3a) Express the following numbers as products of their prime factores \( 60 / 96 \)

To express the fraction \( \frac{60}{96} \) as a product of its prime factors, follow these steps: ### Step 1: Prime Factorization of the Numerator and Denominator **Prime Factorization of 60:** \[ 60 = 2 \times 30 = 2 \times 2 \times 15 = 2^2 \times 3 \times 5 \] **Prime Factorization of 96:** \[ 96 = 2 \times 48 = 2 \times 2 \times 24 = 2 \times 2 \times 2 \times 12 = 2 \times 2 \times 2 \times 2 \times 6 = 2^5 \times 3 \] ### Step 2: Express the Fraction Using Prime Factors \[ \frac{60}{96} = \frac{2^2 \times 3 \times 5}{2^5 \times 3} \] ### Step 3: Simplify the Fraction 1. **Cancel Out Common Factors:** - The factor \( 3 \) appears in both the numerator and the denominator, so they cancel each other out. 2. **Subtract Exponents of Common Bases (for base 2):** \[ \frac{2^2}{2^5} = 2^{2-5} = 2^{-3} \] 3. **Combine Remaining Factors:** \[ 2^{-3} \times 5 = \frac{5}{2^3} = \frac{5}{8} \] ### Final Answer \[ \frac{60}{96} = \frac{5}{2^3} = \frac{5}{8} \] **Prime Factorization Representation:** \[ \frac{60}{96} = \frac{2^2 \times 3 \times 5}{2^5 \times 3} = \frac{5}{2^3} \]