Question
Jessie was given the problem 3 2/5÷3/10=
to solve. Jessie’s work looks like this:
3 2/5÷3/10=
17/5÷3/10=
17/5⋅3/10=17⋅35⋅10
51/50=1 1/50
Jessie’s answer is incorrect. Answer the following questions about Jessie’s work.
a. Find and describe Jessie’s error.
b. What is the correct answer?
(4 points)
to solve. Jessie’s work looks like this:
3 2/5÷3/10=
17/5÷3/10=
17/5⋅3/10=17⋅35⋅10
51/50=1 1/50
Jessie’s answer is incorrect. Answer the following questions about Jessie’s work.
a. Find and describe Jessie’s error.
b. What is the correct answer?
(4 points)
Answers
GPT-4o mini
Let's analyze Jessie’s work to identify the error and find the correct answer.
### a. Find and describe Jessie’s error.
1. Jessie correctly converts \(3 \frac{2}{5}\) to an improper fraction:
\[
3 \frac{2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
\]
This part is correct.
2. However, when Jessie sets up the division:
\[
\frac{17}{5} \div \frac{3}{10}
\]
Jessie mistakenly wrote it as:
\[
\frac{17}{5} \cdot \frac{3}{10}
\]
When dividing by a fraction, the correct operation is to multiply by the reciprocal:
\[
\frac{17}{5} \div \frac{3}{10} \text{ should be rewritten as } \frac{17}{5} \cdot \frac{10}{3}
\]
3. Additionally, Jessie’s multiplication calculation:
\[
17 \cdot 35 \cdot 10
\]
appears to be a typographical error. It seems there was an incorrect interpretation of the multiplication after the division step.
In summary, Jessie's error occurred in misunderstanding how to perform division with fractions by not taking the reciprocal of the fraction when dividing.
### b. What is the correct answer?
Now, let's find the correct answer.
Starting from:
\[
3 \frac{2}{5} \div \frac{3}{10} = \frac{17}{5} \div \frac{3}{10}
\]
We convert the division to multiplication by the reciprocal:
\[
\frac{17}{5} \cdot \frac{10}{3}
\]
Next, we multiply the fractions:
\[
\frac{17 \cdot 10}{5 \cdot 3} = \frac{170}{15}
\]
Now, we simplify \( \frac{170}{15} \):
1. Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
\[
\frac{170 \div 5}{15 \div 5} = \frac{34}{3}
\]
2. \( \frac{34}{3} \) can be expressed as a mixed number:
\[
34 \div 3 = 11 \text{ remainder } 1 \implies 11 \frac{1}{3}
\]
Thus, the correct answer is:
\[
\boxed{11 \frac{1}{3}}
\]
### a. Find and describe Jessie’s error.
1. Jessie correctly converts \(3 \frac{2}{5}\) to an improper fraction:
\[
3 \frac{2}{5} = \frac{15 + 2}{5} = \frac{17}{5}
\]
This part is correct.
2. However, when Jessie sets up the division:
\[
\frac{17}{5} \div \frac{3}{10}
\]
Jessie mistakenly wrote it as:
\[
\frac{17}{5} \cdot \frac{3}{10}
\]
When dividing by a fraction, the correct operation is to multiply by the reciprocal:
\[
\frac{17}{5} \div \frac{3}{10} \text{ should be rewritten as } \frac{17}{5} \cdot \frac{10}{3}
\]
3. Additionally, Jessie’s multiplication calculation:
\[
17 \cdot 35 \cdot 10
\]
appears to be a typographical error. It seems there was an incorrect interpretation of the multiplication after the division step.
In summary, Jessie's error occurred in misunderstanding how to perform division with fractions by not taking the reciprocal of the fraction when dividing.
### b. What is the correct answer?
Now, let's find the correct answer.
Starting from:
\[
3 \frac{2}{5} \div \frac{3}{10} = \frac{17}{5} \div \frac{3}{10}
\]
We convert the division to multiplication by the reciprocal:
\[
\frac{17}{5} \cdot \frac{10}{3}
\]
Next, we multiply the fractions:
\[
\frac{17 \cdot 10}{5 \cdot 3} = \frac{170}{15}
\]
Now, we simplify \( \frac{170}{15} \):
1. Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 5:
\[
\frac{170 \div 5}{15 \div 5} = \frac{34}{3}
\]
2. \( \frac{34}{3} \) can be expressed as a mixed number:
\[
34 \div 3 = 11 \text{ remainder } 1 \implies 11 \frac{1}{3}
\]
Thus, the correct answer is:
\[
\boxed{11 \frac{1}{3}}
\]