Final answer:
To solve the multiplication problem using the standard algorithm, we multiply each digit of the first number by the second number, starting from the rightmost digit. We then add any carried over digits to the next column. The missing digit that Yin should replace y with is 2.
Step-by-step explanation:
To find the missing digit, we need to follow the standard algorithm for multiplication.
First, we multiply the ones digit of 5,819 (which is 9) by 8. This gives us 72. We write down the 2 and carry over the 7 to the tens place.
Next, we multiply the tens digit of 5,819 (which is 1) by 8. We also add the carried over 7. This gives us 15. We write down the 5 and carry over the 1 to the hundreds place.
Continuing this process, we multiply the hundreds digit of 5,819 (which is 8) by 8. We also add the carried over 1. This gives us 65. We write down the 5 and carry over the 6 to the thousands place.
Finally, we multiply the thousands digit of 5,819 (which is 5) by 8. We also add the carried over 6. This gives us 46. We write down the 6 and there are no more digits to multiply, so we write down the 46 next to the 5. The complete multiplication is 46,552.
Therefore, the missing digit that Yin should replace y with is 2.