\( 1 \leqslant \) Question \( 23,6.3 . \mathrm{B}-28 \), HW Score: \( 95.65 \%, 22 \) of 23 If \( \frac{1}{34} \) of all rabbits in a country are in one state and \( \frac{2}{7} \) of the rabbits are in a different state, what total fractional part of the rabbit population is not in those two states? The total fractional part of the rabbit population not living in the two states is 0 of 1 (Type an integer or a simplified fraction.)

To determine the fractional part of the rabbit population **not** living in the two specified states, follow these steps: 1. **Identify the Fractions in the Two States:** - **State 1:** \(\frac{1}{34}\) of all rabbits. - **State 2:** \(\frac{2}{7}\) of all rabbits. 2. **Calculate the Combined Fraction in Both States:** \[ \frac{1}{34} + \frac{2}{7} \] To add these fractions, find a common denominator. The least common multiple (LCM) of 34 and 7 is 238. \[ \frac{1}{34} = \frac{7}{238} \quad \text{and} \quad \frac{2}{7} = \frac{68}{238} \] \[ \frac{7}{238} + \frac{68}{238} = \frac{75}{238} \] 3. **Determine the Fraction Not in Either State:** Subtract the combined fraction from the whole population (which is \(1\) or \(\frac{238}{238}\)). \[ 1 - \frac{75}{238} = \frac{238}{238} - \frac{75}{238} = \frac{163}{238} \] 4. **Simplify the Fraction (if possible):** - **163** is a prime number. - **238** factors into \(2 \times 7 \times 17\). Since there are no common factors between **163** and **238**, the fraction is already in its simplest form. **Final Answer:** \[ \frac{163}{238} \]