To find out how many groups of \( \frac{2}{6} \) are in \( \frac{5}{6} \), we can divide \( \frac{5}{6} \) by \( \frac{2}{6} \).
Step 1: Perform the Division
To divide fractions, we multiply by the reciprocal:
\[ \frac{5}{6} \div \frac{2}{6} = \frac{5}{6} \times \frac{6}{2} \]
Step 2: Simplify
When we multiply:
\[ \frac{5 \times 6}{6 \times 2} = \frac{30}{12} \]
Now we can simplify \( \frac{30}{12} \):
\[ \frac{30 \div 6}{12 \div 6} = \frac{5}{2} = 2.5 \]
Conclusion
There are \( 2.5 \) groups of \( \frac{2}{6} \) in \( \frac{5}{6} \).
Visual Representation
To visually represent this, we can draw a fraction bar for \( \frac{5}{6} \) and then show how \( \frac{2}{6} \) fits into it.
- Draw a rectangle divided into 6 equal parts (to represent \( \frac{6}{6} \)).
- Shade 5 out of the 6 sections to represent \( \frac{5}{6} \).
- Each section represents \( \frac{1}{6} \), so we can create groups of \( \frac{2}{6} \) by shading two sections at a time.
Here’s a simple illustration:
+---------+---------+---------+---------+---------+---------+
| 1 | 2 | 3 | 4 | 5 | 6 |
| (1/6) | (1/6) | (1/6) | (1/6) | (1/6) | (1/6) |
+---------+---------+---------+---------+---------+---------+
| ████ | ████ | | | | | (5/6)
(1) (2)
- The first two segments represent the first \( \frac{2}{6} \).
- The next segments would represent another \( \frac{2}{6} \).
- This shows there are 2 full groups of \( \frac{2}{6} \), and one half group remaining (totaling \( 2.5 \) groups of \( \frac{2}{6} \)).