Multiply Three Fractions: 2/5 × 1/2 × 2/3 Step-by-Step

To solve this problem, we'll proceed with the following steps:

• Step 1: Multiply the numerators together.
• Step 2: Multiply the denominators together.
• Step 3: Simplify the resulting fraction.

Let's perform these calculations:
Step 1: Multiply the numerators: $2 \times 1 \times 2 = 4$.
Step 2: Multiply the denominators: $5 \times 2 \times 3 = 30$.
Step 3: Form the resulting fraction: $\frac{4}{30}$. Now, simplify the fraction

To simplify $\frac{4}{30}$, find the greatest common divisor (GCD) of 4 and 30, which is 2.
Thus, divide both the numerator and the denominator by 2:

$\frac{4 \div 2}{30 \div 2} = \frac{2}{15}$.

Therefore, the solution to the problem is $\frac{2}{15}$.