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\begin{tabular}{|c|c|c|c|}
\hline
[tex]$a$[/tex] & [tex]$b$[/tex] & [tex]$a+b$[/tex] & [tex]$a+(-b)$[/tex] \\
\hline
-5 & -16 & [tex]$-5 + (-16)$[/tex] & [tex]$-5 - (-16)$[/tex] \\
\hline
6 & -18 & [tex]$6 + (-18)$[/tex] & [tex]$6 - (-18)$[/tex] \\
\hline
-12 & 24 & [tex]$-12 + 24$[/tex] & [tex]$-12 - 24$[/tex] \\
\hline
18 & 31 & [tex]$18 + 31$[/tex] & [tex]$18 - 31$[/tex] \\
\hline
-25 & -17 & [tex]$-25 + (-17)$[/tex] & [tex]$-25 - (-17)$[/tex] \\
\hline
31 & -41 & [tex]$31 + (-41)$[/tex] & [tex]$31 - (-41)$[/tex] \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's complete the table by calculating the sums (\(a + b\)) and the differences (\(a - b\)).

Here is the step-by-step breakdown for each pair of \(a\) and \(b\):

1. Pair (-5, -16):
- Sum (\(a + b\)):
[tex]\[ -5 + (-16) = -21 \][/tex]
- Difference (\(a - b\)):
[tex]\[ -5 - (-16) = -5 + 16 = 11 \][/tex]

2. Pair (6, -18):
- Sum (\(a + b\)):
[tex]\[ 6 + (-18) = -12 \][/tex]
- Difference (\(a - b\)):
[tex]\[ 6 - (-18) = 6 + 18 = 24 \][/tex]

3. Pair (-12, 24):
- Sum (\(a + b\)):
[tex]\[ -12 + 24 = 12 \][/tex]
- Difference (\(a - b\)):
[tex]\[ -12 - 24 = -36 \][/tex]

4. Pair (18, 31):
- Sum (\(a + b\)):
[tex]\[ 18 + 31 = 49 \][/tex]
- Difference (\(a - b\)):
[tex]\[ 18 - 31 = -13 \][/tex]

5. Pair (-25, -17):
- Sum (\(a + b\)):
[tex]\[ -25 + (-17) = -42 \][/tex]
- Difference (\(a - b\)):
[tex]\[ -25 - (-17) = -25 + 17 = -8 \][/tex]

6. Pair (31, -41):
- Sum (\(a + b\)):
[tex]\[ 31 + (-41) = -10 \][/tex]
- Difference (\(a - b\)):
[tex]\[ 31 - (-41) = 31 + 41 = 72 \][/tex]

Now, we can fill in the table with the calculated values:

[tex]\[ \begin{tabular}{|c|c|c|c|} \hline [tex]$a$[/tex] & [tex]$b$[/tex] & [tex]$a + b$[/tex] & [tex]$a - b$[/tex] \\
\hline
-5 & -16 & -21 & 11 \\
\hline
6 & -18 & -12 & 24 \\
\hline
-12 & 24 & 12 & -36 \\
\hline
18 & 31 & 49 & -13 \\
\hline
-25 & -17 & -42 & -8 \\
\hline
31 & -41 & -10 & 72 \\
\hline
\end{tabular}
\][/tex]

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