1. **State the problem:** Judy and Faith each bought equal sizes of material to make tablecloths. Judy used $\frac{7}{12}$ of her material, and Faith used $\frac{5}{8}$ of her material. We need to determine who used the longer part of the material. 2. **Formula and approach:** To compare fractions, we find a common denominator or convert them to decimals. 3. **Compare Judy's usage:** $\frac{7}{12}$ 4. **Compare Faith's usage:** $\frac{5}{8}$ 5. **Find common denominator:** The least common denominator of 12 and 8 is 24. 6. **Convert Judy's fraction:** $$\frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24}$$ 7. **Convert Faith's fraction:** $$\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}$$ 8. **Compare numerators:** $14$ (Judy) vs $15$ (Faith) 9. Since $15 > 14$, Faith used a longer part of the material. **Final answer:** Faith used the longest part of the material.