Solve: 3/7 Divided by 1⅔ - Mixed Number Division

To solve the problem of dividing the fraction $\frac{3}{7}$ by the mixed number $1\frac{2}{3}$, we'll follow these steps:

• Step 1: Convert the mixed number $1\frac{2}{3}$ into an improper fraction.
• Step 2: Find the reciprocal of this improper fraction.
• Step 3: Multiply the initial fraction by this reciprocal.

Let's proceed with each step:

Step 1: Convert $1\frac{2}{3}$ to an improper fraction:
A mixed number $a\frac{b}{c}$ can be converted to an improper fraction by multiplying the whole number part by the denominator and adding the numerator. Hence:
$1 \cdot 3 + 2 = 3 + 2 = 5$
This gives us the improper fraction $\frac{5}{3}$.

Step 2: Find the reciprocal of $\frac{5}{3}$:
The reciprocal of a fraction $\frac{a}{b}$ is $\frac{b}{a}$. Therefore, the reciprocal of $\frac{5}{3}$ is $\frac{3}{5}$.

Step 3: Multiply $\frac{3}{7}$ by the reciprocal $\frac{3}{5}$:
$\frac{3}{7} \times \frac{3}{5} = \frac{3 \cdot 3}{7 \cdot 5}$
Compute the multiplication:
$\frac{9}{35}$

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