Question

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

Answer 1

To solve the problem \( 3 \frac{2}{5} \div \frac{3}{10} \), we can follow these steps:

1. **Convert the mixed number to an improper fraction**:
\[
3 \frac{2}{5} = 3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}
\]

2. **Divide by the fraction \(\frac{3}{10}\)**:
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of \(\frac{3}{10}\) is \(\frac{10}{3}\).
\[
\frac{17}{5} \div \frac{3}{10} = \frac{17}{5} \times \frac{10}{3}
\]

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

4. **Simplify the fraction**:
We can simplify \(\frac{170}{15}\) by finding the greatest common divisor (GCD) of 170 and 15. The GCD is 5.
\[
\frac{170 \div 5}{15 \div 5} = \frac{34}{3}
\]

5. **Convert \(\frac{34}{3}\) to a mixed number if desired**:
\[
\frac{34}{3} = 11 \frac{1}{3}
\]

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