Mixed Numbers worksheet for teaching fraction concepts using visual shapes.

Let's solve each part of this "Mixed Numbers" worksheet step by step. The goal is to shade the correct portion of each group of shapes based on the given mixed number.

---

🔹 Understanding the Task:

Each question asks you to shade a mixed number of the pictures (e.g., $1\frac{3}{5}$ means 1 whole picture + 3 out of 5 parts of another). We’ll interpret each mixed number and apply it to the corresponding group of shapes.

---

✔ a. Shade in $1\frac{3}{5}$ of the picture.

- There are 5 pentagons, each divided into 5 equal parts.
- $1\frac{3}{5} = 1 + \frac{3}{5}$
- So, we need to fully shade 1 pentagon and shade 3 out of 5 parts in a second pentagon.
- The remaining 3 pentagons remain unshaded.

✔ Answer:
- Shade all 5 sections of one pentagon.
- In a second pentagon, shade 3 of the 5 sections.
- Leave the other 3 pentagons blank.

---

✔ b. Shade in $4\frac{1}{2}$ of the picture.

- There are 6 diamonds, each divided into 2 equal parts (so each diamond represents a half).
- $4\frac{1}{2} = 4 + \frac{1}{2}$
- That means: fully shade 4 diamonds, and half of one more.
- Since each diamond has 2 parts, shading 1 part of a diamond = $\frac{1}{2}$.

✔ Answer:
- Shade both halves of 4 diamonds (i.e., fully shade 4 diamonds).
- In the fifth diamond, shade 1 of the 2 parts.
- Leave the sixth diamond completely unshaded.

---

✔ c. Shade in $2\frac{3}{4}$ of the picture.

- There are 5 rectangles, each divided into 4 equal parts.
- $2\frac{3}{4} = 2 + \frac{3}{4}$
- So, fully shade 2 rectangles, and shade 3 out of 4 parts in a third rectangle.

✔ Answer:
- Shade all 4 parts of 2 rectangles.
- In the third rectangle, shade 3 of the 4 parts.
- Leave the last 2 rectangles unshaded.

---

✔ d. Shade in $2\frac{1}{5}$ of the picture.

- There are 5 stars, each divided into 5 equal parts.
- $2\frac{1}{5} = 2 + \frac{1}{5}$
- Fully shade 2 stars, and shade 1 part of a third star.

✔ Answer:
- Shade all 5 parts of 2 stars.
- In the third star, shade 1 of the 5 parts.
- Leave the remaining 2 stars unshaded.

---

✔ e. Shade in $1\frac{2}{3}$ of the picture.

- There are 5 circles, each divided into 3 equal parts.
- $1\frac{2}{3} = 1 + \frac{2}{3}$
- Fully shade 1 circle, and shade 2 of the 3 parts in a second circle.

✔ Answer:
- Shade all 3 parts of 1 circle.
- In the second circle, shade 2 of the 3 parts.
- Leave the other 3 circles unshaded.

---

✔ f. Shade in $3\frac{1}{2}$ of the picture.

- There are 6 triangles, each divided into 2 equal parts.
- $3\frac{1}{2} = 3 + \frac{1}{2}$
- Fully shade 3 triangles, and shade 1 part of a fourth triangle.

✔ Answer:
- Shade both parts of 3 triangles.
- In the fourth triangle, shade 1 of the 2 parts.
- Leave the last 2 triangles unshaded.

---

📌 Summary of Shading Instructions:

| Letter | Mixed Number | How to Shade |
|--------|------------------|--------------|
| a | $1\frac{3}{5}$ | 1 full pentagon + 3/5 of another |
| b | $4\frac{1}{2}$ | 4 full diamonds + 1/2 of another |
| c | $2\frac{3}{4}$ | 2 full rectangles + 3/4 of another |
| d | $2\frac{1}{5}$ | 2 full stars + 1/5 of another |
| e | $1\frac{2}{3}$ | 1 full circle + 2/3 of another |
| f | $3\frac{1}{2}$ | 3 full triangles + 1/2 of another |

---

✔ Final Tips for Students:

- Always break down the mixed number: whole number + fraction.
- Use the total number of shapes and their divisions to guide your shading.
- Be careful not to over-shade or under-shade!

Let me know if you'd like a visual sketch explanation!