Question

Use the additive inverse to find −492.89 − (−871.78). step by step please

Answer 1

is the answer negative or positive?

Answer 2

To solve the expression \(-492.89 - (-871.78)\) using additive inverses, follow these steps:

1. **Understand the Problem**: The expression involves subtracting a negative number. Remember that subtracting a negative is the same as adding a positive.

2. **Rewrite the Expression**: The expression can be rewritten as:
\[
-492.89 - (-871.78) = -492.89 + 871.78
\]

3. **Line Up the Numbers**: To add the two numbers, it's helpful to line them up, especially since they have decimal points.
\[
\begin{array}{r}
-492.89 \\
+ 871.78 \\
\hline
\end{array}
\]

4. **Add the Numbers**: Since one number is negative and the other is positive, we can treat this as finding the difference between the two absolute values:
- The absolute value of \(-492.89\) is \(492.89\).
- The absolute value of \(871.78\) is \(871.78\).

5. **Find the Difference**: Subtract the absolute value of the negative number from the absolute value of the positive number:
\[
871.78 - 492.89
\]

To do this, line them up again:
\[
\begin{array}{r}
871.78 \\
- 492.89 \\
\hline
\end{array}
\]

6. **Performing the Subtraction**:
- Start from the right:
- \(8 - 9\) (need to borrow) → becomes \(18 - 9 = 9\)
- Now looking at \(7 - 8\) (again need to borrow) → \(6 - 8\) (after borrowing) converts to \(16 - 8 = 8\)
- Then \(7 - 9\) (after borrowing) converts to \(7 - 0 = 7\)
- And finally, \(8 - 4 = 4\)

Now placing that together:
\[
\begin{array}{r}
871.78 \\
- 492.89 \\
\hline
378.89 \\
\end{array}
\]

7. **Determine the Sign of the Result**: Since \(871.78\) is greater than \(492.89\), the result will be positive:
\[
378.89
\]

Thus, we have the final answer:
\[
-492.89 - (-871.78) = 378.89
\]

Answer 3

The answer to the expression \(-492.89 - (-871.78)\) is positive.

To summarize the calculation:

1. We transformed the expression to \(-492.89 + 871.78\).
2. We found that adding \(871.78\) to \(-492.89\) gives us:
\[
871.78 - 492.89 = 378.89
\]
3. Since \(871.78\) is greater than \(492.89\), the result \(378.89\) is positive.

So, the final answer is \(\mathbf{378.89}\), and it is **positive**.