7. Are $$ \frac{3}{8} $$ and $$ \frac{3}{4} $$ equivalent fractions? Draw a number line to decide.

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UpStudy AI · Accepted Answer

No, $$ \frac{3}{8} $$ and $$ \frac{3}{4} $$ are **not** equivalent fractions. Let's explore why by comparing them on a number line.

### Understanding Equivalent Fractions

Two fractions are **equivalent** if they represent the **same point** on the number line, meaning they have the same value even if they look different.

### Comparing $$ \frac{3}{8} $$ and $$ \frac{3}{4} $$

1. **Convert to a Common Denominator:**
   - To compare the fractions easily, it's helpful to have the same denominator.
   - The denominators here are 8 and 4. The least common denominator (LCD) is 8.

2. **Rewrite $$ \frac{3}{4} $$ with Denominator 8:**
   $$
   \frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
   $$

3. **Now, Compare the Fractions:**
   - $$ \frac{3}{8} $$ remains as it is.
   - $$ \frac{3}{4} $$ is equivalent to $$ \frac{6}{8} $$.

4. **Visualize on a Number Line:**

```
   0 ----|----|----|----|----|----|----|----|---- 1
        1/8  2/8  3/8  4/8  5/8  6/8  7/8
             ●           ●
            3/8         6/8 (which is 3/4)
   ```

- **$$ \frac{3}{8} $$:** Located at the third mark (3/8) on the number line.
   - **$$ \frac{3}{4} $$:** Equivalent to $$ \frac{6}{8} $$, located at the sixth mark (6/8) on the number line.

### Conclusion

Since $$ \frac{3}{8} $$ and $$ \frac{6}{8} $$ (which is $$ \frac{3}{4} $$) are at **different positions** on the number line, they **are not equivalent**.

**Summary:**  
- $$ \frac{3}{8} \neq \frac{3}{4} $$  
- $$ \frac{3}{8} $$ is exactly half of $$ \frac{3}{4} $$.

**Visual Representation:**

```
0 ----|----|----|----|----|----|----|----|---- 1
     1/8  2/8  3/8  4/8  5/8  6/8  7/8
          ●           ●
         3/8         6/8 (3/4)
```

As seen above, $$ \frac{3}{8} $$ is at a different location than $$ \frac{3}{4} $$, confirming they are not equivalent.
$$ \frac{3}{8} $$ and $$ \frac{3}{4} $$ are not equivalent fractions.

7. Are \( \frac{3}{8} \) and \( \frac{3}{4} \) equivalent fractions? Draw a number line to decide.

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