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To determine which ratios have a unit rate of 5, let’s examine each option and calculate if the ratio simplifies to a unit rate (a value per 1 unit of time) of 5.

We’ll convert each ratio into the form \( \text{kilometers} : 1 \text{ minute} \) and see if it equals 5 kilometers per minute.

### Ratios Analysis

1. **\( \frac{6}{4} \) kilometers : \( \frac{1}{4} \) minutes**
   - Simplify the ratio:
     \[
     \frac{\frac{6}{4}}{\frac{1}{4}} = \frac{6}{4} \times \frac{4}{1} = 6 \text{ kilometers per minute}
     \]
   - This does **not equal 5**, so it does not match.

2. **\( \frac{1}{3} \) kilometer : \( \frac{2}{3} \) minutes**
   - Simplify the ratio:
     \[
     \frac{\frac{1}{3}}{\frac{2}{3}} = \frac{1}{3} \times \frac{3}{2} = \frac{1}{2} \text{ kilometers per minute}
     \]
   - This does **not equal 5**, so it does not match.

3. **\( \frac{1}{2} \) kilometer : 2 minutes**
   - Simplify the ratio:
     \[
     \frac{\frac{1}{2}}{2} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \text{ kilometers per minute}
     \]
   - This does **not equal 5**, so it does not match.

4. **1 kilometer : \( \frac{1}{5} \) minute**
   - Simplify the ratio:
     \[
     \frac{1}{\frac{1}{5}} = 1 \times 5 = 5 \text{ kilometers per minute}
     \]
   - This **equals 5**, so it matches.

5. **\( \frac{4}{5} \) kilometer : 5 minutes**
   - Simplify the ratio:
     \[
     \frac{\frac{4}{5}}{5} = \frac{4}{5} \times \frac{1}{5} = \frac{4}{25} \text{ kilometers per minute}
     \]
   - This does **not equal 5**, so it does not match.

6. **\( \frac{3}{10} \) kilometers : \( \frac{3}{10} \) minutes**
   - Simplify the ratio:
     \[
     \frac{\frac{3}{10}}{\frac{3}{10}} = 1 \text{ kilometer per minute}
     \]
   - This does **not equal 5**, so it does not match.

### Conclusion

The only ratio that has a unit rate of 5 kilometers per minute is:

- **1 kilometer : \( \frac{1}{5} \) minute**

Would you like a detailed explanation on any specific part, or have further questions?

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Here are some related questions to explore further:

1. What is a unit rate, and how is it used in real-world scenarios?
2. How do you convert complex ratios with fractions into simpler unit rates?
3. Why is it important to simplify ratios in unit rate problems?
4. How would you solve unit rate problems involving different units, such as miles per hour?
5. What are some common mistakes to avoid when calculating unit rates?

**Tip:** Always double-check calculations by simplifying both the numerator and denominator separately before finding the final unit rate.

Which ratios have a unit rate of 5? Choose ALL that apply.

Learn how to determine which ratios have a unit rate of 5 using fractions. This question requires knowledge of simplifying ratios and converting them to a unit rate of 5 kilometers per minute. Suitable for Grade 7 students studying unit rates and ratios.

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