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

Answer 1

To solve the problem $3\frac{2}{5}÷\frac{3}{10}$, 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: $$\frac{17}{5}÷\frac{3}{10}$$

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

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: $$\frac{170÷5}{15÷5}=\frac{34}{3}$$

6. The result $\frac{34}{3}$ can be converted back to a mixed number:

   • $34÷3=11$ remainder $1$, which gives us the mixed number $11\frac{1}{3}$.

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