To divide the fractions \( \frac{3}{5} \) by \( \frac{1}{3} \) using fraction bars, we can follow these steps:
Step 1: Understanding the Problem
We can restate the problem as "How many \( \frac{1}{3} \) are in \( \frac{3}{5} \)?"
Step 2: Visualizing with Fraction Bars
- We can visualize \( \frac{3}{5} \) as 3 out of 5 equal parts.
When divided into 15 equal parts (the least common multiple of 5 and 3), we have:
- \( \frac{3}{5} \) can be represented as 9 out of 15 (since \( 3 \times 3 = 9 \) and \( 5 \times 3 = 15 \)).
- \( \frac{1}{3} \) can be represented as 5 out of 15 (since \( 1 \times 5 = 5 \) and \( 3 \times 5 = 15 \)).
Step 3: Dividing
Now, we need to find out how many \( \frac{1}{3} \)'s fit into \( \frac{3}{5} \):
- We know that \( \frac{3}{5} \) is equivalent to \( \frac{9}{15} \).
- We need to see how many \( \frac{5}{15} \) sections fit into \( \frac{9}{15} \).
Step 4: Calculation
To find how many \( \frac{1}{3} \) (or \( \frac{5}{15} \)) fit into \( \frac{9}{15} \):
\[ \frac{9}{15} \div \frac{5}{15} = \frac{9}{15} \times \frac{15}{5} = \frac{9 \times 15}{15 \times 5} = \frac{9}{5} \]
Conclusion
Thus, the answer to \( \frac{3}{5} \div \frac{1}{3} \) is:
\[ \frac{9}{5} \text{ or } 1 \frac{4}{5} \]
So, we can conclude that there are \( 1 \frac{4}{5} \) (or \( 1.8 \) as a decimal) sections of \( \frac{1}{3} \) in \( \frac{3}{5} \).