Solve 3/4 ÷ 1 2/3: Mixed Number Division Step-by-Step

To solve the problem $\frac{3}{4}:1\frac{2}{3}$, follow these steps:

• Step 1: Convert the mixed number $1\frac{2}{3}$ to an improper fraction.
• Step 2: Rewrite the division problem using the reciprocal of the divisor.
• Step 3: Multiply the fractions.

Let’s proceed through each step:

Step 1: Convert the mixed number to an improper fraction.

$1\frac{2}{3} = \frac{1 \times 3 + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}$

Step 2: The division $\frac{3}{4} : \frac{5}{3}$ becomes $\frac{3}{4} \times \frac{3}{5}$ (multiply by the reciprocal).

Step 3: Multiply the two fractions:

$\frac{3}{4} \times \frac{3}{5} = \frac{3 \times 3}{4 \times 5} = \frac{9}{20}$

Thus, the answer is $\frac{9}{20}$.

The correct answer is choice 3: $\frac{9}{20}$.