Compute.
$\begin{array}{r}
8.53-14.898= \\
9.37+(-4.63)=
\end{array}$
The objective is to compute the results of two specific arithmetic operations involving decimal numbers: \(8.53 - 14.898\) and \(9.37 + (-4.63)\). For the first operation, we are subtracting a larger number from a smaller number, which will result in a negative value. For the second operation, adding a negative number is equivalent to subtraction, so we subtract \(4.63\) from \(9.37\).
To solve \(8.53 - 14.898\), we first identify that the result will be negative because \(14.898 > 8.53\). We can rewrite the expression as \( -(14.898 - 8.53) \). Aligning the decimal points, we calculate:
\[14.898 - 8.530 = 6.368\]
Applying the negative sign, the result is \(-6.368\).
For the second operation, \(9.37 + (-4.63)\), this is equivalent to the subtraction \(9.37 - 4.63\). Aligning the decimal points:
\[9.37 - 4.63 = 4.74\]
Thus, the result of the second operation is \(4.74\).
The computed results are:
\[8.53 - 14.898 = -6.368\]
\[9.37 + (-4.63) = 4.74\]
The final answers are \(\boxed{-6.368}\) and \(\boxed{4.74}\).
These types of decimal arithmetic operations are common in financial transactions, such as calculating account balances. For instance, if you have a balance of \(\$9.37\) and incur a fee of \(\$4.63\), calculating the new balance requires subtracting the fee: \(\$9.37 - \$4.63 = \$4.74\). Similarly, if you have a budget of \(\$8.53\) and make a purchase of \(\$14.898\) (perhaps due to fractional units), your resulting debt would be \(\$8.53 - \$14.898 = -\$6.368\). Understanding how to handle signs and decimals ensures precision in managing resources.