Amber's Math Error: Spot The Mistake!

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Hey guys! Let's dive into a tricky math problem today. We're going to analyze a step-by-step evaluation of an expression and pinpoint the exact moment where things went wrong. It's like being a math detective! So, get your thinking caps on, and let's get started!

The Problem

Amber tried to evaluate the following expression:

  -3-(-5)+4 
= -3+5+4 
= -3+9 
= -12

Our mission, should we choose to accept it (and we totally do!), is to find Amber's first mistake. We have two options presented to us:

A) The opposite of -5 is -5, not 5. B) Adding from right to left changes the sum.

Let's break down this problem step-by-step and figure out where Amber went astray.

Analyzing Amber's Steps

To identify Amber's mistake, we need to meticulously examine each step of her calculation. This involves understanding the order of operations and the rules of dealing with negative numbers. Let's go through it slowly, guys, no need to rush!

Step 1: -3 - (-5) + 4 = -3 + 5 + 4

The first step Amber took was to address the subtraction of a negative number. Remember, subtracting a negative number is the same as adding its positive counterpart. So, -(-5) becomes +5. This is a crucial concept in basic arithmetic.

In this initial step, Amber correctly applied the rule of subtracting a negative number. The expression -3 - (-5) + 4 correctly transforms into -3 + 5 + 4. This indicates a solid understanding of the foundational principles at play. To clearly understand, subtracting a negative number is the same as adding the positive of that number. For example, subtracting -5 is the same as adding +5. This is because two negatives cancel each other out.

The transformation from -3 - (-5) + 4 to -3 + 5 + 4 demonstrates a correct application of this principle. There's no error here. The step aligns perfectly with established mathematical rules, showing a clear grasp of how to handle negative numbers in subtraction. This foundational understanding is critical for solving more complex problems down the line.

Step 2: -3 + 5 + 4 = -3 + 9

In this step, Amber added 5 and 4 to get 9. This is a simple addition operation. Let's see if it's correct.

Here, Amber also executed the addition correctly. 5 + 4 indeed equals 9. So, the transformation from -3 + 5 + 4 to -3 + 9 is accurate. This showcases her ability to perform basic arithmetic operations without error. It's like she's building a solid foundation for the rest of the problem! The ability to correctly perform simple addition is crucial in more complex arithmetic. This step is a testament to her basic computational skills.

Step 3: -3 + 9 = -12

This is the final step where Amber combines -3 and 9. This is where we need to be extra careful. Is -3 + 9 really -12?

This is where the mistake lies! -3 + 9 actually equals 6, not -12. Amber seems to have incorrectly subtracted 9 from 3 and kept the negative sign, which is a common error. Understanding the rules for adding integers with different signs is key here.

The correct way to think about this is that you have 9 positive units and 3 negative units. When you combine them, the negative units cancel out 3 of the positive units, leaving you with 6 positive units. Therefore, -3 + 9 = 6.

Identifying the Mistake

So, we've pinpointed the error! Amber's mistake occurred in the last step when she calculated -3 + 9 as -12 instead of 6.

Now, let's revisit the options:

A) The opposite of -5 is -5, not 5. - This is incorrect. Amber correctly identified the opposite of -5 as 5. B) Adding from right to left changes the sum. - This is a true statement in some contexts (like subtraction or division), but it wasn't the error Amber made in this specific problem. The order of operations (addition and subtraction from left to right) was followed correctly until the final calculation.

Therefore, neither of the provided options directly addresses Amber's mistake.

The Correct Solution

Let's quickly solve the problem correctly to reinforce our understanding:

-3-(-5)+4
= -3+5+4
= -3+9
= 6

The correct answer is 6.

Key Takeaways

  • Careful Calculation: Even a small mistake in arithmetic can lead to a wrong answer. Always double-check your work!
  • Rules of Integers: Make sure you understand how to add and subtract positive and negative numbers.
  • Step-by-Step Approach: Breaking down a problem into smaller steps makes it easier to identify errors.

Conclusion

Great job, guys! We successfully identified Amber's mistake and corrected it. Remember, math is all about precision and attention to detail. By carefully analyzing each step, we can avoid common errors and arrive at the correct solution. Keep practicing, and you'll become math detectives in no time! This exercise highlights the importance of understanding basic arithmetic principles and paying close attention to detail when performing calculations. Math can be tricky, but with practice and a methodical approach, we can all conquer it! Stay sharp, and happy calculating!