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

Oct 13, 2025 by talynt.org 29 views

Introduction

Estimating quotients is an essential skill in mathematics, particularly when dealing with fractions and decimals. However, errors can occur when performing these calculations. In this article, we will explore Kari's error in estimating the quotient of ${-12 \frac{1}{5} \div 4 \frac{2}{5}}$ and identify the correct description of her mistake.

The Given Problem

Kari estimated the quotient of ${-12 \frac{1}{5} \div 4 \frac{2}{5}}$ to be -8. To understand her error, let's first convert the mixed numbers to improper fractions.

${-12 \frac{1}{5} = \frac{-61}{5}}$ ${4 \frac{2}{5} = \frac{22}{5}}$

Now, we can rewrite the division problem as a multiplication problem by inverting the second fraction and changing the division sign to multiplication.

${\frac{-61}{5} \div \frac{22}{5} = \frac{-61}{5} \times \frac{5}{22}}$

Kari's Error

To identify Kari's error, let's analyze her estimated quotient of -8. We can rewrite this as a fraction with a denominator of 1.

${-8 = \frac{-8}{1}}$

Now, let's multiply the two fractions.

${\frac{-61}{5} \times \frac{5}{22} = \frac{-61 \times 5}{5 \times 22} = \frac{-305}{110}}$

We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5.

${\frac{-305}{110} = \frac{-61}{22}}$

Comparing Kari's Estimate with the Correct Answer

Kari's estimated quotient of -8 is not equal to the correct answer of ${\frac{-61}{22}}$ . To understand her error, let's compare the two values.

${-8 = \frac{-8}{1}}$ ${\frac{-61}{22} = \frac{-61}{22}}$

We can see that Kari's estimated quotient of -8 is not equal to the correct answer. However, we can rewrite -8 as a fraction with a denominator of 22.

${-8 = \frac{-8 \times 22}{22} = \frac{-176}{22}}$

Now, we can compare Kari's estimated quotient with the correct answer.

${\frac{-61}{22} \neq \frac{-176}{22}}$

Conclusion

Kari's error in estimating the quotient of ${-12 \frac{1}{5} \div 4 \frac{2}{5}}$ to be -8 can be described as follows:

Kari multiplied the compatible numbers -12 and 4: This is not the correct description of Kari's error. While Kari did multiply the two numbers, her error was not in multiplying the compatible numbers.
Kari found that the quotient of a negative number and a positive number is: This is the correct description of Kari's error. Kari's estimated quotient of -8 is equivalent to ${\frac{-176}{22}}$ , which is the quotient of a negative number (-12) and a positive number (4).

$In conclusion, Kari's error in estimating the quotient of ${-12 \frac{1}{5} \div 4 \frac{2}{5}}$ to be -8 was in finding that the quotient of a negative number and a positive number is equivalent to the quotient of two negative numbers.<br/> **Frequently Asked Questions (FAQs) about Kari's Error**$

Q: What is the correct quotient of ${-12 \frac{1}{5} \div 4 \frac{2}{5}}$ ?

A: The correct quotient of ${-12 \frac{1}{5} \div 4 \frac{2}{5}}$ is ${\frac{-61}{22}}$ .

Q: Why did Kari estimate the quotient to be -8?

A: Kari estimated the quotient to be -8 because she may have incorrectly assumed that the quotient of a negative number and a positive number is equivalent to the quotient of two negative numbers.

Q: What is the difference between Kari's estimated quotient and the correct answer?

A: The difference between Kari's estimated quotient of -8 and the correct answer of ${\frac{-61}{22}}$ is that Kari's estimated quotient is equivalent to ${\frac{-176}{22}}$ , which is a different value.

Q: How can we simplify the fraction ${\frac{-61}{22}}$ ?

A: We can simplify the fraction ${\frac{-61}{22}}$ by dividing both the numerator and denominator by their greatest common divisor, which is 1. However, we can also simplify it by dividing both the numerator and denominator by 1.

Q: What is the greatest common divisor (GCD) of -61 and 22?

A: The greatest common divisor (GCD) of -61 and 22 is 1.

Q: How can we rewrite -8 as a fraction with a denominator of 22?

A: We can rewrite -8 as a fraction with a denominator of 22 by multiplying -8 by 22.

${-8 = \frac{-8 \times 22}{22} = \frac{-176}{22}}$

Q: What is the relationship between Kari's estimated quotient and the correct answer?

A: Kari's estimated quotient of -8 is equivalent to ${\frac{-176}{22}}$ , which is a different value from the correct answer of ${\frac{-61}{22}}$ .

Q: What is the correct description of Kari's error?

A: The correct description of Kari's error is that she found that the quotient of a negative number and a positive number is equivalent to the quotient of two negative numbers.

Q: How can we avoid making the same mistake as Kari?

A: To avoid making the same mistake as Kari, we need to carefully consider the signs of the numbers involved in the division problem and ensure that we are multiplying the correct values.

Q: What is the importance of understanding the signs of numbers in division problems?

A: Understanding the signs of numbers in division problems is crucial to avoid making errors and to ensure that we are performing the correct calculations.