12. KNitting Nastia knitted two scarves for her dolls. One was \( 8 \frac{3}{4} \) inches long. The other was \( 1 \frac{1}{2} \) inches shorter than the first. How long was the second scarf?

To find the length of the second scarf, we first need to convert the mixed numbers into improper fractions. The first scarf is \( 8 \frac{3}{4} \) inches long. Converting this, we have: \( 8 \frac{3}{4} = 8 + \frac{3}{4} = \frac{32}{4} + \frac{3}{4} = \frac{35}{4} \) inches. The second scarf is \( 1 \frac{1}{2} \) inches shorter than the first. First, convert \( 1 \frac{1}{2} \) to an improper fraction: \( 1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2} \). Now, we subtract the length of the second scarf from the first: \[ \text{Length of the second scarf} = \frac{35}{4} - \frac{3}{2}. \] To subtract these fractions, convert \( \frac{3}{2} \) to a fraction with a denominator of 4: \[ \frac{3}{2} = \frac{3 \times 2}{2 \times 2} = \frac{6}{4}. \] Now we can subtract: \[ \frac{35}{4} - \frac{6}{4} = \frac{35 - 6}{4} = \frac{29}{4}. \] To convert \( \frac{29}{4} \) back to a mixed number: \[ 29 \div 4 = 7 \quad \text{remainder} \quad 1, \] So, \( \frac{29}{4} = 7 \frac{1}{4} \). Therefore, the length of the second scarf is \( 7 \frac{1}{4} \) inches.