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To determine which ratios have a unit rate of 4, we need to calculate the unit rate for each ratio and check if it equals 4. The unit rate is found by dividing the first quantity by the second.

### 1. \( \frac{2 \frac{1}{2} \text{ cups}}{ \frac{5}{8} \text{ cup}} \):
Convert mixed number:
\( 2 \frac{1}{2} = \frac{5}{2} \)
So, the ratio is \( \frac{5}{2} : \frac{5}{8} \).
Divide: 
\[
\frac{\frac{5}{2}}{\frac{5}{8}} = \frac{5}{2} \times \frac{8}{5} = 4.
\]
This ratio has a unit rate of 4.

### 2. \( \frac{\frac{1}{8} \text{ cup}}{1 \text{ cup}} \):
\[
\frac{\frac{1}{8}}{1} = \frac{1}{8} \neq 4.
\]
This ratio does not have a unit rate of 4.

### 3. \( \frac{4 \frac{1}{3} \text{ cups}}{3 \text{ cups}} \):
Convert mixed number:
\( 4 \frac{1}{3} = \frac{13}{3} \).
So, the ratio is \( \frac{13}{3} : 3 \).
Divide:
\[
\frac{\frac{13}{3}}{3} = \frac{13}{3} \times \frac{1}{3} = \frac{13}{9} \neq 4.
\]
This ratio does not have a unit rate of 4.

### 4. \( \frac{\frac{7}{8} \text{ cup}}{3 \frac{1}{2} \text{ cups}} \):
Convert mixed number:
\( 3 \frac{1}{2} = \frac{7}{2} \).
So, the ratio is \( \frac{7}{8} : \frac{7}{2} \).
Divide:
\[
\frac{\frac{7}{8}}{\frac{7}{2}} = \frac{7}{8} \times \frac{2}{7} = \frac{1}{4} \neq 4.
\]
This ratio does not have a unit rate of 4.

### 5. \( \frac{2 \text{ cups}}{\frac{1}{2} \text{ cup}} \):
\[
\frac{2}{\frac{1}{2}} = 2 \times 2 = 4.
\]
This ratio has a unit rate of 4.

### 6. \( \frac{4 \text{ cups}}{1 \frac{1}{4} \text{ cups}} \):
Convert mixed number:
\( 1 \frac{1}{4} = \frac{5}{4} \).
So, the ratio is \( 4 : \frac{5}{4} \).
Divide:
\[
\frac{4}{\frac{5}{4}} = 4 \times \frac{4}{5} = \frac{16}{5} \neq 4.
\]
This ratio does not have a unit rate of 4.

### Conclusion:
The ratios with a unit rate of 4 are:
- \( 2 \frac{1}{2} \text{ cups} : \frac{5}{8} \text{ cup} \)
- \( 2 \text{ cups} : \frac{1}{2} \text{ cup} \)

Would you like further details or explanations? Here are 5 related questions you can explore:

1. How do you convert a mixed number to an improper fraction?
2. Why is dividing by a fraction the same as multiplying by its reciprocal?
3. What is the significance of the unit rate in real-world contexts?
4. How can you simplify complex fractions step by step?
5. How do unit rates help in comparing different ratios effectively?

**Tip:** When dividing fractions, remember to multiply by the reciprocal (flip the second fraction).

Which ratios have a unit rate of 4? Choose ALL that apply.

Learn how to determine which ratios have a unit rate of 4 by dividing the first quantity by the second in each ratio. This problem focuses on ratios involving fractions and mixed numbers, and it is suitable for students in Grades 6-8.

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