To divide the fractions \( \frac{3}{5} \div \frac{1}{3} \), we can think about it as asking how many \( \frac{1}{3} \) are in \( \frac{3}{5} \).
Using the fraction bars to visualize:
- Full Whole: The fraction bars represent \( 1 \) whole.
- Thirds: There are \( 3 \) thirds in one whole, so we can label \( 1 \) whole as \( 3/3 \).
- Fifths: There are \( 5 \) fifths in one whole, representing how \( 1 \) whole can also be divided into \( 5/5 \).
- Fifteenths: To work with both thirds and fifths, we can convert them to fifteenths to compare. Each \( \frac{1}{3} \) is equivalent to \( \frac{5}{15} \) (since \( 3 \times 5 = 15 \)), and each \( \frac{1}{5} \) is equivalent to \( \frac{3}{15} \) (since \( 5 \times 3 = 15 \)).
Now, since we want to find out how many \( \frac{1}{3} \) (or \( \frac{5}{15} \)) fit into \( \frac{3}{5} \) (or \( \frac{9}{15} \) since \( \frac{3}{5} = \frac{9/15} \)):
So we can fill in the blank:
Think: How many \( \frac{1}{3} \) are in \( \frac{3}{5} \)?
To find the answer mathematically:
- Flip the second fraction: \( \frac{3}{5} \div \frac{1}{3} \) is the same as \( \frac{3}{5} \times \frac{3}{1} \).
- Multiply: \( \frac{3 \times 3}{5 \times 1} = \frac{9}{5} \).
So, the result of \( \frac{3}{5} \div \frac{1}{3} = \frac{9}{5} \), or \( 1 \frac{4}{5} \).
1 answer