Fia needs $$ \frac{3}{4} $$ of a cup of brown sugar. She only has a $$ \frac{1}{3} $$-cup measuring cup and a $$ \frac{1}{8} $$-cup measuring cup. Which should she use and why?

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Fia should use the **$$ \frac{1}{3} $$-cup measuring cup** to measure $$ \frac{3}{4} $$ cup of brown sugar. Here's why:

### **Efficiency in Measurement**

1. **Using the $$ \frac{1}{3} $$-Cup:**
   - **First Fill:** $$ \frac{1}{3} $$ cup
   - **Second Fill:** $$ \frac{1}{3} + \frac{1}{3} = \frac{2}{3} $$ cups
   - **Third Fill (Partial):** To reach $$ \frac{3}{4} $$ cup, Fia needs an additional $$ \frac{3}{4} - \frac{2}{3} = \frac{1}{12} $$ cup. While she doesn't have a $$ \frac{1}{12} $$-cup measure, estimating a bit less than a full $$ \frac{1}{3} $$-cup for the third fill will get her close to $$ \frac{3}{4} $$ cup.

**Total Measures Needed:** Approximately 2 and a small portion of the third $$ \frac{1}{3} $$-cup.

2. **Using the $$ \frac{1}{8} $$-Cup:**
   - To reach $$ \frac{3}{4} $$ cup, Fia would need to fill the $$ \frac{1}{8} $$-cup **six times** because $$ 6 	imes \frac{1}{8} = \frac{6}{8} = \frac{3}{4} $$ cup.

**Total Measures Needed:** 6 full fills.

### **Why the $$ \frac{1}{3} $$-Cup is Preferable**

- **Fewer Fills:** Using the $$ \frac{1}{3} $$-cup requires fewer measurements (around 2 to 3 fills) compared to six fills with the $$ \frac{1}{8} $$-cup.
- **Speed and Convenience:** Fewer measurements mean the process is quicker and less prone to errors from repeated filling.
- **Ease of Estimation:** It's easier to estimate the slight additional amount needed after two $$ \frac{1}{3} $$-cup measures than to manage six separate $$ \frac{1}{8} $$-cup measures accurately.

### **Alternative Approach: Combining Both Cups**

If Fia has both measuring cups available and wishes to increase accuracy while minimizing the number of measurements, she can use a combination:

- **Two $$ \frac{1}{3} $$-Cup Measures:** $$ \frac{2}{3} $$ cups
- **One $$ \frac{1}{8} $$-Cup Measure:** $$ \frac{1}{8} $$ cup

**Total:** $$ \frac{2}{3} + \frac{1}{8} = \frac{16}{24} + \frac{3}{24} = \frac{19}{24} \approx 0.792 $$ cups

This combination gets her slightly over $$ \frac{3}{4} $$ cups, but it's a quicker method than using six $$ \frac{1}{8} $$-cup measures.

### **Conclusion**

Using the $$ \frac{1}{3} $$-cup is more efficient and practical for measuring $$ \frac{3}{4} $$ cup of brown sugar. It reduces the number of measurements needed and simplifies the process, making it the better choice between the two available measuring cups.

**Answer:**  
She should use the larger 1⁄3-cup measure because it allows her to reach three fourths of a cup with fewer fillings than the smaller 1⁄8-cup cup.
Fia should use the $$ \frac{1}{3} $$-cup measuring cup because it requires fewer measurements and is more efficient for measuring $$ \frac{3}{4} $$ cup of brown sugar compared to the $$ \frac{1}{8} $$-cup measuring cup.

Fia needs \( \frac{3}{4} \) of a cup of brown sugar. She only has a \( \frac{1}{3} \)-cup measuring cup and a \( \frac{1}{8} \)-cup measuring cup. Which should she use and why?

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