To calculate \(-123.45 - (-234.76)\) using the concept of the additive inverse, we can first rewrite the expression:
\[ -123.45 - (-234.76) = -123.45 + 234.76 \]
Now, we simply add \(-123.45\) and \(234.76\):
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Align the numbers: \[ \begin{array}{r} -123.45 \ +234.76 \ \hline \end{array} \]
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Add the numbers:
- When adding, we can separate the addition into two parts (the whole numbers and the decimals):
- First, we deal with the whole number part: \(234 + (-123) = 234 - 123 = 111\)
- Then, for the decimal part: \(0.76 + (-0.45) = 0.76 - 0.45 = 0.31\)
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Thus, adding the whole number and decimal results: \[ 111 + 0.31 = 111.31 \]
Therefore, the final result of \(-123.45 - (-234.76)\) is:
\[ \boxed{111.31} \]