1. **State the problem:** We need to verify if Pearl's solution to the subtraction problem $$7 \frac{5}{8} - 4 \frac{2}{3}$$ is correct. 2. **Recall the formula and rules:** To subtract mixed numbers, convert them to improper fractions or subtract whole parts and fractional parts carefully, ensuring common denominators for fractions. 3. **Pearl's solution steps:** - First, subtract the whole number parts: $$7 \frac{5}{8} - 4 = 3 \frac{5}{8}$$ - Then subtract the fractional part $$\frac{2}{3}$$ from $$3 \frac{5}{8}$$. 4. **Check the fractional subtraction:** - Convert $$3 \frac{5}{8}$$ to an improper fraction: $$3 \frac{5}{8} = \frac{24}{8} + \frac{5}{8} = \frac{29}{8}$$. - Convert $$\frac{2}{3}$$ to have denominator 24 (LCM of 8 and 3): $$\frac{2}{3} = \frac{16}{24}$$. - Convert $$\frac{29}{8}$$ to denominator 24: $$\frac{29}{8} = \frac{87}{24}$$. - Subtract: $$\frac{87}{24} - \frac{16}{24} = \frac{71}{24}$$. 5. **Convert back to mixed number:** $$\frac{71}{24} = 2 \frac{23}{24}$$ because $$24 \times 2 = 48$$ and $$71 - 48 = 23$$. 6. **Compare with Pearl's answer:** Pearl wrote $$3 \frac{1}{24}$$, but the correct answer is $$2 \frac{23}{24}$$. 7. **Conclusion:** Pearl's solution is incorrect because she subtracted the whole number 4 first, then subtracted $$\frac{2}{3}$$ from the fractional part incorrectly without adjusting the whole number part properly. The correct answer is $$2 \frac{23}{24}$$. **Final answer:** $$7 \frac{5}{8} - 4 \frac{2}{3} = 2 \frac{23}{24}$$.