Chapter 5: Problem 44
Add or subtract the decimals, as indicated. \(6-(-8.4)\)
Short Answer
Expert verified
The result is 14.4.
Step by step solution
01
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 \(6 + 8.4\).
02
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: \[\begin{array}{c}6.0 \+8.4 \\hline\end{array}\]
03
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: \(14.4\).
04
Record the Result
The solution to the operation \(6 - (-8.4)\) is \(14.4\). Write this clearly as your final answer.
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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:
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 \(+8.4\).
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:
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.
- Consider writing \(6\) as \(6.0\)
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 \(6.0 + 8.4\):
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.
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: \(6 + 8 = 14\).
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.