Problem 39 - Prealgebra

Question

Add or subtract the decimals, as indicated. \(-7-1.504\)

Step-by-Step Solution

Answer

The result is -8.504.

Step 1: Understand the Operation

The problem requires us to subtract 1.504 from -7. This can be represented as \(-7 - 1.504\).

Step 2: Realize Negative Addition

Subtracting a positive number from a negative number is the same as adding two negative numbers. So, this expression \(-7 - 1.504\) can be re-written as \(-7 + (-1.504)\).

Step 3: Align the Decimals

To add the decimals correctly, align the numbers vertically by their decimal points: \[ \begin{array}{r} -7.000 \ -1.504 \ \hline \end{array} \]Keep in mind the invisible zeroes in the decimal parts to maintain proper alignment.

Step 4: Perform the Addition

Add the numbers considering both are negative, which involves adding as if they were positive, then applying the negative sign: \[ \begin{array}{r} -7.000 \ -1.504 \ \hline -8.504 \end{array} \]This means the result of \(-7 - 1.504\) is \(-8.504\).

Key Concepts

Understanding Negative Numbers

Negative numbers can often be tricky to grasp, especially when it comes to performing operations like addition and subtraction. Negative numbers are numbers less than zero and are represented with a negative sign (−).
- When you subtract a number from a negative number, it is the same as adding its opposite. For example, subtracting a positive number, like 1.504, from -7 can be thought of as adding the negative of 1.504 (which is -1.504) to -7.
- This helps because adding two negative numbers, such as -7 and -1.504, gives us a clear path to find a solution.
In summary, when you encounter problems involving negative numbers, remember that subtracting a number from a negative is the same as adding the negative of that number. This will help you manage calculations smoothly.

Concept of Adding Decimals

Adding decimals requires a similar approach to adding whole numbers, with a few key differences.
- Decimals are numbers with a fractional part separated by a decimal point, like 1.504.
Here's a simple process to add decimals:

• Align the decimals to ensure the digits fall into the correct columns (e.g., tenths under tenths, hundredths under hundredths).
• Add the numbers as you would with integers, starting from the rightmost digit and moving left.
• Don't forget to place the decimal point in the result directly beneath the other decimal points.

Remember, the key is accuracy - misplacing decimal points can drastically change the result.

Importance of Aligning Decimal Points

Aligning decimal points is crucial when adding or subtracting decimals to ensure accurate computation. Without proper alignment, the values might not be added correctly, leading to errors.
- When dealing with decimals, each digit must occupy the right place value, such as tenths, hundredths, etc.
For example: when adding -7.000 and -1.504, align them vertically by their decimal points:
\[\begin{array}{r}-7.000 \-1.504 \\hline-8.504\end{array}\]- Also, it's important to remember any blank spaces can be filled with zeroes to keep alignment accurate.
This practice ensures that the addition or subtraction of decimals is both effective and precise.