A farmer uses \( \frac{3}{4} \) of his field to plant com, \( \frac{1}{6} \) of his field to plant beans, and the rest to plant wheat. What fraction of his field is used for wheat?

To find the fraction of the field used for wheat, we need to first add the fractions of the field used for corn and beans. The farmer uses \( \frac{3}{4} \) of the field for corn and \( \frac{1}{6} \) for beans. To add these fractions, we need a common denominator. The least common multiple of 4 and 6 is 12. Now, convert \( \frac{3}{4} \) and \( \frac{1}{6} \) to have a denominator of 12: - \( \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \) - \( \frac{1}{6} = \frac{1 \times 2}{6 \times 2} = \frac{2}{12} \) Now, add them: \[ \frac{9}{12} + \frac{2}{12} = \frac{11}{12} \] Since \( \frac{11}{12} \) of the field is used for corn and beans, the remaining fraction for wheat is: \[ 1 - \frac{11}{12} = \frac{1}{12} \] So, the fraction of the field used for wheat is \( \frac{1}{12} \).