Solving the Fraction Equation: Uncover X in 2/5x = 40

To solve the equation $\frac{2}{5}x = 40$, follow these steps:

• Step 1: Identify the reciprocal of the fraction $\frac{2}{5}$, which is $\frac{5}{2}$.
• Step 2: Multiply both sides of the equation by $\frac{5}{2}$ to isolate $x$.
• Step 3: Simplify the equation to find the value of $x$.

Let's perform the calculation:

Step 1: Multiply both sides by the reciprocal:
$\frac{5}{2} \times \frac{2}{5}x = \frac{5}{2} \times 40$.

The left side simplifies to:
$x = \frac{5}{2} \times 40$.

Step 2: Calculate the right side:
$x = 200 \div 2 = 100$.

Therefore, the solution to the equation $\frac{2}{5}x = 40$ is $x = 100$.