Unraveling Kari's Quotient Error In Math: A Detailed Analysis

Hey math enthusiasts! Let's dive into a common math problem and see if we can understand a student's mistake. In this case, we're looking at Kari's attempt to estimate the quotient of $-12 \frac{1}{5} \div 4 \frac{2}{5}$. She estimated the answer to be -8. Our task is to figure out what went wrong. Did she mess up with multiplication? Did she get the signs mixed up? Or something else entirely? Let's break it down.

First off, understanding the question is key. We're not just looking for the correct answer; we want to pinpoint the error Kari made. This kind of problem is super helpful because it forces us to think critically about the concepts behind the numbers, not just the calculations. It also shows us how important it is to be careful with negative numbers and fractions! So, let's explore the possible answers and see which one fits best. And the main question we are asking is: What exactly did Kari do wrong?

Diving into the Options

We have three choices to consider:

A. Kari multiplied the compatible numbers -12 and 4.

B. Kari found that the quotient of a negative number and a positive number is negative.

C. Kari made an error in calculating the correct quotient.

Let's analyze each one, shall we?

A. Kari Multiplied the Compatible Numbers -12 and 4

This option suggests Kari accidentally did multiplication instead of division. That is a pretty common mistake, so let's check it out! In this scenario, she would have taken the whole numbers from each mixed fraction (-12 and 4) and multiplied them. However, since the question deals with division, this is very unlikely. If she multiplied these numbers, the answer would not be -8, which she has stated to have obtained. If the question was asking for the product of $-12 \frac{1}{5}$ and $4 \frac{2}{5}$, the answer would not even be -8, since you have to include the fractional parts. Thus, we can conclude that option A is the incorrect choice and the least probable one. Therefore, we can cross this off the list!

B. Kari Found That the Quotient of a Negative Number and a Positive Number Is Negative.

Okay, so this option focuses on the rules of signs in division. The rule is indeed correct: dividing a negative number by a positive number (or vice versa) results in a negative quotient. For example, dividing -10 by 2 gives -5. However, did Kari actually demonstrate an understanding of this rule? Well, since Kari's final answer was -8, this statement might be correct, since the sign is also negative. The only question now, is whether the magnitude of the number is correct. Let's find out by doing the actual calculation!

We need to convert the mixed numbers to improper fractions first. So, $-12 \frac{1}{5}$ becomes $-\frac{61}{5}$, and $4 \frac{2}{5}$ becomes $\frac{22}{5}$. Now we can perform the division: $-\frac{61}{5} \div \frac{22}{5}$. Remember, dividing by a fraction is the same as multiplying by its reciprocal. So, this problem becomes: $-\frac{61}{5} \times \frac{5}{22}$. We can simplify this by canceling out the 5s, leaving us with: $-\frac{61}{22}$. Now, let's convert this improper fraction to a mixed number. We can divide 61 by 22, which goes twice (2 x 22 = 44). That leaves a remainder of 17. Thus, the real answer is $-2 \frac{17}{22}$. Now you can clearly see that Kari was incorrect in her calculations, since the answer is not -8. So, Kari does not have a good idea of how to do the math. Thus, B is not the correct answer either, since we're looking for the cause of Kari's error.

C. Kari made an error in calculating the correct quotient.

This appears to be the most accurate explanation. Option C accurately identifies that Kari made a mistake when calculating the quotient, without making assumptions about the specific type of error. The correct approach to the problem would have involved converting the mixed numbers into improper fractions and then performing the division. If she did something else, we will never know without more context. Since we already know the answer is not -8, it is safe to say that she made an error. So, C is the answer!

Conclusion

So, after looking at the options, we can confidently say that C. Kari made an error in calculating the correct quotient best describes Kari's mistake. While she might have had an idea that the answer was negative, she had a problem understanding how to work the math. This also shows us how it's super important to be careful and double-check our steps, especially when dealing with fractions and signs.

Remember, math is all about understanding the processes. Keep practicing, and you'll get the hang of it! Keep asking questions and learning. And when you make mistakes, that is okay! This is how we learn to improve.

Key Takeaways:

• Always check your work carefully.
• Understand the rules of signs in division.
• Practice converting between mixed numbers and improper fractions.

I hope this explanation helped you understand the problem better! Keep up the great work in the world of math, you guys!