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: \[ 11 \frac{1}{3} \]