Math worksheet for converting visual representations of fractions into mixed numbers and improper fractions.

Explanation:
We are asked to write each amount as a mixed number (for problems 1–5) and as an improper fraction (for problems 6–11). Let’s go one by one.

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Problem 1:
There are 4 rectangles, each divided into 4 equal parts.
- First 3 rectangles are fully shaded → 3 × 4/4 = 3 wholes.
- Fourth rectangle has 3 out of 4 parts shaded → 3/4.
So total = 3 + 3/4 = 3 3/4.

Problem 2:
Two circles, each divided into 3 equal parts.
- First circle: all 3 parts shaded → 1 whole.
- Second circle: 2 out of 3 parts shaded → 2/3.
Total = 1 + 2/3 = 1 2/3.

Problem 3:
9 rectangles, each divided into 4 parts.
- First 8 rectangles are fully shaded → 8 wholes.
- Ninth rectangle: 3 out of 4 parts shaded → 3/4.
Total = 8 + 3/4 = 8 3/4.

Problem 4:
Two circles, each divided into 4 parts.
- First circle: all 4 parts shaded → 1 whole.
- Second circle: 2 out of 4 parts shaded → 2/4 = 1/2.
Total = 1 + 1/2 = 1 1/2.

Problem 5:
Four rectangles, each divided into 5 parts.
- First 3 rectangles fully shaded → 3 wholes.
- Fourth rectangle: 3 out of 5 parts shaded → 3/5.
Total = 3 + 3/5 = 3 3/5.

Now improper fractions (numerator > denominator):

Problem 6:
7 full rectangles (each with 5 parts), plus 1 rectangle with 3 out of 5 shaded.
Each rectangle = 5/5 = 1.
So total parts = 7×5 + 3 = 35 + 3 = 38/5.

Problem 7:
Three circles, each divided into 2 parts.
Each full circle = 2/2 = 1.
All three circles have 1 part shaded? Wait — look carefully:
- First circle: 1 shaded (out of 2) → 1/2
- Second: same → 1/2
- Third: half shaded → 1/2
Wait — actually, the image shows:
Each circle is split in half, and in each, exactly one half is shaded. So each is 1/2.
Three halves = 1/2 + 1/2 + 1/2 = 3/2.
So improper fraction = 3/2.

Problem 8:
Two circles, each divided into 6 parts.
- First circle: 5 shaded → 5/6
- Second circle: 5 shaded → 5/6
Total = 5/6 + 5/6 = 10/6 = simplify? But we want improper fraction — keep as 10/6 or reduce? Usually improper fractions are simplified unless told otherwise. But standard is to simplify.
10/6 = 5/3.

Wait — let’s double-check: The problem says “Write each amount as an improper fraction.” It doesn’t say *simplified*, but conventionally we simplify. Let’s verify other problems for pattern.

Problem 9:
Four circles, each divided into 3 parts.
- First 3 circles: all 3 parts shaded → 3 × 3/3 = 3 wholes = 9/3
- Fourth circle: 2 out of 3 shaded → 2/3
Total = 9/3 + 2/3 = 11/3
→ 11/3

Problem 10:
Four rectangles, each divided into 5 parts.
- First 3 rectangles fully shaded → 3 × 5/5 = 15/5
- Fourth rectangle: 2 out of 5 shaded → 2/5
Total = 15/5 + 2/5 = 17/5
→ 17/5

Problem 11:
Three circles, each divided into 6 parts.
Each circle has 5 shaded parts → 5/6 each.
3 × 5/6 = 15/6 = simplify → divide numerator & denominator by 3 → 5/2

Let’s now verify all:

1) 3 3/4
2) 1 2/3
3) 8 3/4
4) 1 1/2
5) 3 3/5
6) 38/5
7) 3/2
8) 10/6 = 5/3
9) 11/3
10) 17/5
11) 15/6 = 5/2

Yes — all consistent.

Final Answer:
1. 3 3/4
2. 1 2/3
3. 8 3/4
4. 1 1/2
5. 3 3/5
6. 38/5
7. 3/2
8. 5/3
9. 11/3
10. 17/5
11. 5/2