Find each sum or difference. See Example 1. -12.31 - (-2.13)

Verified step by step guidance

1. Recognize that subtracting a negative number is equivalent to adding its positive counterpart. So, rewrite the expression \(-12.31 - (-2.13)\) as \(-12.31 + 2.13\).
2. Identify the operation now as addition of two numbers with different signs: a negative number \(-12.31\) and a positive number \$2.13$.
3. To add numbers with different signs, subtract the smaller absolute value from the larger absolute value: calculate \$12.31 - 2.13$.
4. Determine the sign of the result by looking at which number has the larger absolute value. Since \$12.31\( is larger than \)2.13\(, the result will have the sign of \)-12.31$, which is negative.
5. Combine the sign and the difference to write the final expression as \(-(12.31 - 2.13)\), which simplifies to the final sum or difference.

Key Concepts

Understanding Addition and Subtraction of Real Numbers

This concept involves knowing how to add and subtract positive and negative numbers. Subtracting a negative number is equivalent to adding its positive counterpart, which changes the operation and affects the result.

Handling Negative Signs in Expressions

Recognizing how to correctly interpret and simplify expressions with multiple negative signs is crucial. For example, subtracting a negative number turns into addition, which simplifies the calculation.

Basic Arithmetic Operations

Performing basic arithmetic operations such as addition and subtraction accurately is essential. This includes aligning decimal points and carefully calculating the result to avoid errors.