倒数

Find the reciprocal of \(\frac{1}{-2} \cdot \left(-\frac{1}{3}\right) \cdot \frac{1}{-4} \cdot \left( -\frac{1}{5} \right)\).
计算\(\frac{1}{-2} \cdot \left(-\frac{1}{3}\right) \cdot \frac{1}{-4} \cdot \left( -\frac{1}{5} \right)\)的倒数。

What is the sum of the reciprocal of \(\frac{1}{12}\) and the reciprocal of \(-\frac{1}{5}\)?
\(\frac{1}{12}\)与\(-\frac{1}{5}\)两个数的倒数之和是多少？

What is the result when you multiply the product of two nonzero numbers by the product of their reciprocals?
将两个非零数字的乘积，乘以这两个数字各自倒数的乘积，所得结果是多少？

Find \(-\frac{1}{-3}\cdot\frac{1}{\frac{1}{-3}}.\)
计算 \(-\frac{1}{-3}\cdot\frac{1}{\frac{1}{-3}}.\)

Find \(64 \cdot \frac{1}{8} + 28 \cdot \frac{1}{7}\).
计算\(64 \cdot \frac{1}{8} + 28 \cdot \frac{1}{7}\).

What is the reciprocal of \(\frac{1}{\phantom{i}\frac{1}{17}\phantom{i}}\)?
\(\frac{1}{\phantom{i}\frac{1}{17}\phantom{i}}\) 的倒数是多少？

Find \(\frac{1}{9}\cdot 5\cdot \frac{1}{-2}\cdot 9\cdot 7\cdot 2\).
计算 \(\frac{1}{9}\cdot 5\cdot \frac{1}{-2}\cdot 9\cdot 7\cdot 2\).

Beginning with an integer \(n,\) Jake goes through the following steps:

1. Take the reciprocal of the starting number.

2. Double the number obtained in Step \(1\).

3. Take the reciprocal of the number obtained in Step \(2\).

At the end of the third step, Jake ends up with the number \(16.\) What number did Jake start with?
杰克从整数 \(n\) 开始，依次进行下列操作：
1. 求出起始数字的倒数。
2. 将第 1 步得到的数乘以 \(2\)。
3. 求出第 2 步所得数字的倒数。
完成第三步后，杰克得到数字 \(16\)。请问杰克一开始的数字是多少？

Find \(-\left(\frac{1}{-11}\right)(77+1100)\).
计算\(-\left(\frac{1}{-11}\right)(77+1100)\).

Let \(a=\frac{1}{5}\), let \(b=\frac{1}{2}\), let \(c=3\), and let \(d=-\frac{1}{4}\). Calculate \(\frac{1}{a \cdot \frac{1}{c}} + \frac{1}{b \cdot d}\).
假设 \(a=\frac{1}{5}\), \(b=\frac{1}{2}\), \(c=3\), \(d=-\frac{1}{4}\). 计算 \(\frac{1}{a \cdot \frac{1}{c}} + \frac{1}{b \cdot d}\).