Solve Fraction Division: 2/5 ÷ 4/7 Step-by-Step

To solve this problem, we'll employ the division of fractions technique:

• Step 1: Find the reciprocal of the divisor. Here, the divisor is $\frac{4}{7}$. Its reciprocal is $\frac{7}{4}$.
• Step 2: Multiply the dividend $\frac{2}{5}$ by the reciprocal of the divisor.
• Step 3: Calculate $\frac{2}{5} \times \frac{7}{4}$.
• Step 4: Simplify the result, if possible.

Now, let's work through these steps:

Step 1: The reciprocal of $\frac{4}{7}$ is $\frac{7}{4}$.

Step 2: Multiply the fractions: $\frac{2}{5} \times \frac{7}{4} = \frac{2 \times 7}{5 \times 4} = \frac{14}{20}$.

Step 3: Simplify $\frac{14}{20}$. The greatest common divisor (GCD) of 14 and 20 is 2, so divide both the numerator and the denominator by 2:

$\frac{14}{20} = \frac{14 \div 2}{20 \div 2} = \frac{7}{10}$.

Therefore, the solution to the problem is $\frac{7}{10}$.