What is the smallest fraction that describes 150 out of 1600?

To determine the smallest fraction that represents 150 out of 1600, you first convert the fraction into its simplest form by finding the greatest common divisor (GCD) of the numerator (150) and the denominator (1600).

1. Finding the GCD: You can do this by factoring both numbers.

   • The prime factorization of 150 is (2 \times 3 \times 5^2).
   • The prime factorization of 1600 is (2^6 \times 5^2).

2. Identifying common factors: The common factors in these factorizations are (2) and (5^2). Therefore, the GCD is (2 \times 5^2 = 2 \times 25 = 50).

3. Simplifying the fraction: Now you divide both the numerator and the denominator by the GCD:

   • (150 \div 50 = 3)
   • (1600 \div 50 = 32)

This gives you the fraction ( \frac{3}{32} ).

Next, we need to assess which of the given options can be expressed as a fraction equivalent