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Mateo is working with the fraction \( \frac{4}{6} \) and is using a number line to find equivalent fractions with different denominators. Let's break this problem down step by step:

1. **Understanding Equivalent Fractions**: Fractions are equivalent if they represent the same portion of a whole. For \( \frac{4}{6} \), equivalent fractions can be found by multiplying or dividing both the numerator and denominator by the same number.

2. **Finding an Equivalent Fraction with a Denominator Greater than 6**:
   - To find an equivalent fraction with a denominator greater than 6, multiply both the numerator and denominator by the same number. For example:
     \[
     \frac{4}{6} \times \frac{2}{2} = \frac{8}{12}.
     \]
     Thus, \( \frac{8}{12} \) is equivalent to \( \frac{4}{6} \), and its denominator is greater than 6.

3. **Finding an Equivalent Fraction with a Denominator Less than 6**:
   - To find an equivalent fraction with a smaller denominator, divide both the numerator and denominator by their greatest common factor (GCF). The GCF of 4 and 6 is 2, so:
     \[
     \frac{4}{6} \div \frac{2}{2} = \frac{2}{3}.
     \]
     Thus, \( \frac{2}{3} \) is equivalent to \( \frac{4}{6} \), and its denominator is less than 6.

4. **Using the Number Line**:
   - The number line shows fractions divided into sixths (denominator = 6). Mateo can relabel the number line by dividing each interval into more parts (for a greater denominator) or by grouping intervals together (for a smaller denominator) to find these equivalent fractions.

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Would you like further explanation of equivalent fractions or help visualizing the relabeling process?  

### 5 Related Questions:
1. How can we verify that two fractions are equivalent?
2. What happens to a fraction when both the numerator and denominator are multiplied by the same number?
3. Can you find more equivalent fractions for \( \frac{4}{6} \)?
4. What does it mean to simplify a fraction, and how is it related to equivalent fractions?
5. How would the number line look if divided into twelfths instead of sixths?

### Tip:
Always simplify fractions to their lowest terms by dividing both the numerator and denominator by their GCF to make comparisons easier!

Mateo is using a number line to find fractions equivalent to 4/6. He says he can find an equivalent fraction with a denominator greater than 6 and an equivalent fraction with a denominator less than 6. How can he do this using the number line?

Learn how to find equivalent fractions of 4/6 with denominators greater than and less than 6 using a number line. This detailed explanation covers multiplying and dividing fractions, simplifying with GCF, and visualizing fraction equivalence for Grades 4-6.

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