Q. \( \frac{2}{3} \times \frac{1}{16} \)

Problem: Multiply the fractions \( \frac{2}{3} \times \frac{1}{16} \).

Step 1 — Understand how to multiply fractions. To multiply two fractions, multiply their numerators to get the numerator of the product and multiply their denominators to get the denominator of the product. Symbolically, for fractions \( \frac{a}{b} \) and \( \frac{c}{d} \), the product is \( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} \).

Step 2 — Multiply numerators and denominators. Apply the rule to the given fractions:
\[ \frac{2}{3} \times \frac{1}{16} = \frac{2 \times 1}{3 \times 16}. \]
Compute the products:
\[ 2 \times 1 = 2 \quad\text{and}\quad 3 \times 16 = 48. \]
So the product is
\[ \frac{2}{48}. \]

Step 3 — Simplify the fraction by dividing by the greatest common divisor. Find the greatest common divisor of 2 and 48. Since 2 divides 48, the greatest common divisor is 2. Divide numerator and denominator by 2:
\[ \frac{2 \div 2}{48 \div 2} = \frac{1}{24}. \]
This fraction is in lowest terms because 1 has no common factor with 24 except 1.

Alternative (cross-cancellation before multiplying): Observe that the numerator 2 and the denominator 16 share a common factor 2. Cancel that factor first:
\[ \frac{2}{3} \times \frac{1}{16} = \frac{\cancel{2}}{3} \times \frac{1}{\cancel{16}/2} = \frac{1}{3} \times \frac{1}{8} = \frac{1 \times 1}{3 \times 8} = \frac{1}{24}. \]
This gives the same simplified result without multiplying large numbers first.

Final answer: \( \frac{1}{24} \).