A sporting goods manufacturer has \( 16 \frac{1}{3} \) yd of fabric to make soccer shorts. Each pair of soccer shorts requires \( \frac{2}{7} \) yd of fabric. a. How many pairs of soccer shorts can be made? b. How much material will be left over?

To determine how many pairs of soccer shorts can be made and how much material will be left over, let's follow these steps: ### a. **Number of Pairs of Soccer Shorts That Can Be Made** 1. **Convert Mixed Number to Improper Fraction:** \[ 16 \frac{1}{3} \text{ yards} = \frac{16 \times 3 + 1}{3} = \frac{49}{3} \text{ yards} \] 2. **Determine the Number of Pairs:** Each pair requires \(\frac{2}{7}\) yard of fabric. To find out how many pairs can be made: \[ \text{Number of pairs} = \frac{\text{Total Fabric}}{\text{Fabric per Pair}} = \frac{\frac{49}{3}}{\frac{2}{7}} = \frac{49}{3} \times \frac{7}{2} = \frac{343}{6} = 57 \frac{1}{6} \] Since you can't produce a fraction of a pair, **57 full pairs** of soccer shorts can be made. ### b. **Amount of Material Left Over** 1. **Calculate Fabric Used for 57 Pairs:** \[ \text{Fabric used} = 57 \times \frac{2}{7} = \frac{114}{7} = 16 \frac{2}{7} \text{ yards} \] 2. **Determine Remaining Fabric:** \[ \text{Total Fabric} = 16 \frac{1}{3} \text{ yards} = \frac{49}{3} \text{ yards} \] \[ \text{Remaining Fabric} = \frac{49}{3} - \frac{114}{7} \] Convert to a common denominator (21): \[ \frac{49}{3} = \frac{343}{21}, \quad \frac{114}{7} = \frac{342}{21} \] \[ \text{Remaining Fabric} = \frac{343}{21} - \frac{342}{21} = \frac{1}{21} \text{ yard} \] Therefore, **\(\frac{1}{21}\) yard of fabric** will be left over. ### **Summary** - **a.** 57 pairs of soccer shorts can be made. - **b.** \(\frac{1}{21}\) yard of fabric will remain.