Q. \(\frac{2}{3} \times \frac{1}{2}\) as a fraction

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

1. Write the multiplication of fractions in terms of numerators and denominators.

   The two fractions are \( \frac{2}{3} \) and \( \frac{1}{2} \). When multiplying fractions, multiply the numerators together and the denominators together. So we form

   \[ \frac{2}{3} \times \frac{1}{2} = \frac{2 \times 1}{3 \times 2} \]

2. Multiply the numerators.

   Compute the product of the numerators: \( 2 \times 1 = 2 \). Thus the numerator of the result is 2.

3. Multiply the denominators.

   Compute the product of the denominators: \( 3 \times 2 = 6 \). Thus the denominator of the result is 6.

4. Write the unsimplified result.

   Putting the results of steps 2 and 3 together gives

   \[ \frac{2 \times 1}{3 \times 2} = \frac{2}{6} \]

5. Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD).

   The GCD of 2 and 6 is 2. Divide numerator and denominator by 2:

   \[ \frac{2 \div 2}{6 \div 2} = \frac{1}{3} \]

   Therefore the fraction simplifies to \( \frac{1}{3} \).

6. Alternative (cancellation before multiplying):

   Observe that the numerator 2 of the first fraction and the denominator 2 of the second fraction share a common factor 2. Canceling that common factor first yields

   \[ \frac{2}{3} \times \frac{1}{2} = \frac{1}{3} \times \frac{1}{1} = \frac{1}{3} \]

   This gives the same simplified result without computing the intermediate \( \frac{2}{6} \).

Final answer: \( \frac{1}{3} \).