Solve: 3/5 Divided by 2⅓ - Mixed Number Division

To solve this problem, we'll follow these steps:

• Step 1: Convert the mixed number $2\frac{1}{3}$ into an improper fraction.
• Step 2: Take the reciprocal of this improper fraction.
• Step 3: Multiply $\frac{3}{5}$ by this reciprocal.
• Step 4: Simplify the resulting fraction if needed.

Now, let's work through each step:

Step 1: Convert $2\frac{1}{3}$ to an improper fraction.
A mixed number like $2\frac{1}{3}$ means $2 + \frac{1}{3}$. To convert it, multiply the whole number part by the denominator of the fractional part and add the numerator: $2 \times 3 + 1 = 6 + 1 = 7$. Thus, the improper fraction is $\frac{7}{3}$.

Step 2: Find the reciprocal of $\frac{7}{3}$.
The reciprocal of $\frac{7}{3}$ is $\frac{3}{7}$.

Step 3: Multiply $\frac{3}{5}$ by $\frac{3}{7}$.
When multiplying fractions, multiply numerators and denominators: $\frac{3}{5} \times \frac{3}{7} = \frac{3 \times 3}{5 \times 7} = \frac{9}{35}$.

Step 4: Simplify $\frac{9}{35}$ if necessary.
The fraction $\frac{9}{35}$ is already in its simplest form, as 9 and 35 have no common factors other than 1.

Therefore, the solution to the problem is $\frac{9}{35}$.