Stretch Your Thinking For a woodworking project, Tyler has cut 14 boards that are each \( \frac{3}{4} \) yard and one board that is \( 2 \frac{1}{4} \) yards. What is the total length of the boards Ty has cut? Show your work.

To find the total length of the boards Tyler has cut, we'll first calculate the total length contributed by the 14 boards that are each \( \frac{3}{4} \) yard long. 1. Calculate the total length of the 14 boards: \[ 14 \times \frac{3}{4} = \frac{14 \times 3}{4} = \frac{42}{4} = 10.5 \text{ yards} \] 2. Now, convert \( 2 \frac{1}{4} \) yards to an improper fraction: \[ 2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \text{ yards} \] 3. Now, add the length of the 14 boards to the length of the one board: \[ 10.5 + \frac{9}{4} \] To add these, we convert \( 10.5 \) to an improper fraction: \[ 10.5 = \frac{21}{2} \] To add \( \frac{21}{2} \) and \( \frac{9}{4} \), we need a common denominator (which is 4): \[ \frac{21}{2} = \frac{21 \times 2}{2 \times 2} = \frac{42}{4} \] So now we can add: \[ \frac{42}{4} + \frac{9}{4} = \frac{42 + 9}{4} = \frac{51}{4} \] 4. Finally, we can convert \( \frac{51}{4} \) back to a mixed number: \[ \frac{51}{4} = 12 \frac{3}{4} \text{ yards} \] Therefore, the total length of the boards Tyler has cut is \( 12 \frac{3}{4} \) yards.