Compute.
$\begin{array}{r}
-6.42+(-3.25)= \\
-5.6+27.4=
\end{array}$
We are tasked with performing two basic arithmetic operations involving decimal numbers:
For the first operation, since both numbers are negative, we calculate the sum of their absolute values and then assign a negative sign to the result.
For the second operation, we are adding numbers with different signs. We find the difference between their absolute values and keep the sign of the number with the larger magnitude.
To calculate \(-6.42 + (-3.25)\), we add the magnitudes \(6.42\) and \(3.25\):
\[6.42 + 3.25 = 9.67\]
Since both original numbers were negative, the result is negative:
\[-6.42 + (-3.25) = -9.67\]
To calculate \(-5.6 + 27.4\), we observe that \(27.4\) has a larger magnitude than \(5.6\). We subtract the smaller magnitude from the larger magnitude:
\[27.4 - 5.6 = 21.8\]
Since \(27.4\) is positive and has a larger magnitude, the final result is positive:
\[-5.6 + 27.4 = 21.8\]
Combining our calculations, we have:
\[-6.42 + (-3.25) = -9.67\]
\[-5.6 + 27.4 = 21.8\]
The final results for the given expressions are \(\boxed{-9.67}\) and \(\boxed{21.8}\).
In real life, these operations are common when tracking your bank account balance. If you make two consecutive withdrawals from your account, say \(\$6.42\) and \(\$3.25\), you can represent the change as \(-6.42 + (-3.25) = -9.67\), meaning you have removed \(\$9.67\) in total. If you have a debt of \(\$5.60\) (represented as \(-5.6\)) and you deposit \(\$27.40\), your new balance is \(-5.6 + 27.4 = 21.8\), or \(\$21.80\). Understanding how to combine these positive and negative values is essential for managing personal finances and understanding credit and debit.