To simplify each ratio, both quantities must be in a common unit. Let's simplify each ratio step by step.

a) $5 : 15$

• Both values are in dollars, so no unit conversion is needed.
• Simplify $\frac{5}{15} = \frac{1}{3}$.

Simplified Ratio: $1 : 3$

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b) $24 : 16$

• Both values are in dollars, so no unit conversion is needed.
• Simplify $\frac{24}{16} = \frac{3}{2}$.

Simplified Ratio: $3 : 2$

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c) $125 \, \text{g} : 300 \, \text{g}$

• Both values are in grams, so no unit conversion is needed.
• Simplify $\frac{125}{300} = \frac{5}{12}$.

Simplified Ratio: $5 : 12$

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d) $34 \, \text{kg} : 30 \, \text{kg}$

• Both values are in kilograms, so no unit conversion is needed.
• Simplify $\frac{34}{30} = \frac{17}{15}$.

Simplified Ratio: $17 : 15$

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e) $2.50 \, \text{dollars} : 70 \, \text{cents}$

• Convert $2.50 into cents: $2.50 \, \text{dollars} = 250 \, \text{cents}$.
• Now the ratio is $250 \, \text{cents} : 70 \, \text{cents}$.
• Simplify $\frac{250}{70} = \frac{25}{7}$.

Simplified Ratio: $25 : 7$

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f) $4 \, \text{weeks} : 14 \, \text{days}$

• Convert 4 weeks to days: $4 \, \text{weeks} = 4 \times 7 = 28 \, \text{days}$.
• Now the ratio is $28 \, \text{days} : 14 \, \text{days}$.
• Simplify $\frac{28}{14} = 2$.

Simplified Ratio: $2 : 1$

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g) $600 \, \text{m} : 2 \, \text{km}$

• Convert 2 kilometers to meters: $2 \, \text{km} = 2000 \, \text{m}$.
• Now the ratio is $600 \, \text{m} : 2000 \, \text{m}$.
• Simplify $\frac{600}{2000} = \frac{3}{10}$.

Simplified Ratio: $3 : 10$

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h) $465 \, \text{mm} : 3 \, \text{m}$

• Convert 3 meters to millimeters: $3 \, \text{m} = 3000 \, \text{mm}$.
• Now the ratio is $465 \, \text{mm} : 3000 \, \text{mm}$.
• Simplify $\frac{465}{3000} = \frac{31}{200}$.

Simplified Ratio: $31 : 200$

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i) $15 \, \text{hours} : 1 \, \text{day}$

• Convert 1 day to hours: $1 \, \text{day} = 24 \, \text{hours}$.
• Now the ratio is $15 \, \text{hours} : 24 \, \text{hours}$.
• Simplify $\frac{15}{24} = \frac{5}{8}$.

Simplified Ratio: $5 : 8$

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Do you have any questions or need further details?

Here are some related questions:

1. How do you convert mixed units when simplifying ratios?
2. How would you simplify a ratio involving time units like months and years?
3. Can ratios be simplified if one of the quantities is zero?
4. What is the best way to approach simplifying ratios involving different units of volume?
5. How can we represent ratios in decimal form, and how does that affect interpretation?

Tip: Always ensure both parts of a ratio are in the same unit before simplifying for accurate results.