Evaluate each expression.
$\begin{array}{r}
-2.52 \div 4= \\
-366.3-(-1000)=
\end{array}$
The problem requires evaluating two distinct numerical expressions involving signed numbers and basic arithmetic operations. The first expression is a division of a negative decimal by a positive integer, \(-2.52 \div 4\). The second expression is a subtraction of a negative value from another negative value, \(-366.3 - (-1000)\). We will solve these step-by-step using standard arithmetic rules.
To evaluate \(-2.52 \div 4\), we first ignore the signs and perform the division: \(2.52 \div 4 = 0.63\). According to the rules of signs, a negative number divided by a positive number results in a negative quotient. Therefore, \(-2.52 \div 4 = -0.63\).
To evaluate \(-366.3 - (-1000)\), we use the property of subtraction for negative numbers, which states that subtracting a negative is equivalent to adding a positive: \(-a - (-b) = -a + b\). Thus, the expression becomes \(-366.3 + 1000\). This is equivalent to calculating \(1000 - 366.3\). Subtracting 366.3 from 1000 gives \(633.7\). Therefore, \(-366.3 - (-1000) = 633.7\).
Combining the calculations, we have determined that:
\[-2.52 \div 4 = -0.63\]
\[-366.3 - (-1000) = 633.7\]
The final answers are \(\boxed{-0.63}\) and \(\boxed{633.7}\).
Imagine you are managing a small budget. If you have an outstanding debt of \(\$2.52\) that you split evenly into 4 payments, each payment would represent a reduction of \(\$0.63\) from your total (hence the \(-0.63\)). Conversely, if you have a balance of \(- \366.30\) and you receive a credit or refund of \(\$1000\), your new balance is calculated as \(-366.3 + 1000\), leaving you with a positive balance of \(\$633.70\). Mastering these operations is essential for tracking personal finances and understanding how debt and credit interact.