Problem 44 - Prealgebra

Question

Add or subtract the decimals, as indicated. \(6-(-8.4)\)

Step-by-Step Solution

Answer

The result is 14.4.

Step 1: Understand the Operation

The given operation is to subtract a negative number. Mathematically, subtracting a negative is the same as adding the positive of that number. So, we can rewrite the expression as an addition: \(6 - (-8.4)\) becomes \(6 + 8.4\).

Step 2: Align Decimals for Addition

To add \(6\) and \(8.4\), align the numbers by their decimal places to ensure correct addition. Imagine them stacked vertically: \[\begin{array}{c}6.0 \+8.4 \\hline\end{array}\]

Step 3: Perform the Addition

Start by adding the numbers from the rightmost digit (the tenths place in this case). - Add the tenths: \(0 + 4 = 4\).- Add the units: \(6 + 8 = 14\).Combine these results to find the sum: \(14.4\).

Step 4: Record the Result

The solution to the operation \(6 - (-8.4)\) is \(14.4\). Write this clearly as your final answer.

Key Concepts

Subtracting Negative Numbers

Subtracting a negative number might seem confusing at first, but it's simpler once you remember a key rule in basic arithmetic. When you subtract a negative, you are actually adding the number's positive counterpart.
Think of it like this: If you have a neutral state of zero and you remove negative influence (subtracting a negative), you actually end up adding a positive impact. To put it simply, subtracting a negative is equal to adding its positive equivalent:

• Thus, subtracting \(-(-8.4)\) becomes \(+8.4\).

This transformation helps prevent mistakes and eases the process when tackling many mathematical problems. This basic concept is not only critical for solving arithmetic equations but also essential for understanding algebraic expressions and equations.

Decimal Alignment

Decimal alignment is a significant aspect of adding and subtracting decimals. When dealing with decimals, it's crucial to line them up correctly according to their decimal points.
Imagine this as a way to "line up" the friends, so no one stands on anyone else's toes. By aligning the decimal points, you ensure every number from each column corresponds accurately:

• These columns represent place values, such as units, tenths, hundredths, etc.

When adding decimals like \(6 + 8.4\), don't forget:

• Consider writing \(6\) as \(6.0\)

This makes the decimal places easy to match. Correctly aligning ensures a smooth calculation and helps avoid misplaced numbers which can upset all your efforts.

Basic Arithmetic Operations

Basic arithmetic operations—addition, subtraction, multiplication, and division—form the foundation for all mathematical calculations. Focusing on addition and subtraction of decimals includes remembering a few straightforward principles.
When you are adding decimals like \(6.0 + 8.4\):

• Start by adding the smallest place value. Here, the tenths: \(0 + 4 = 4\).
• Follow with the next place value. Here, adding the units: \(6 + 8 = 14\).

Understanding these basic steps and applying them with care ensures that no errors disrupt your calculations.
Moreover, record your result accurately to reflect the calculation you have done, which in this case is:\[14.4\]Basic arithmetic competence aids in clarifying and solving more complicated mathematical tasks.