Complete the pattern: \[ \begin{array}{l} 184.38 \div \square \\ 1,843.8 \div \square=1.8438 \\ 18,438 \div \square \\ 184,380 \div \square=18.438 \\ =1,843.38\end{array} \]

To complete the pattern, let's analyze the given equations step by step. 1. The first equation is: \[ 184.38 \div \square \] We need to find the value of \(\square\) that will allow us to establish a pattern. 2. The second equation is: \[ 1,843.8 \div \square = 1.8438 \] To find \(\square\), we can rearrange this equation: \[ \square = \frac{1,843.8}{1.8438} \] 3. Let's calculate \(\square\) using the above equation: \[ \square = \frac{1,843.8}{1.8438} \] 4. The third equation is: \[ 18,438 \div \square \] We will use the same \(\square\) value we found earlier. 5. The fourth equation is: \[ 184,380 \div \square = 18.438 \] Rearranging gives us: \[ \square = \frac{184,380}{18.438} \] Now, let's calculate the values of \(\square\) from both equations to see if they are consistent. I'll perform the calculations for both equations. Calculate the value by following steps: - step0: Calculate: \(\frac{1843.8}{1.8438}\) - step1: Convert the expressions: \(\frac{\frac{9219}{5}}{\frac{9219}{5000}}\) - step2: Multiply by the reciprocal: \(\frac{9219}{5}\times \frac{5000}{9219}\) - step3: Reduce the numbers: \(1\times 1000\) - step4: Simplify: \(1000\) Calculate or simplify the expression \( 184380/18.438 \). Calculate the value by following steps: - step0: Calculate: \(\frac{184380}{18.438}\) - step1: Convert the expressions: \(\frac{184380}{\frac{9219}{500}}\) - step2: Multiply by the reciprocal: \(184380\times \frac{500}{9219}\) - step3: Reduce the numbers: \(20\times 500\) - step4: Multiply the numbers: \(10000\) The calculations yield the following results for \(\square\): 1. From the second equation: \[ \square = \frac{1,843.8}{1.8438} = 1000 \] 2. From the fourth equation: \[ \square = \frac{184,380}{18.438} = 10000 \] Now, we can summarize the pattern: - The first equation \(184.38 \div \square\) should use \(\square = 1000\). - The second equation \(1,843.8 \div \square = 1.8438\) uses \(\square = 1000\). - The third equation \(18,438 \div \square\) should use \(\square = 10000\). - The fourth equation \(184,380 \div \square = 18.438\) uses \(\square = 10000\). Thus, the completed pattern is: \[ \begin{array}{l} 184.38 \div 1000 \\ 1,843.8 \div 1000 = 1.8438 \\ 18,438 \div 10000 \\ 184,380 \div 10000 = 18.438 \\ = 1,843.38 \end{array} \] The values of \(\square\) are \(1000\) and \(10000\) for the respective divisions.