One yard of gravel has been delivered to a jobsite and you have been instructed to spread \( 11 / 2 \) of it in front of the temporary steps to a building and \( \frac{1}{3} \) of it in front of the door to the jobsite trailer. How much gravel will be left over? Your answer should be in the form of a fraction reduced to its lowest terms. The amount of gravel remaining is \( \square \) of a yard.

To solve the problem, we need to determine how much gravel has been used and then subtract that from the total amount of gravel delivered. 1. **Total gravel delivered**: 1 yard 2. **Gravel used in front of the temporary steps**: \[ \frac{11}{2} \text{ yards} \] 3. **Gravel used in front of the jobsite trailer**: \[ \frac{1}{3} \text{ yards} \] Next, we need to add the amounts of gravel used: \[ \text{Total gravel used} = \frac{11}{2} + \frac{1}{3} \] To add these fractions, we need a common denominator. The least common multiple of 2 and 3 is 6. Now, we convert each fraction: \[ \frac{11}{2} = \frac{11 \times 3}{2 \times 3} = \frac{33}{6} \] \[ \frac{1}{3} = \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \] Now we can add the two fractions: \[ \text{Total gravel used} = \frac{33}{6} + \frac{2}{6} = \frac{33 + 2}{6} = \frac{35}{6} \] Now, we subtract the total gravel used from the total gravel delivered: \[ \text{Gravel remaining} = 1 - \frac{35}{6} \] To perform this subtraction, we convert 1 to a fraction with a denominator of 6: \[ 1 = \frac{6}{6} \] Now we can subtract: \[ \text{Gravel remaining} = \frac{6}{6} - \frac{35}{6} = \frac{6 - 35}{6} = \frac{-29}{6} \] Since the result is negative, it indicates that more gravel was used than was delivered. Therefore, there is no gravel left over, and we have a deficit of \( \frac{29}{6} \) yards. Thus, the amount of gravel remaining is: \[ \text{The amount of gravel remaining is } -\frac{29}{6} \text{ of a yard.} \]