Solve the Fraction Division: 6/7 ÷ 3 Step-by-Step

To solve the problem of dividing $\frac{6}{7}$ by 3, we follow these steps:

• Step 1: Understand that dividing by a number is the same as multiplying by its reciprocal.
• Step 2: Write 3 as a fraction: $3 = \frac{3}{1}$.
• Step 3: Find the reciprocal of $\frac{3}{1}$, which is $\frac{1}{3}$.
• Step 4: Multiply $\frac{6}{7}$ by $\frac{1}{3}$.
• Step 5: Perform the multiplication: $\frac{6}{7} \times \frac{1}{3} = \frac{6 \times 1}{7 \times 3} = \frac{6}{21}$
• Step 6: Simplify $\frac{6}{21}$ by finding the greatest common divisor of 6 and 21, which is 3.
• Step 7: Divide both the numerator and the denominator by 3: $\frac{6 \div 3}{21 \div 3} = \frac{2}{7}$

Thus, the result of the division $\frac{6}{7} \div 3$ is $\frac{2}{7}$.

The correct choice from the provided options is $\frac{2}{7}$, which matches choice number 4.