If \( \frac{4}{41} \) of all rabbits in a country are in one state and \( \frac{1}{6} \) of the rabbits are in a different state, vhat fotal fractional part of the rabbit population is in those two states? The total fractional part of the rabbit population living in the two states is (Type an integer or a simplified fraction.)

To determine the total fractional part of the rabbit population residing in the two states, you'll need to add the two given fractions: \[ \frac{4}{41} \quad \text{and} \quad \frac{1}{6} \] ### Step 1: Find a Common Denominator The first step is to find a common denominator for the two fractions. The least common denominator (LCD) of 41 and 6 is: \[ 41 \times 6 = 246 \] ### Step 2: Convert Each Fraction Convert each fraction to an equivalent fraction with the denominator of 246. \[ \frac{4}{41} = \frac{4 \times 6}{41 \times 6} = \frac{24}{246} \] \[ \frac{1}{6} = \frac{1 \times 41}{6 \times 41} = \frac{41}{246} \] ### Step 3: Add the Fractions Now, add the two fractions: \[ \frac{24}{246} + \frac{41}{246} = \frac{24 + 41}{246} = \frac{65}{246} \] ### Step 4: Simplify the Fraction Check if the fraction can be simplified by finding the greatest common divisor (GCD) of 65 and 246. - **Factors of 65:** 1, 5, 13, 65 - **Factors of 246:** 1, 2, 3, 6, 41, 82, 123, 246 The only common factor is **1**, so the fraction is already in its simplest form. \[ \frac{65}{246} \] ### Final Answer The total fractional part of the rabbit population living in the two states is: \[ \boxed{\dfrac{65}{246}} \]