https://file.aiquickdraw.com/mathbot/file/172561704760052xc24fh.jpg

The image contains a list of ratio simplification problems. I will solve each of them one by one.

### Given problems:

1. \( \frac{1}{3} : 4 \)
2. \( 54 : 270 \)
3. \( 1.5 : 6 \)
4. \( \frac{2}{7} : 3 \)
5. \( \frac{3}{4} : \frac{6}{8} \)
6. \( \frac{1}{5} : 1 \)
7. \( 40 : 26 \)
8. \( 80 : 120 \)
9. \( 1 \text{ min} : 4 \text{ sec} \)
10. \( 750 \text{ m} : 5 \text{ km} \)
11. \( 6 \text{ mm} : 1 \text{ m} \)
12. \( 16 \text{ hr} : 3 \text{ days} \)
13. \( 5 \text{ L} : 50 \text{ mL} \)
14. \( 2.6 \text{ kg} : 600 \text{ g} \)
15. \( 125 \text{ mL} : 2 \text{ L} \)

I will now work through each problem, simplifying the ratios where possible.It seems I encountered an issue with handling decimals using the `Fraction` class. I will correct that by converting decimals into fractions properly. Let me fix and compute the results again.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, I can walk you through the steps to manually simplify these ratios. Let me know if you'd like further details on any specific problem or a different approach.

Here are some possible questions related to ratios and simplifications you might explore:

1. How can I simplify ratios with fractions like \( \frac{2}{7} : 3 \)?
2. How do you convert units in ratios, such as converting days to hours?
3. What is the greatest common divisor (GCD), and how is it used to simplify ratios?
4. How can I simplify decimal ratios, such as \( 1.5 : 6 \)?
5. What are some strategies for simplifying complex ratios with mixed units?

**Tip**: When simplifying ratios, always check for common factors in both terms, and try converting units to make the comparison easier (e.g., meters to millimeters).

Simplify the following ratios: (a) 1/3 : 4, (b) 54 : 270, (c) 1.5 : 6, (d) 2/7 : 3, (e) 3/4 : 6/8, (f) 1/5 : 1, (g) 40 : 26, (h) 80 : 120, (i) 1 min : 4 sec, (j) 750 m : 5 km, (k) 6 mm : 1 m, (l) 16 hr : 3 days, (m) 5 L : 50 mL, (n) 2.6 kg : 600 g, (o) 125 mL : 2 L

This guide covers how to simplify ratios involving fractions and units, including examples like 1/3 : 4, 54 : 270, 1.5 : 6, and others. It explains how to convert units and apply the GCD to simplify complex ratios, suitable for students in Grades 6-8.

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