Math worksheet for converting fraction models into mixed numbers and improper fractions.

To solve the problem, we need to analyze each fraction model and determine the corresponding mixed number and improper fraction. Let's go through each row step by step.

Row 1: Circles

- Fraction Model: There are 3 circles, each divided into 4 equal parts.
- The first two circles are completely shaded.
- The third circle has 2 out of 4 parts shaded.
- Mixed Number:
- Completely shaded circles: \(2\) (since 2 full circles are shaded).
- Remaining shaded parts: \(2\) out of \(4\) in the third circle.
- Mixed number: \(2 \frac{2}{4}\).
- Improper Fraction:
- Total shaded parts: \(2 \times 4 + 2 = 8 + 2 = 10\).
- Denominator: \(4\) (since each circle is divided into 4 parts).
- Improper fraction: \(\frac{10}{4}\).

Row 2: Hexagons

- Fraction Model: There are 3 hexagons, each divided into 6 equal parts.
- The first two hexagons are completely shaded.
- The third hexagon has 5 out of 6 parts shaded.
- Mixed Number:
- Completely shaded hexagons: \(2\) (since 2 full hexagons are shaded).
- Remaining shaded parts: \(5\) out of \(6\) in the third hexagon.
- Mixed number: \(2 \frac{5}{6}\).
- Improper Fraction:
- Total shaded parts: \(2 \times 6 + 5 = 12 + 5 = 17\).
- Denominator: \(6\) (since each hexagon is divided into 6 parts).
- Improper fraction: \(\frac{17}{6}\).

Row 3: Pentagons

- Fraction Model: There are 4 pentagons, each divided into 5 equal parts.
- The first three pentagons are completely shaded.
- The fourth pentagon has 3 out of 5 parts shaded.
- Mixed Number:
- Completely shaded pentagons: \(3\) (since 3 full pentagons are shaded).
- Remaining shaded parts: \(3\) out of \(5\) in the fourth pentagon.
- Mixed number: \(3 \frac{3}{5}\).
- Improper Fraction:
- Total shaded parts: \(3 \times 5 + 3 = 15 + 3 = 18\).
- Denominator: \(5\) (since each pentagon is divided into 5 parts).
- Improper fraction: \(\frac{18}{5}\).

Row 4: Octagons

- Fraction Model: There are 2 octagons, each divided into 8 equal parts.
- The first octagon is completely shaded.
- The second octagon has 5 out of 8 parts shaded.
- Mixed Number:
- Completely shaded octagons: \(1\) (since 1 full octagon is shaded).
- Remaining shaded parts: \(5\) out of \(8\) in the second octagon.
- Mixed number: \(1 \frac{5}{8}\).
- Improper Fraction:
- Total shaded parts: \(1 \times 8 + 5 = 8 + 5 = 13\).
- Denominator: \(8\) (since each octagon is divided into 8 parts).
- Improper fraction: \(\frac{13}{8}\).

Final Answer

Putting it all together, the completed table looks like this:

| Fraction Model | Mixed Number | Improper Fraction |
|-------------------------------------------------------------------------------|------------------|--------------------|
| Example: | \(1 \frac{3}{4}\) | \(\frac{7}{4}\) |
| Circles: | \(2 \frac{2}{4}\) | \(\frac{10}{4}\) |
| Hexagons: | \(2 \frac{5}{6}\) | \(\frac{17}{6}\) |
| Pentagons: | \(3 \frac{3}{5}\) | \(\frac{18}{5}\) |
| Octagons: | \(1 \frac{5}{8}\) | \(\frac{13}{8}\) |

Thus, the final answer is:

\[
\boxed{
\begin{array}{ccc}
\text{Circles} & 2 \frac{2}{4} & \frac{10}{4} \\
\text{Hexagons} & 2 \frac{5}{6} & \frac{17}{6} \\
\text{Pentagons} & 3 \frac{3}{5} & \frac{18}{5} \\
\text{Octagons} & 1 \frac{5}{8} & \frac{13}{8} \\
\end{array}
}
\]