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To find fractions equivalent to \( \frac{4}{12} \), let's first simplify it.

### Step 1: Simplify \( \frac{4}{12} \)
Divide both the numerator and the denominator by their greatest common divisor, which is 4:
\[
\frac{4 \div 4}{12 \div 4} = \frac{1}{3}
\]
So, \( \frac{4}{12} \) simplifies to \( \frac{1}{3} \).

### Step 2: Identify Equivalent Fractions
We need to look for fractions that are either equal to \( \frac{1}{3} \) or can simplify to \( \frac{1}{3} \).

#### Options:
1. \( \frac{1}{9} \): Cannot be simplified to \( \frac{1}{3} \).
2. \( \frac{1}{6} \): Cannot be simplified to \( \frac{1}{3} \).
3. \( \frac{2}{6} \): Simplifies to \( \frac{1}{3} \) (divide numerator and denominator by 2).
4. \( \frac{1}{3} \): Already equal to \( \frac{1}{3} \).
5. \( \frac{2}{10} \): Simplifies to \( \frac{1}{5} \), not \( \frac{1}{3} \).

### Conclusion
The fractions equivalent to \( \frac{4}{12} \) are:
- \( \frac{2}{6} \)
- \( \frac{1}{3} \)

Would you like a detailed explanation of fraction simplification?

Here are some additional questions to explore:

1. What is the process to find the greatest common divisor of two numbers?
2. How can you identify equivalent fractions without simplifying?
3. Why does \( \frac{2}{6} \) simplify to \( \frac{1}{3} \)?
4. How would you convert improper fractions to find equivalents?
5. How can you verify if two fractions are equivalent using cross-multiplication?

**Tip:** When simplifying fractions, always look for the largest number that divides both the numerator and denominator.

Which fractions are equivalent to 4/12? Choose ALL the correct answers.

Find out which fractions are equivalent to 4/12 by simplifying and comparing options. This math problem covers essential concepts in fractions and simplification, ideal for students in Grades 4-6.

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