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To determine which ratios are equivalent to \(3:5\), let's break down each ratio:

### 1. \(9:30\)
To simplify \(9:30\), divide both the numerator and the denominator by 3:
\[
\frac{9}{30} = \frac{9 \div 3}{30 \div 3} = \frac{3}{10}
\]
Thus, \(9:30\) is not equivalent to \(3:5\).

### 2. \(1:10\)
This ratio is already in its simplest form, and it clearly does not match \(3:5\), so it's not equivalent.

### 3. \(15:25\)
To simplify \(15:25\), divide both the numerator and the denominator by 5:
\[
\frac{15}{25} = \frac{15 \div 5}{25 \div 5} = \frac{3}{5}
\]
Thus, \(15:25\) is equivalent to \(3:5\).

### Correct answers:
- **\(15:25\)** is equivalent to \(3:5\).
- **\(9:30\)** and **\(1:10\)** are not equivalent.

Would you like more details or explanations? Here are some follow-up questions you could explore:

1. How can we use cross-multiplication to verify if two ratios are equivalent?
2. What is the process of simplifying a ratio?
3. Are there other ways to express equivalent ratios?
4. How do ratios apply to real-world problems?
5. Can you give an example of a ratio problem involving scaling?

**Tip:** When simplifying ratios, always look for the greatest common divisor (GCD) to ensure you're simplifying correctly.

Select all ratios equivalent to 3:5. (Given options: 9:30, 1:10, 15:25)

Learn how to determine which ratios are equivalent to 3:5 by simplifying ratios and comparing them. Explore key concepts like finding the greatest common divisor (GCD) and the cross-multiplication theorem. Perfect for students in Grades 5-7.

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