Question

7 thirds divided by 2 thirds equals 3 whole groups and 1 fractional part.
what fraction of a group is left over? 1 third/ 2 thirds
I have ________ of a group left over.

Answer 1

To find the leftover fraction after dividing \( \frac{7}{3} \) by \( \frac{2}{3} \):

1. **Perform the division**:
\[
\frac{7}{3} \div \frac{2}{3} = \frac{7}{3} \times \frac{3}{2} = \frac{7 \times 3}{3 \times 2} = \frac{21}{6} = \frac{7}{2} = 3 \frac{1}{2}
\]

2. **Interpret the result**:
From the calculation, \( \frac{7}{2} \) is equal to \( 3 \) whole groups and \( \frac{1}{2} \).

3. **Finding the leftover part**:
Since you indicated that your result is "3 whole groups and 1 fractional part," it seems you're looking for what fraction remains after taking the whole number.

In terms of your question about left over after grouping, when you have:

- **3 whole groups**: this accounts for \( 3 \)
- **Fractional part**: since you calculated it was \( \frac{1}{2} \), not \( \frac{1}{3} \) or \( \frac{2}{3} \).

Thus, you have:

\[
\text{I have } \frac{1}{2} \text{ of a group left over.}
\]

So you would fill in the blank with \( \frac{1}{2} \).