What is a Mixed Number - Free Printable

Problem Explanation and Solution

The worksheet is divided into two main sections: Part A and Part B. Let's solve each part step by step.

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Part A: Understanding Mixed Numbers

#### Instructions:
- Each shaded fraction circle represents a whole.
- Write down the mixed numbers represented by these fraction circles.
- The first one is done for you: \( 2 \frac{1}{2} \).

#### Solution:

We need to count the number of completely shaded circles (which represent whole numbers) and the partially shaded circles (which represent fractions). Then, combine them to form mixed numbers.

1. Row 1 (Already Done):
- Completely shaded circles: 2
- Partially shaded circle: \( \frac{1}{2} \)
- Mixed number: \( 2 \frac{1}{2} \)

2. Row 2:
- Completely shaded circles: 1
- Partially shaded circle: \( \frac{1}{4} \)
- Mixed number: \( 1 \frac{1}{4} \)

3. Row 3:
- Completely shaded circles: 1
- Partially shaded circle: \( \frac{2}{3} \)
- Mixed number: \( 1 \frac{2}{3} \)

4. Row 4:
- Completely shaded circles: 1
- Partially shaded circle: \( \frac{3}{8} \)
- Mixed number: \( 1 \frac{3}{8} \)

5. Row 5:
- Completely shaded circles: 2
- Partially shaded circle: \( \frac{1}{4} \)
- Mixed number: \( 2 \frac{1}{4} \)

6. Row 6:
- Completely shaded circles: 4
- Partially shaded circle: \( \frac{1}{3} \)
- Mixed number: \( 4 \frac{1}{3} \)

7. Row 7:
- Completely shaded circles: 1
- Partially shaded circle: \( \frac{2}{5} \)
- Mixed number: \( 1 \frac{2}{5} \)

8. Row 8:
- Completely shaded circles: 4
- Partially shaded circle: \( \frac{4}{8} = \frac{1}{2} \)
- Mixed number: \( 4 \frac{1}{2} \)

9. Row 9:
- Completely shaded circles: 2
- Partially shaded circle: \( \frac{2}{3} \)
- Mixed number: \( 2 \frac{2}{3} \)

10. Row 10:
- Completely shaded circles: 4
- Partially shaded circle: \( \frac{1}{5} \)
- Mixed number: \( 4 \frac{1}{5} \)

#### Final Answers for Part A:
\[
\begin{array}{c|c}
\text{Row} & \text{Mixed Number} \\
\hline
1 & 2 \frac{1}{2} \\
2 & 1 \frac{1}{4} \\
3 & 1 \frac{2}{3} \\
4 & 1 \frac{3}{8} \\
5 & 2 \frac{1}{4} \\
6 & 4 \frac{1}{3} \\
7 & 1 \frac{2}{5} \\
8 & 4 \frac{1}{2} \\
9 & 2 \frac{2}{3} \\
10 & 4 \frac{1}{5} \\
\end{array}
\]

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Part B: Shading Fractions

#### Instructions:
- Shade the fractions to represent each of the given mixed numbers.

#### Solution:

For each mixed number, we need to shade the appropriate number of whole circles and the fractional part in the next circle.

1. Row 1: \( 1 \frac{3}{4} \)
- Shade 1 whole circle.
- In the next circle, shade 3 out of 4 parts.

2. Row 2: \( 1 \frac{2}{3} \)
- Shade 1 whole circle.
- In the next circle, shade 2 out of 3 parts.

3. Row 3: \( 3 \frac{1}{2} \)
- Shade 3 whole circles.
- In the next circle, shade 1 out of 2 parts.

4. Row 4: \( 2 \frac{1}{4} \)
- Shade 2 whole circles.
- In the next circle, shade 1 out of 4 parts.

5. Row 5: \( 1 \frac{4}{5} \)
- Shade 1 whole circle.
- In the next circle, shade 4 out of 5 parts.

6. Row 6: \( 3 \frac{1}{6} \)
- Shade 3 whole circles.
- In the next circle, shade 1 out of 6 parts.

7. Row 7: \( 3 \frac{3}{4} \)
- Shade 3 whole circles.
- In the next circle, shade 3 out of 4 parts.

8. Row 8: \( 2 \frac{1}{3} \)
- Shade 2 whole circles.
- In the next circle, shade 1 out of 3 parts.

9. Row 9: \( 1 \frac{5}{6} \)
- Shade 1 whole circle.
- In the next circle, shade 5 out of 6 parts.

10. Row 10: \( 3 \frac{3}{5} \)
- Shade 3 whole circles.
- In the next circle, shade 3 out of 5 parts.

#### Final Answers for Part B:
- Follow the instructions above to shade the circles accordingly.

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Final Answer:

\[
\boxed{
\begin{array}{c|c}
\text{Row} & \text{Mixed Number} \\
\hline
1 & 2 \frac{1}{2} \\
2 & 1 \frac{1}{4} \\
3 & 1 \frac{2}{3} \\
4 & 1 \frac{3}{8} \\
5 & 2 \frac{1}{4} \\
6 & 4 \frac{1}{3} \\
7 & 1 \frac{2}{5} \\
8 & 4 \frac{1}{2} \\
9 & 2 \frac{2}{3} \\
10 & 4 \frac{1}{5} \\
\end{array}
}
\]