\( \left. \begin{array} { | l | l | l | l | l | l | } \hline & { } & { } & { } & { } & { 8 } \\ \hline + & { } & { } & { } & { } & { } \\ \hline 5 & { 5 } & { 8 } & { 0 } & { 9 } & { 3 } \\ \hline \end{array} \right. \)

To solve the problem represented in the table, we need to fill in the missing values in the addition operation. The table shows a vertical addition where the numbers are aligned in columns. The addition can be interpreted as follows: ``` ? ? ? ? 8 + ? ? ? ? ? ----------------- 5 5 8 0 9 3 ``` We can denote the missing values in the first number as \( a, b, c, d \) (from top to bottom) and the missing values in the second number as \( e, f, g, h \) (from top to bottom). The last digit of the sum is 3, which means we need to find values for \( a, b, c, d, e, f, g, h \) that satisfy the addition. Starting from the rightmost column: 1. **Rightmost column (units place)**: \[ 8 + h \equiv 3 \mod 10 \] This means \( h = 3 - 8 = -5 \), which is not valid. Instead, we can think of it as: \[ 8 + h = 13 \quad \text{(carry 1)} \] Thus, \( h = 5 \). 2. **Second column from the right**: \[ 9 + g + 1 \equiv 9 \mod 10 \] This means \( g + 10 = 9 \), so \( g = -1 \), which is not valid. Instead, we can think of it as: \[ 9 + g + 1 = 19 \quad \text{(carry 1)} \] Thus, \( g = 9 \). 3. **Third column from the right**: \[ 0 + f + 1 \equiv 8 \mod 10 \] This means \( f + 1 = 8 \), so \( f = 7 \). 4. **Fourth column from the right**: \[ 5 + e \equiv 5 \mod 10 \] This means \( e = 0 \). Now we have: - \( e = 0 \) - \( f = 7 \) - \( g = 9 \) - \( h = 5 \) Now we can fill in the first number: - The first number is \( a, b, c, d, 8 \). - The second number is \( 0, 7, 9, 5 \). Now we can find \( a, b, c, d \) by working from the leftmost column: 1. **Leftmost column**: \[ a + 0 \equiv 5 \mod 10 \] Thus, \( a = 5 \). 2. **Second column from the left**: \[ b + 7 \equiv 5 \mod 10 \] This means \( b + 7 = 15 \), so \( b = 8 \). 3. **Third column from the left**: \[ c + 9 \equiv 8 \mod 10 \] This means \( c + 9 = 18 \), so \( c = 9 \). 4. **Fourth column from the left**: \[ d + 5 \equiv 0 \mod 10 \] This means \( d + 5 = 10 \), so \( d = 5 \). Now we have: - \( a = 5 \) - \( b = 8 \) - \( c = 9 \) - \( d = 5 \) Thus, the completed addition looks like this: ``` 5 8 9 5 8 + 0 7 9 5 ----------------- 5 5 8 0 9 3 ``` The missing values are: - First number: \( 5, 8, 9, 5, 8 \) - Second number: \( 0, 7, 9, 5 \) So the final answer is: - First number: \( 58958 \) - Second number: \( 0795 \)