Question

Jessie was given the problem 3 2/5÷3/10=

Answer 1

To solve the problem \( 3 \frac{2}{5} \div \frac{3}{10} \), we first convert the mixed number \( 3 \frac{2}{5} \) into an improper fraction.

1. Convert \( 3 \frac{2}{5} \):
- \( 3 \) can be written as \( \frac{15}{5} \) (since \( 3 \times 5 = 15 \)).
- Adding \( \frac{2}{5} \):
\[
3 \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}
\]

2. Now we have:
\[
\frac{17}{5} \div \frac{3}{10}
\]

3. To divide by a fraction, we multiply by its reciprocal:
\[
\frac{17}{5} \div \frac{3}{10} = \frac{17}{5} \times \frac{10}{3}
\]

4. Multiply the fractions:
\[
= \frac{17 \times 10}{5 \times 3} = \frac{170}{15}
\]

5. Now simplify \( \frac{170}{15} \):
- Both the numerator and the denominator can be divided by 5:
\[
\frac{170 \div 5}{15 \div 5} = \frac{34}{3}
\]

6. The result \( \frac{34}{3} \) can be converted back to a mixed number:
- \( 34 \div 3 = 11\) remainder \( 1\), which gives us the mixed number \( 11 \frac{1}{3} \).

Thus, the final answer is:
\[
3 \frac{2}{5} \div \frac{3}{10} = \frac{34}{3} \text{ or } 11 \frac{1}{3}
\]