Question
Jessie was given the problem 3 2/5 divided by 3/10 = to solve, Jessie’s work looks like this:
3 2/5 divided by 3/10
17/5 divided by 3/10
17/5 x 3/10 equals 17 x 3
————
5 x 10
51/50 equals 1 1/50
Jessie’s answer is incorrect
1. Find and describe the error Jessie made
2. What is the correct answer
3 2/5 divided by 3/10
17/5 divided by 3/10
17/5 x 3/10 equals 17 x 3
————
5 x 10
51/50 equals 1 1/50
Jessie’s answer is incorrect
1. Find and describe the error Jessie made
2. What is the correct answer
Answers
GPT-4o mini
Let's analyze Jessie's work step by step to identify the error she made.
### 1. Finding and Describing the Error
When Jessie rewrote the division problem from:
\[
3 \frac{2}{5} \div \frac{3}{10}
\]
to:
\[
\frac{17}{5} \div \frac{3}{10}
\]
she correctly converted \(3 \frac{2}{5}\) into \( \frac{17}{5} \). The initial part of her work was accurate.
Next, she proceeded to convert the division of fractions into multiplication by the reciprocal:
\[
\frac{17}{5} \times \frac{10}{3}
\]
However, in her calculations, it seems that she incorrectly wrote:
\[
\frac{17}{5} \times \frac{3}{10}
\]
Instead of multiplying by \( \frac{10}{3} \), she mistakenly multiplied by \( \frac{3}{10} \). Thus, this is where her error occurs, leading to an incorrect multiplication setup.
The correct multiplication after applying the reciprocal should have been:
\[
\frac{17}{5} \times \frac{10}{3}
\]
### 2. The Correct Answer
Now, let's compute the correct answer step by step:
1. Convert \(3 \frac{2}{5}\) to an improper fraction:
\[
3 \frac{2}{5} = \frac{3 \cdot 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
\]
2. Set up the division problem as multiplication by the reciprocal:
\[
\frac{17}{5} \div \frac{3}{10} = \frac{17}{5} \times \frac{10}{3}
\]
3. Perform the multiplication:
\[
= \frac{17 \cdot 10}{5 \cdot 3} = \frac{170}{15}
\]
4. Simplifying \(\frac{170}{15}\):
To simplify, find the greatest common divisor (GCD) of 170 and 15. The GCD is 5.
\[
\frac{170 \div 5}{15 \div 5} = \frac{34}{3}
\]
5. Finally, convert \(\frac{34}{3}\) to a mixed number:
\[
34 \div 3 = 11 \quad \text{remainder } 1 \quad \Rightarrow \quad 11 \frac{1}{3}
\]
Thus, the correct answer is:
\[
\boxed{11 \frac{1}{3}}
\]
### 1. Finding and Describing the Error
When Jessie rewrote the division problem from:
\[
3 \frac{2}{5} \div \frac{3}{10}
\]
to:
\[
\frac{17}{5} \div \frac{3}{10}
\]
she correctly converted \(3 \frac{2}{5}\) into \( \frac{17}{5} \). The initial part of her work was accurate.
Next, she proceeded to convert the division of fractions into multiplication by the reciprocal:
\[
\frac{17}{5} \times \frac{10}{3}
\]
However, in her calculations, it seems that she incorrectly wrote:
\[
\frac{17}{5} \times \frac{3}{10}
\]
Instead of multiplying by \( \frac{10}{3} \), she mistakenly multiplied by \( \frac{3}{10} \). Thus, this is where her error occurs, leading to an incorrect multiplication setup.
The correct multiplication after applying the reciprocal should have been:
\[
\frac{17}{5} \times \frac{10}{3}
\]
### 2. The Correct Answer
Now, let's compute the correct answer step by step:
1. Convert \(3 \frac{2}{5}\) to an improper fraction:
\[
3 \frac{2}{5} = \frac{3 \cdot 5 + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
\]
2. Set up the division problem as multiplication by the reciprocal:
\[
\frac{17}{5} \div \frac{3}{10} = \frac{17}{5} \times \frac{10}{3}
\]
3. Perform the multiplication:
\[
= \frac{17 \cdot 10}{5 \cdot 3} = \frac{170}{15}
\]
4. Simplifying \(\frac{170}{15}\):
To simplify, find the greatest common divisor (GCD) of 170 and 15. The GCD is 5.
\[
\frac{170 \div 5}{15 \div 5} = \frac{34}{3}
\]
5. Finally, convert \(\frac{34}{3}\) to a mixed number:
\[
34 \div 3 = 11 \quad \text{remainder } 1 \quad \Rightarrow \quad 11 \frac{1}{3}
\]
Thus, the correct answer is:
\[
\boxed{11 \frac{1}{3}}
\]