Solve: 2/3 Divided by 1¾ - Mixed Number Division

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

• Step 1: Convert the mixed number $1\frac{3}{4}$ to an improper fraction.

• Step 2: Replace the division with multiplication by the reciprocal of the improper fraction.

• Step 3: Perform the multiplication and simplify if necessary.

Now, let's work through each step:
Step 1: Convert $1\frac{3}{4}$ to an improper fraction.
A mixed number $a \frac{b}{c}$ is converted to an improper fraction $\frac{ac + b}{c}$.
So, $1\frac{3}{4} = \frac{1 \times 4 + 3}{4} = \frac{7}{4}$.

Step 2: Replace the division with multiplication by the reciprocal of $\frac{7}{4}$.
The reciprocal of $\frac{7}{4}$ is $\frac{4}{7}$, so the expression becomes: $\frac{2}{3} \times \frac{4}{7}$.

Step 3: Perform the multiplication:
Multiply the numerators: $2 \times 4 = 8$.
Multiply the denominators: $3 \times 7 = 21$.
Thus, the product is $\frac{8}{21}$.

No further simplification is needed as 8 and 21 have no common factors.

Therefore, the solution to the problem is $\frac{8}{21}$.