《2025年学习目标与检测同步测试卷七年级数学上册人教版》

20. (11 分)阅读以下材料,完成相关的填空和计算.
(1) 根据倒数的定义我们知道,若 $(a + b)÷ c = -2$,则 $c÷ (a + b) =$- \frac {1}{2}.
(2) 计算 $(\frac{5}{12} - \frac{1}{9} + \frac{2}{3})÷ \frac{1}{36}$.
(3) 根据以上信息可知: $(-\frac{1}{36})÷ (\frac{5}{12} - \frac{1}{9} + \frac{2}{3}) =$- \frac {1}{35}.

答案： 20.解
(1)因为 (a + b)÷c = -2，所以$ c÷(a + b) = - \frac {1}{2}. $故答案为$ - \frac {1}{2}.$
$(2)(\frac {5}{12} - \frac {1}{9} + \frac {2}{3})÷\frac {1}{36} = (\frac {5}{12} - \frac {1}{9} + \frac {2}{3})×36 = \frac {5}{12}×36 - \frac {1}{9}×36 + \frac {2}{3}×36 = 15 - 4 + 24 = 35.$
(3)由
(2)知$ (\frac {5}{12} - \frac {1}{9} + \frac {2}{3})÷\frac {1}{36} = 35，$所以$ (- \frac {1}{36})÷(\frac {5}{12} - \frac {1}{9} + \frac {2}{3}) = - \frac {1}{35}. $故答案为$ - \frac {1}{35}.$