1. **Problem:** Denise’s math binder weighs $\frac{3}{4}$ pound and Rebecca’s binder weighs $\frac{5}{9}$ pound. What is the total weight when both binders are placed on the scale together? 2. **Formula:** To find the total weight, add the two fractions: $$\text{Total weight} = \frac{3}{4} + \frac{5}{9}$$ 3. **Important rule:** To add fractions, they must have a common denominator. 4. **Find the common denominator:** The denominators are 4 and 9. The least common denominator (LCD) is 36. 5. **Convert fractions:** $$\frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36}$$ $$\frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}$$ 6. **Add the fractions:** $$\frac{27}{36} + \frac{20}{36} = \frac{27 + 20}{36} = \frac{47}{36}$$ 7. **Simplify or convert to mixed number:** $$\frac{47}{36} = 1 \frac{11}{36}$$ 8. **Answer:** The scale would indicate $1 \frac{11}{36}$ pounds. **Check options:** The closest matching option is D: $11 \frac{8}{36}$ pounds, but the correct sum is $1 \frac{11}{36}$ pounds, which is not exactly listed. Since $11 \frac{8}{36}$ is not a valid weight here, the correct total weight is $1 \frac{11}{36}$ pounds. **Final answer:** $1 \frac{11}{36}$ pounds.