To solve the expression \(-492.89 - (-871.78)\) using additive inverses, follow these steps:
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Understand the Problem: The expression involves subtracting a negative number. Remember that subtracting a negative is the same as adding a positive.
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Rewrite the Expression: The expression can be rewritten as: \[ -492.89 - (-871.78) = -492.89 + 871.78 \]
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Line Up the Numbers: To add the two numbers, it's helpful to line them up, especially since they have decimal points. \[ \begin{array}{r} -492.89 \
- 871.78 \ \hline \end{array} \]
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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 \(871.78\).
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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: \[ \begin{array}{r} 871.78 \
- 492.89 \ \hline \end{array} \]
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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: \[ \begin{array}{r} 871.78 \
- 492.89 \ \hline 378.89 \ \end{array} \]
- Start from the right:
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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: \[ -492.89 - (-871.78) = 378.89 \]
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