Simplify This Expression: 19 − ( − 8 ) − ( − 14 ) = ? 19 - (-8) - (-14) = ? 19 − ( − 8 ) − ( − 14 ) = ? A) -3 B) 25 C) 41 D) -7

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Understanding the Expression

When dealing with expressions that involve negative numbers, it's essential to understand the concept of absolute value and how it affects the overall result. In this case, we have an expression that involves subtracting two negative numbers from a positive number. To simplify this expression, we need to apply the rules of arithmetic operations, specifically the rule for subtracting negative numbers.

The Rule for Subtracting Negative Numbers

When we subtract a negative number, it's equivalent to adding the absolute value of that number. In other words, subtracting a negative number is the same as adding its positive counterpart. This rule can be applied to the given expression to simplify it.

Applying the Rule to the Expression

Let's apply the rule for subtracting negative numbers to the given expression:

$19 - (-8) - (-14)$

Using the rule, we can rewrite the expression as:

$19 + 8 + 14$

Simplifying the Expression

Now that we have rewritten the expression, we can simplify it by adding the numbers together:

$19 + 8 + 14 = 41$

Conclusion

Therefore, the simplified expression is $41$. This is the correct answer to the given problem.

Why is this the Correct Answer?

To understand why this is the correct answer, let's consider what happens when we subtract a negative number. When we subtract a negative number, we are essentially adding its positive counterpart. In this case, subtracting $-8$ is equivalent to adding $8$, and subtracting $-14$ is equivalent to adding $14$. Therefore, the expression $19 - (-8) - (-14)$ is equivalent to $19 + 8 + 14$, which simplifies to $41$.

Common Mistakes to Avoid

When dealing with expressions that involve negative numbers, it's essential to avoid common mistakes. One common mistake is to confuse subtracting a negative number with adding a negative number. Remember that subtracting a negative number is equivalent to adding its positive counterpart.

Real-World Applications

Understanding how to simplify expressions that involve negative numbers has real-world applications in various fields, including finance, science, and engineering. For example, in finance, understanding how to simplify expressions that involve negative numbers can help you make informed decisions about investments and financial transactions.

Practice Problems

To practice simplifying expressions that involve negative numbers, try the following problems:

• $5 - (-3) - (-2) = ?$
• $2 - (-4) - (-6) = ?$
• $1 - (-2) - (-5) = ?$

Solutions to Practice Problems

• $5 - (-3) - (-2) = 5 + 3 + 2 = 10$
• $2 - (-4) - (-6) = 2 + 4 + 6 = 12$
• $1 - (-2) - (-5) = 1 + 2 + 5 = 8$

Conclusion

In conclusion, simplifying expressions that involve negative numbers requires understanding the rule for subtracting negative numbers and applying it correctly. By following this rule and simplifying the expression step by step, we can arrive at the correct answer. Remember to avoid common mistakes and practice simplifying expressions to become proficient in this skill.

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Understanding the Expression

When dealing with expressions that involve negative numbers, it's essential to understand the concept of absolute value and how it affects the overall result. In this case, we have an expression that involves subtracting two negative numbers from a positive number. To simplify this expression, we need to apply the rules of arithmetic operations, specifically the rule for subtracting negative numbers.

Q&A

Q: What is the rule for subtracting negative numbers?

A: When we subtract a negative number, it's equivalent to adding the absolute value of that number. In other words, subtracting a negative number is the same as adding its positive counterpart.

Q: How do I apply the rule to the given expression?

A: To apply the rule, we can rewrite the expression as $19 + 8 + 14$.

Q: Why is this the correct answer?

A: This is the correct answer because subtracting $-8$ is equivalent to adding $8$, and subtracting $-14$ is equivalent to adding $14$. Therefore, the expression $19 - (-8) - (-14)$ is equivalent to $19 + 8 + 14$, which simplifies to $41$.

Q: What are some common mistakes to avoid when dealing with expressions that involve negative numbers?

A: One common mistake is to confuse subtracting a negative number with adding a negative number. Remember that subtracting a negative number is equivalent to adding its positive counterpart.

Q: How does understanding how to simplify expressions that involve negative numbers have real-world applications?

A: Understanding how to simplify expressions that involve negative numbers has real-world applications in various fields, including finance, science, and engineering. For example, in finance, understanding how to simplify expressions that involve negative numbers can help you make informed decisions about investments and financial transactions.

Q: Can you provide some practice problems to help me become proficient in simplifying expressions that involve negative numbers?

A: Here are some practice problems:

• $5 - (-3) - (-2) = ?$
• $2 - (-4) - (-6) = ?$
• $1 - (-2) - (-5) = ?$

Q: What are the solutions to the practice problems?

A: Here are the solutions to the practice problems:

• $5 - (-3) - (-2) = 5 + 3 + 2 = 10$
• $2 - (-4) - (-6) = 2 + 4 + 6 = 12$
• $1 - (-2) - (-5) = 1 + 2 + 5 = 8$

Conclusion

In conclusion, simplifying expressions that involve negative numbers requires understanding the rule for subtracting negative numbers and applying it correctly. By following this rule and simplifying the expression step by step, we can arrive at the correct answer. Remember to avoid common mistakes and practice simplifying expressions to become proficient in this skill.

Additional Resources

• For more practice problems and exercises, visit Mathway.
• For a comprehensive guide to arithmetic operations, visit Khan Academy.
• For real-world applications of arithmetic operations, visit Investopedia.

Final Thoughts

Simplifying expressions that involve negative numbers is an essential skill in mathematics. By understanding the rule for subtracting negative numbers and applying it correctly, we can arrive at the correct answer. Remember to practice regularly and seek help when needed to become proficient in this skill.