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Chapter 3: Problem 209

Explain why the difference of 9 and \(-6\) is 15

Short Answer

Expert verified
The difference of 9 and -6 is 15 because subtracting a negative number is the same as adding its positive.

Step by step solution

01

Understand the Problem

The problem asks for the difference between the numbers 9 and -6.
02

Identify the Operation

To find the difference of two numbers, you perform a subtraction operation: 9 - (-6).
03

Apply the Rule for Subtracting Negative Numbers

When you subtract a negative number, it is the same as adding its positive equivalent. Therefore, 9 - (-6) becomes 9 + 6.
04

Perform the Addition

Add the two numbers: 9 + 6 = 15.
05

Conclusion

The difference between 9 and -6 is 15.

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Key Concepts

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

Difference of Numbers
The term 'difference' in mathematics refers to the result of subtracting one number from another. In simpler terms, it answers the question, 'How much more or less is one number compared to another?' The difference is always found through subtraction, which we'll explore further. While subtracting numbers may seem straightforward, it's vital to ensure you're applying the correct rules, especially when negative numbers are involved.
Subtraction
Subtraction is one of the fundamental arithmetic operations. It involves taking one number away from another. For instance, in the original problem, you're asked to find the difference between 9 and (-6), written as 9 - (-6). Initially, subtraction can look intimidating with negative numbers, but remember these key points:
  • Subtraction can be visualized on a number line, moving to the left for normal subtractions.
  • Subtracting a negative number means moving to the right on the number line.
  • This is because subtracting a negative number turns into an addition.
Following these rules helps to simplify what appears at first as a complex problem.
Addition
When you're asked to subtract a negative number, it鈥檚 helpful to translate it into an addition problem. This makes the calculation much simpler. In our example, converting 9 - (-6) to 9 + 6 allows for straightforward addition. Here鈥檚 why:
  • Two negatives make a positive. When you subtract a negative, you add the positive equivalent.
  • Mathematically speaking, (9 - (-6)) can be rephrased as (9 + 6) because the two negative signs cancel each other out.
Addition then gives you the result of 15. By breaking down complex tasks into simpler addition, you ensure accuracy and ease in solving the problem.

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