Sometimes the last digits of numbers can help you decide whether calculator computations are correct. Given that one of 19,\( 379 ; 19,387 \); and 19,383 is the correct result of multiplying 213 by 91 , which answer is correct? Tell how a consideration of last digits helped you answer part (a). Choose the correct answer below. Use the Show Work feature to provide related calculations and additional reasoning to support your answer. A. 19,379 B. 19,387 C. 19,383

To determine which of the numbers \(19,379\), \(19,387\), or \(19,383\) is the correct result of multiplying \(213\) by \(91\), we can first calculate the product and then analyze the last digits of the potential answers. ### Step 1: Calculate the product of \(213\) and \(91\) Let's perform the multiplication: \[ P = 213 \times 91 \] ### Step 2: Analyze the last digits Next, we will find the last digit of \(P\) and compare it with the last digits of the given options. 1. **Last digit of \(213\)**: The last digit is \(3\). 2. **Last digit of \(91\)**: The last digit is \(1\). Now, we can find the last digit of the product \(P\) by multiplying the last digits of \(213\) and \(91\): \[ \text{Last digit of } P = 3 \times 1 = 3 \] ### Step 3: Check the last digits of the options Now, let's check the last digits of the options: - **Last digit of \(19,379\)**: \(9\) - **Last digit of \(19,387\)**: \(7\) - **Last digit of \(19,383\)**: \(3\) ### Conclusion Since the last digit of the product \(P\) is \(3\), the only option that matches this last digit is \(19,383\). Thus, the correct answer is: **C. 19,383** ### Reasoning The consideration of last digits helped us quickly eliminate \(19,379\) and \(19,387\) as possible correct answers because their last digits do not match the last digit of the product \(P\). This method is a useful check for verifying calculations without performing the full multiplication.