}{3}$
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