Pregunta
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Fred tried to evaluate an expression step by step. \[ \begin{aligned} & (-10+6)-5 \\ = & -4-5 \\ =-4+(-5) & \text { Step 1 } \\ = & \text { Step 2 } \\ = & \text { Step 3 } \end{aligned} \] Find Fred's first mistake. Choose 1 answer: (A) -10 plus 6 equals -16 not -4 .

Ask by Bernard Fleming. in the United States
Feb 03,2025

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Fred did not make a mistake in the first step. The correct calculation is \(-10 + 6 = -4\).

Solución

Fred's first mistake is incorrectly stated in option (A). Let's break down the steps to identify the error: 1. **Original Expression:** \[ (-10 + 6) - 5 \] 2. **First Calculation:** \[ -10 + 6 = -4 \] So, the expression becomes: \[ -4 - 5 \] 3. **Second Calculation:** \[ -4 - 5 = -9 \] 4. **Rewriting as Addition:** \[ -4 + (-5) = -9 \] **Option (A) states:** > -10 plus 6 equals -16 not -4. This is incorrect because: \[ -10 + 6 = -4 \] not -16. Therefore, Fred did **not** make a mistake in the first step; in fact, the first step was correct. Option (A) incorrectly claims there was an error where there was none. **Correct Identification:** Fred did not make a mistake in the first step. The first step where \(-10 + 6 = -4\) is correct. **Answer:** **(A) -10 plus 6 equals -16 not -4 .**

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Bonus Knowledge

Oops! Fred's mistake isn't with the addition of -10 and 6; he correctly calculated that -10 + 6 equals -4. It looks like Fred's first error actually occurred later when subtracting 5 from -4. Instead of correctly calculating -4 - 5, which equals -9, he might have been confused about how to approach the operation. To clarify things a bit, Fred primarily needs to remember that subtracting a positive number is the same as adding a negative. So, -4 - 5 can also be seen as -4 + (-5)!

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