Question

Jessie was given the problem 3 2/5 divide 3/10 = to solve. jessie's work like this 3 2/5 divide 3/10 = 17/5 divide 3/10 17/5 x 3/10 = 17x3/5x10 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?

Answer 1

Let's analyze Jessie's work step by step:

### a. Jessie's Error

1. **Identifying the Division Process**: Jessie correctly recognized that dividing by a fraction is equivalent to multiplying by its reciprocal. However, instead of correctly applying this rule, Jessie incorrectly multiplied \( \frac{17}{5} \) by \( \frac{3}{10} \) right away.

2. **The Correct Operation**: For the division of fractions:
\[
\frac{17}{5} \div \frac{3}{10}
\]
should be converted to multiplication by the reciprocal of \( \frac{3}{10} \):
\[
\frac{17}{5} \div \frac{3}{10} = \frac{17}{5} \times \frac{10}{3}
\]

3. **Calculating Directly**: Jessie directly multiplied without taking the reciprocal first:
\[
\frac{17}{5} \times \frac{3}{10} \neq \frac{17}{5} \div \frac{3}{10}
\]

Thus, Jessie's fundamental error was in not correctly applying the division of fractions by not using the reciprocal.

### b. The Correct Answer

Now, let's compute the correct answer:

1. **Set up the division**:
\[
\frac{17}{5} \div \frac{3}{10} = \frac{17}{5} \times \frac{10}{3}
\]

2. **Multiply across**:
\[
\frac{17 \times 10}{5 \times 3} = \frac{170}{15}
\]

3. **Simplify**:
- Find the greatest common divisor (GCD) of 170 and 15. The GCD is 5.
- Thus, we can simplify:
\[
\frac{170 \div 5}{15 \div 5} = \frac{34}{3}
\]

4. **Convert to Mixed Number**:
\[
\frac{34}{3} = 11 \frac{1}{3}
\]

Therefore, the correct answer to the problem \( 3 \frac{2}{5} \div \frac{3}{10} \) is:
\[
11 \frac{1}{3}
\]