Problem 20 - Elementary Algebra

Question

Perform the indicated operations. $$18.3-(-7.4)$$

Step-by-Step Solution

Answer

18.3 - (-7.4) = 25.7

Step 1: Understand the Operation

The expression given is \(18.3 - (-7.4)\). Notice that subtracting a negative number is equivalent to adding its positive counterpart.

Step 2: Convert Subtraction to Addition

Since \(-(-7.4)\) is the same as adding \(7.4\), we can rewrite the expression as \(18.3 + 7.4\).

Step 3: Perform the Addition

Add the numbers: \(18.3 + 7.4\). Start by adding the whole numbers: 18 + 7 = 25, and then the decimal parts: 0.3 + 0.4 = 0.7, resulting in \(25 + 0.7 = 25.7\).

Key Concepts

Negative Numbers

Understanding negative numbers is crucial in math. Think of negative numbers as temperatures below zero, or money you owe, called a debt. They are numbers less than zero and are typically written with a minus sign (-) before them, like -7.4.

Negative numbers are part of the number line and are located to the left of zero. When you subtract a negative number, it’s different from subtracting a positive one. It's actually similar to adding. For example, subtracting -7.4 from 18.3 means seeing it as adding the positive 7.4 instead. This concept often leads to confusion, but remembering that subtracting a negative results in a positive can help simplify calculations.

Key points about negative numbers:

• They signify values below zero.
• Subtracting a negative number is the same as adding its positive.
• Visualize them as debts or locations on the left of zero on the number line.

Converting Subtraction to Addition

When dealing with subtraction especially involving negative numbers, it is often helpful to convert the operation into addition. This simplifies the process and reduces errors.

The original problem appears as a subtraction: \(18.3 - (-7.4)\). However, two negative signs in this case can be transformed into a plus. This is due to the rule that subtracting a negative is equivalent to adding its positive.

Here is how it works practically:

• Start with the original expression: \(18.3 - (-7.4)\).
• Recognize the double negative: two "minuses" become a plus here.
• Turn it into an addition problem: \(18.3 + 7.4\).

This adjustment transforms the problem, making it straightforward to handle using standard addition techniques.

Decimal Arithmetic

Decimal arithmetic involves dealing with numbers that have a decimal point, indicating parts of a whole. It's a fundamental skill similar to whole number operations but requires careful alignment of decimal points.

In the given problem \(18.3 + 7.4\), it is essential to align the numbers by their decimal places:

• Add the whole numbers first: \(18 + 7 = 25\).
• Then add the decimal parts: \(0.3 + 0.4 = 0.7\).
• Combine them: \(25 + 0.7 = 25.7\).

Always ensure decimal points are aligned vertically to avoid mistakes. Decimal arithmetic can seem intimidating at first, but with practice, it becomes routine, just like simple addition or subtraction of whole numbers.

Key aspects of decimal arithmetic include:

• Align numbers with their decimal points before performing operations.
• Separate the whole number addition from the decimal parts.
• Combine results for the final answer.