Question

1 divided by (1/30 + 1/92)

Explanation:

Step1: Find a common denominator for the fractions in the denominator

The denominators are 30 and 92. First, find the least common multiple (LCM) of 30 and 92. Prime factorize 30: \(30 = 2\times3\times5\), prime factorize 92: \(92 = 2^2\times23\). So LCM is \(2^2\times3\times5\times23 = 1380\). Then convert \(\frac{1}{30}\) and \(\frac{1}{92}\) to have denominator 1380: \(\frac{1}{30}=\frac{46}{1380}\), \(\frac{1}{92}=\frac{15}{1380}\).

Step2: Add the fractions in the denominator

\(\frac{46}{1380}+\frac{15}{1380}=\frac{46 + 15}{1380}=\frac{61}{1380}\)

Step3: Divide 1 by the result from Step2

We have \(\frac{1}{\frac{61}{1380}}\), which is equivalent to \(1\times\frac{1380}{61}=\frac{1380}{61}\approx22.62\) (if we want a decimal approximation) or as a fraction \(\frac{1380}{61}\).

Answer:

\(\frac{1380}{61}\) (or approximately \(22.62\))