The problem asks to simplify the fraction $\frac{30}{75}$ to its lowest terms.

1. Problem Description

The problem asks to simplify the fraction $\frac{30}{75}$ to its lowest terms.

2. Solution Steps

To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD.

First, find the prime factorization of 30 and

7

5. $30 = 2 \times 3 \times 5$

$75 = 3 \times 5 \times 5 = 3 \times 5^2$

The common factors are 3 and

5. The GCD of 30 and 75 is $3 \times 5 = 15$.

Now, divide both the numerator and the denominator by 15:

$\frac{30}{75} = \frac{30 \div 15}{75 \div 15} = \frac{2}{5}$

3. Final Answer

The fraction $\frac{30}{75}$ in its lowest terms is $\frac{2}{5}$.