Multiply the Fraction Sequence: 1/4 × 4/3 × 3/2

To solve this problem, we'll multiply the given fractions step-by-step:

Step 1: Multiply the numerators and the denominators.
Numerators: $1 \times 4 \times 3 = 12$.
Denominators: $4 \times 3 \times 2 = 24$.

Step 2: Write the new fraction from the results of multiplying the numerators and denominators.
$\frac{12}{24}$.

Step 3: Simplify the fraction by finding common factors in the numerator and denominator.
The greatest common divisor of 12 and 24 is 12. Divide both the numerator and the denominator by 12:
$\frac{12}{24} = \frac{12 \div 12}{24 \div 12} = \frac{1}{2}$.

Therefore, the product of the fractions $\frac{1}{4}$, $\frac{4}{3}$, and $\frac{3}{2}$ is $\frac{1}{2}$.