explain or show why thw point on the number line describes both 3/5 and 6/10

To understand why the point on the number line can represent both \( \frac{3}{5} \) and \( \frac{6}{10} \), we need to explore the concept of equivalent fractions.

### Step-by-Step Explanation:

1. **What are Equivalent Fractions?**
   Two fractions are equivalent if they represent the same value. This happens when both the numerator (top number) and the denominator (bottom number) of one fraction can be multiplied or divided by the same non-zero number to give the numerator and denominator of the other fraction.

2. **Converting \( \frac{3}{5} \) to \( \frac{6}{10} \):**
   \[
   \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
   \]
   By multiplying both the numerator and denominator of \( \frac{3}{5} \) by 2, we get \( \frac{6}{10} \). This shows that \( \frac{3}{5} \) and \( \frac{6}{10} \) are equivalent fractions.

3. **Visualizing on the Number Line:**
   - If we divide the number line between 0 and 1 into 5 equal parts, \( \frac{3}{5} \) represents a point 3 parts to the right of 0.
   - Similarly, if we divide the same segment (between 0 and 1) into 10 equal parts, \( \frac{6}{10} \) represents a point 6 parts to the right of 0.
   - Both points end up in the same location on the number line because \( \frac{3}{5} = \frac{6}{10} \).

### Conclusion:
The fraction \( \frac{3}{5} \) and \( \frac{6}{10} \) are different representations of the same point on the number line, meaning they describe the same quantity. Therefore, whether you use \( \frac{3}{5} \) or \( \frac{6}{10} \), you are describing the same position.

Would you like more details on this? Let me know if you have questions. Here are some related questions:

1. How can I find other equivalent fractions for \( \frac{3}{5} \)?
2. How do we convert any fraction to its simplest form?
3. Why do fractions need to have the same denominator to be compared?
4. What is the decimal form of \( \frac{3}{5} \) and \( \frac{6}{10} \)?
5. Can all fractions be represented on the number line?

**Tip:** To check if two fractions are equivalent, cross-multiply. If the cross products are equal, the fractions are equivalent!

explain or show why the point on the number line describes both 3/5 and 6/10

Understand why the point on the number line represents both 3/5 and 6/10 by exploring equivalent fractions and visualizing their position on the number line. Learn the key concept of equivalent fractions, suitable for students in Grades 5-7.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation