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Chapter 5: Problem 7

For Exercises \(6-8,\) add or subtract as indicated. $$-33.072-(-41.03)$$

Short Answer

Expert verified
-33.072 - (-41.03) = 7.958

Step by step solution

01

Understand the Problem

We need to subtract $$-33.072 - (-41.03)$$
02

Rewrite the Expression

Notice that subtracting a negative number is the same as adding its positive counterpart. Rewrite the expression: $$-33.072 + 41.03$$
03

Perform the Addition

Add the numbers $$41.03 - 33.072.$$ Perform the operation by aligning the decimal points: \[ 41.030 -33.072 ------ 7.958 \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Integer Operations
Integer operations involve basic arithmetic operations such as addition, subtraction, multiplication, and division applied to whole numbers and their negatives. Understanding how to handle negative signs is crucial in these operations. In the given exercise, we need to subtract \(-33.072\) from \(-41.03\). Since both numbers are negative, the key principle is realizing that subtracting a negative number is the same as adding its positive counterpart. This means \(-33.072 - (-41.03)\) becomes \(-33.072 + 41.03\). Remember:
  • Subtraction of a negative number turns into addition.
  • Always pay attention to the signs to avoid mistakes.
Adding and Subtracting Decimals
When adding or subtracting decimals, aligning the decimal points is the first and most important step. This ensures that each digit is in the correct place value column, which is crucial for accurate calculation. Here鈥檚 how to handle the operation \(-33.072 + 41.03\):
  • Rewrite the problem ensuring the decimals are aligned as follows:
    \[ \begin{array}{r} 41.030 \ -33.072 \ \end{array} \]
  • Adding zeros where necessary can help align the numbers correctly.
  • Perform the addition column by column, starting from the right.
The solution yields: \[ 41.030 - 33.072 = 7.958 \]. Remember to keep the decimal points aligned throughout the process.
Solving Algebraic Expressions
Solving algebraic expressions typically involves combining like terms and applying basic arithmetic principles. In our example, the expression is relatively straightforward but requires careful handling of negative signs and decimal numbers. Here鈥檚 the step-by-step approach:
  • First, rewrite the expression taking into account the rule that subtracting a negative is equivalent to addition, turning \(-33.072 - (-41.03)\) into \(-33.072 + 41.03\).
  • Next, solve the simpler expression by aligning the decimal points.
  • Finally, perform the operation to get the result.
Always make sure to double-check your work, particularly when dealing with negatives and decimals, as small mistakes in alignment can lead to incorrect answers.

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