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Let's analyze the given ratios and determine which are equivalent to 16:36.

1. First, simplify the ratio 16:36. To do this, divide both the numerator (16) and the denominator (36) by their greatest common divisor (GCD).
   - GCD of 16 and 36 is 4.
   - \( \frac{16}{36} = \frac{16 \div 4}{36 \div 4} = \frac{4}{9} \).

So, the ratio 16:36 simplifies to 4:9.

Now, let's check the given options:

- **4:9**: This is exactly equal to the simplified form of 16:36, so it's correct.
- **12:27**: Simplify 12:27 by dividing both terms by their GCD, which is 3.
  - \( \frac{12}{27} = \frac{12 \div 3}{27 \div 3} = \frac{4}{9} \). So, 12:27 is also equivalent to 16:36.
- **24:54**: Simplify 24:54 by dividing both terms by their GCD, which is 6.
  - \( \frac{24}{54} = \frac{24 \div 6}{54 \div 6} = \frac{4}{9} \). So, 24:54 is also equivalent to 16:36.

### Conclusion:
All the ratios provided (4:9, 12:27, and 24:54) are equivalent to 16:36.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How do you find the greatest common divisor (GCD) of two numbers?
2. What is the general process for simplifying ratios?
3. Can any fraction or ratio be simplified? Why or why not?
4. How can you convert a ratio to a percentage?
5. What are some real-life applications of ratios?

**Tip:** When simplifying ratios or fractions, always look for the greatest common divisor (GCD) to reduce them to their simplest form efficiently.

Learn how to simplify the ratio 16:36 and find equivalent ratios using the greatest common divisor (GCD). This problem involves understanding the concept of ratios and simplification techniques. Suitable for students in Grades 6-8.

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