Solve Fraction Division: 2/5 ÷ 6/7 Step-by-Step

To solve the problem $\frac{2}{5} : \frac{6}{7}$, we can follow these steps:

• Step 1: Identify the operation and fractions involved. We are dividing $\frac{2}{5}$ by $\frac{6}{7}$.
• Step 2: Convert the division of fractions into multiplication by the reciprocal. We rewrite $\frac{2}{5} : \frac{6}{7}$ as $\frac{2}{5} \times \frac{7}{6}$.
• Step 3: Perform the multiplication of fractions. Multiply the numerators together and the denominators together:
• Numerator: $2 \times 7 = 14$
• Denominator: $5 \times 6 = 30$
• Step 4: Form the resulting fraction: $\frac{14}{30}$.
• Step 5: Simplify the fraction $\frac{14}{30}$ by finding the greatest common divisor (GCD) of 14 and 30, which is 2:
• Divide both 14 and 30 by their GCD:
• Simplified numerator: $14 \div 2 = 7$
• Simplified denominator: $30 \div 2 = 15$
• Resulting simplified fraction: $\frac{7}{15}$

Therefore, the solution to the problem is $\mathbf{\frac{7}{15}}$.