Yin starts to use the standard algorithm to solve \( 5,819 \times 8 \). Her work i shown below. \begin{tabular}{l}\( y 7 \) \\ 5,819 \\ \( \times \quad 8 \) \\ \hline \( \begin{array}{l}52\end{array} \) \\ What number should Yin replace \( y \) with? \end{tabular} ?

To find the value of \( y \) in the multiplication \( 5,819 \times 8 \), we can perform the multiplication step by step. 1. **Multiply the last digit of 5,819 by 8**: - \( 9 \times 8 = 72 \) - Write down 2 and carry over 7. 2. **Multiply the next digit (1) by 8 and add the carry (7)**: - \( 1 \times 8 = 8 \) - Adding the carry: \( 8 + 7 = 15 \) - Write down 5 and carry over 1. 3. **Multiply the next digit (8) by 8 and add the carry (1)**: - \( 8 \times 8 = 64 \) - Adding the carry: \( 64 + 1 = 65 \) - Write down 5 and carry over 6. 4. **Multiply the next digit (5) by 8 and add the carry (6)**: - \( 5 \times 8 = 40 \) - Adding the carry: \( 40 + 6 = 46 \) - Write down 46. Now, let's summarize the results from the multiplication: - From the last digit: 2 - From the second digit: 5 - From the third digit: 5 - From the fourth digit: 46 Putting it all together, we have: \[ \begin{array}{r} 4 \\ 5 \\ 5 \\ 2 \\ \end{array} \] Thus, the complete multiplication gives us \( 46,552 \). Now, we can see that \( y \) corresponds to the second digit from the right, which is 5. Therefore, Yin should replace \( y \) with \( 5 \).