Improper Fractions Worksheet: Name the improper fractions represented by the diagrams.

Let’s solve each problem step by step.

We are looking for improper fractions — that means the numerator (top number) is bigger than or equal to the denominator (bottom number). Each diagram shows shaded parts of shapes divided into equal pieces. We count total shaded pieces and divide by how many pieces make one whole shape.

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Problem 1:
- First circle: divided into 4 parts, all 4 shaded → 4/4 = 1 whole
- Second circle: divided into 4 parts, 2 shaded → 2/4
- Total shaded = 4 + 2 = 6 parts out of 4 per whole → 6/4

But we can also think: first circle is 1 whole (4/4), second is 2/4 → total = 6/4
✔ Improper fraction: 6/4

*(Note: Sometimes they want it simplified, but the worksheet says “name the improper fractions represented”, so we leave as is unless told otherwise.)*

Wait — let’s double-check: The instruction is to name the improper fraction shown by the diagrams. So we add up all shaded parts over the size of one whole.

Yes, 6 shaded quarters → 6/4

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Problem 2:
- First square: 3x3 grid = 9 parts, all 9 shaded → 9/9 = 1
- Second square: 3x3 grid = 9 parts, 6 shaded → 6/9
- Total shaded = 9 + 6 = 15 parts out of 9 per whole → 15/9

✔ Improper fraction: 15/9

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Problem 3:
- First circle: divided into 8 parts, 7 shaded → 7/8
- Second circle: divided into 8 parts, 3 shaded → 3/8
- Total shaded = 7 + 3 = 10 parts out of 8 per whole → 10/8

✔ Improper fraction: 10/8

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Problem 4:
- First rectangle: 4x3 grid? Wait — actually, looking at the diagram description: it's a grid with 4 rows and 3 columns? No — wait, in the image, problem 4 has two rectangles.

Actually, from standard interpretation:

First rectangle: 4 rows × 3 columns = 12 small squares? But no — let me re-think based on common worksheets.

Wait — better approach: Count total shaded units and what one whole is.

In Problem 4:
- First shape: 4 rows, 3 columns → 12 small squares, all shaded → 12/12 = 1
- Second shape: same size, 4 rows × 3 columns = 12 squares, top row shaded → 3 shaded → 3/12
- Total shaded = 12 + 3 = 15 parts out of 12 per whole → 15/12

✔ Improper fraction: 15/12

Wait — but maybe the grid is 3x4? Same thing.

Alternatively, perhaps it’s 4 columns and 3 rows? Still 12.

Yes, 15/12.

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Problem 5:
- First circle: divided into 10 parts, all 10 shaded → 10/10 = 1
- Second circle: divided into 10 parts, 4 shaded → 4/10
- Total shaded = 10 + 4 = 14 parts out of 10 per whole → 14/10

✔ Improper fraction: 14/10

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Problem 6:
- Three circles, each divided into 5 parts.
- First circle: all 5 shaded → 5/5
- Second circle: all 5 shaded → 5/5
- Third circle: 1 shaded → 1/5
- Total shaded = 5 + 5 + 1 = 11 parts out of 5 per whole → 11/5

✔ Improper fraction: 11/5

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Now, let’s verify each again quickly:

1. Two circles, 4 parts each: 4 + 2 = 6 → 6/4 ✔️
2. Two 3x3 grids: 9 + 6 = 15 → 15/9 ✔️
3. Two 8-part circles: 7 + 3 = 10 → 10/8 ✔️
4. Two 12-part grids: 12 + 3 = 15 → 15/12 ✔️
5. Two 10-part circles: 10 + 4 = 14 → 14/10 ✔️
6. Three 5-part circles: 5 + 5 + 1 = 11 → 11/5 ✔️

All correct.

Final Answer:
1. 6/4
2. 15/9
3. 10/8
4. 15/12
5. 14/10
6. 11/5