Math worksheet for converting improper fractions using visual fraction models.

Let's solve each problem on "Convert Improper Fractions Sheet 5" step by step.

We are given diagrams of circles divided into equal parts, with some shaded. Each circle represents a whole. We need to convert the mixed numbers (shown visually) into improper fractions.

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🔍 How to Convert Mixed Numbers to Improper Fractions:

For a mixed number:
$$
a \frac{b}{c} = \frac{(a \times c) + b}{c}
$$

- $ a $: whole number
- $ b $: numerator of fraction part
- $ c $: denominator of fraction part

We'll use this formula for each problem.

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✔ Problem-by-Problem Solutions:

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#### 1)
Given: $ 3 \frac{2}{3} = \frac{11}{3} $

✔ Already solved correctly.

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#### 2)
Diagram: 3 full circles (each divided into 5), and 2/5 shaded in the last one.

So:
- Whole number: 3
- Fraction: $ \frac{2}{5} $
- So: $ 3 \frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} $

✔ Answer: $ \frac{17}{5} $

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#### 3)
Diagram: 3 full circles (divided into 4), and 1/4 shaded in the last.

So: $ 3 \frac{1}{4} = \frac{(3 \times 4) + 1}{4} = \frac{12 + 1}{4} = \frac{13}{4} $

✔ Answer: $ \frac{13}{4} $

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#### 4)
Diagram: 2 full circles (divided into 8), and 1/8 shaded in third.

So: $ 2 \frac{1}{8} = \frac{(2 \times 8) + 1}{8} = \frac{16 + 1}{8} = \frac{17}{8} $

✔ Answer: $ \frac{17}{8} $

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#### 5)
Diagram: 2 full circles (divided into 8), and 1/8 shaded in third.

Wait — actually, only 2 full and 1/8 shaded → same as #4?

Wait — let’s check:
- First two circles fully shaded → 2 wholes
- Third circle has only 1 out of 8 shaded → $ \frac{1}{8} $

So yes: $ 2 \frac{1}{8} = \frac{17}{8} $

✔ Answer: $ \frac{17}{8} $

Wait! But #4 and #5 look identical? Let's double-check.

Actually, looking at the image:

- #4: Three circles, first two full, third has 1/8 shaded → $ 2 \frac{1}{8} $
- #5: Two full circles, third has 1/8 shaded → also $ 2 \frac{1}{8} $

But wait — no, in #5, the third circle has only 1/8 shaded, so it's still $ 2 \frac{1}{8} $. So both #4 and #5 are the same?

Wait — perhaps there's a typo in labeling? Let's recheck.

Actually, looking again:

Wait — in #4, the third circle has 1/8 shaded → $ 2 \frac{1}{8} $

In #5, the third circle has 1/8 shaded → same thing?

But let's look more carefully:

No — #5: The third circle has only 1 section shaded → yes, $ \frac{1}{8} $

So both #4 and #5 are $ 2 \frac{1}{8} $? That seems odd.

Wait — maybe I'm misreading.

Let me re-express:

Actually, #4: 3 circles, first two full, third has 1/8 shaded → total = $ 2 + \frac{1}{8} = 2\frac{1}{8} $

#5: 3 circles, first two full, third has 1/8 shaded → same!

But that can't be — probably a mistake in the worksheet or my reading.

Wait — no, actually, #5 shows two full circles and one circle with only 1/8 shaded, so yes, $ 2 \frac{1}{8} $

But then why is it listed separately?

Wait — perhaps I made an error in counting.

Let’s go back and re-analyze all diagrams carefully.

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Let’s now go through each diagram based on visual interpretation.

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🔎 Re-evaluate Each Diagram Carefully

Each circle is divided into equal parts. Shaded portions represent the value.

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#### 1)
- 3 full circles (each divided into 3)
- One additional circle with 2/3 shaded
- Total: $ 3 + \frac{2}{3} = 3\frac{2}{3} = \frac{11}{3} $ ✔ Given

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#### 2)
- 3 full circles (each divided into 5)
- One circle with 2/5 shaded
- Total: $ 3 + \frac{2}{5} = 3\frac{2}{5} = \frac{17}{5} $

✔ $ \frac{17}{5} $

---

#### 3)
- 3 full circles (divided into 4)
- One circle with 1/4 shaded
- Total: $ 3 + \frac{1}{4} = 3\frac{1}{4} = \frac{13}{4} $

✔ $ \frac{13}{4} $

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#### 4)
- 2 full circles (divided into 8)
- One circle with 1/8 shaded
- Total: $ 2 + \frac{1}{8} = 2\frac{1}{8} = \frac{17}{8} $

✔ $ \frac{17}{8} $

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#### 5)
- 2 full circles (divided into 8)
- One circle with 1/8 shaded
- Same as #4 → $ 2\frac{1}{8} = \frac{17}{8} $

Wait — but that would make #4 and #5 the same.

But looking closely: Is #5 really the same?

Wait — no! In #5, the third circle has only 1/8 shaded, but the second circle is not full?

Wait — no, the second circle is fully shaded. First two are full, third has 1/8 shaded.

Yes — same as #4.

But maybe the labels are wrong?

Wait — perhaps I misread the divisions.

Let me describe what I see:

- #4: 3 circles, each divided into 8 parts.
- First two: all 8 shaded → full
- Third: only 1 part shaded → $ \frac{1}{8} $
- Total: $ 2\frac{1}{8} $

- #5: 3 circles, each divided into 8 parts.
- First two: all shaded → full
- Third: only 1 part shaded → $ \frac{1}{8} $
- Same as #4

So both are $ 2\frac{1}{8} $

But maybe the worksheet has a typo? Or perhaps I'm missing something.

Wait — perhaps #5 has only 2 circles, not 3?

No — three circles shown.

Wait — unless the third circle is not shaded at all? No — it has 1/8 shaded.

So yes — both #4 and #5 are $ 2\frac{1}{8} $

But that’s unlikely. Let’s continue and see.

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#### 6)
- 3 full circles (divided into 8)
- One circle with 1/8 shaded
- Wait — no: 3 full circles? Let’s count:

- First circle: full (8/8)
- Second: full (8/8)
- Third: 1/8 shaded → so total: $ 2 + \frac{1}{8} = 2\frac{1}{8} $

Same as above?

Wait — no: #6 has three circles, but only first two full, third has 1/8 shaded

So again $ 2\frac{1}{8} $

This suggests multiple problems have the same answer — possible, but let's check others.

Wait — maybe I miscounted the number of full circles.

Let’s list them clearly.

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Let’s go down the list with careful observation.

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🔍 Detailed Analysis of Each Diagram

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#### 1)
- 3 full circles (divided into 3 parts)
- 1 circle with 2/3 shaded
- Total: $ 3 + \frac{2}{3} = \frac{11}{3} $ ✔

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#### 2)
- 3 full circles (divided into 5)
- 1 circle with 2/5 shaded
- $ 3 + \frac{2}{5} = \frac{17}{5} $

✔ $ \frac{17}{5} $

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#### 3)
- 3 full circles (divided into 4)
- 1 circle with 1/4 shaded
- $ 3 + \frac{1}{4} = \frac{13}{4} $

✔ $ \frac{13}{4} $

---

#### 4)
- 2 full circles (divided into 8)
- 1 circle with 1/8 shaded
- $ 2 + \frac{1}{8} = \frac{17}{8} $

✔ $ \frac{17}{8} $

---

#### 5)
- 2 full circles (divided into 8)
- 1 circle with 1/8 shaded
- Same as #4 → $ \frac{17}{8} $

Wait — but now I notice: #5 has only two circles?

No — there are three circles.

First two full, third has 1/8 shaded → $ 2 + \frac{1}{8} = \frac{17}{8} $

Still same.

But maybe #5 is different?

Wait — look: #5 has three circles, each divided into 8.

- First: full
- Second: full
- Third: only 1/8 shaded → $ \frac{1}{8} $

So $ 2\frac{1}{8} = \frac{17}{8} $

Yes.

Now #6:

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#### 6)
- 3 full circles (divided into 8)
- 1 circle with 1/8 shaded
- Wait — how many circles? 4?

Wait — no: #6 has four circles?

Let’s count:

- First: full (8/8)
- Second: full (8/8)
- Third: full (8/8)
- Fourth: 1/8 shaded → so $ 3 + \frac{1}{8} = 3\frac{1}{8} = \frac{25}{8} $

Ah! Here’s the difference.

So #6 has three full circles and one with 1/8 shaded

So $ 3 + \frac{1}{8} = \frac{25}{8} $

✔ $ \frac{25}{8} $

But earlier I thought #4, #5, #6 were similar — but now:

- #4: 2 full + 1/8 → $ \frac{17}{8} $
- #5: 2 full + 1/8 → $ \frac{17}{8} $
- #6: 3 full + 1/8 → $ \frac{25}{8} $

But #6 is labeled as "6)" twice? Wait — no.

Wait — the sheet has:

- 1) to 6)
- Then 7) to 12)

But #6 appears twice? Look:

After #5, we have:

> 6) [diagram] =
> 6) [another diagram] =

Wait — that must be a typo. It says:

```
5) [diagram]
6) [diagram]
6) [diagram] ← duplicate label?
```

Wait — no — looking at the image:

It says:

```
5) [diagram]
6) [diagram]
6) [diagram] ← wait, two 6s?
```

No — actually, it's:

- 5)
- 6)
- 7)
- ...
- 12)

But in the table, row 6 has two entries: left and right.

Wait — no, the layout is:

| 1) | 7) |
| 2) | 8) |
| 3) | 9) |
| 4) | 10) |
| 5) | 11) |
| 6) | 12) |

So #6 is the bottom-left, and #12 is bottom-right.

But in the text, it says:

> 6) [diagram] =
> 6) [diagram] =

Wait — no, that’s a typo in your description.

Looking at the original image:

- Row 6: left side is labeled "6)", right side is labeled "12)"

Wait — no — let's read:

The rows are:

1) | 7)
2) | 8)
3) | 9)
4) | 10)
5) | 11)
6) | 12)

So #6 is left-bottom, #12 is right-bottom.

But in the user's image, it says:

> 6) [diagram] =
> 6) [diagram] =

That’s a mistake — probably a duplication.

But in the actual image, it should be:

- 6) (left): 3 full circles (divided into 8), and 1/8 shaded in fourth → $ 3 + \frac{1}{8} = \frac{25}{8} $
- 12) (right): 4 full circles (divided into 8), and 1/8 shaded in fifth → $ 4 + \frac{1}{8} = \frac{33}{8} $

But let's do them properly.

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Let’s now correctly analyze each one.

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✔ Final Corrected Answers

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#### 1)
- 3 full (3/3), and 2/3 shaded in fourth
- $ 3\frac{2}{3} = \frac{11}{3} $ ✔

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#### 2)
- 3 full (5/5), and 2/5 shaded in fourth
- $ 3\frac{2}{5} = \frac{17}{5} $

✔ $ \frac{17}{5} $

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#### 3)
- 3 full (4/4), and 1/4 shaded in fourth
- $ 3\frac{1}{4} = \frac{13}{4} $

✔ $ \frac{13}{4} $

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#### 4)
- 2 full (8/8), and 1/8 shaded in third
- $ 2\frac{1}{8} = \frac{17}{8} $

✔ $ \frac{17}{8} $

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#### 5)
- 2 full (8/8), and 1/8 shaded in third
- Same as #4 → $ \frac{17}{8} $

✔ $ \frac{17}{8} $

(Though likely a duplication or typo in the worksheet.)

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#### 6)
- 3 full (8/8), and 1/8 shaded in fourth
- $ 3 + \frac{1}{8} = \frac{25}{8} $

✔ $ \frac{25}{8} $

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#### 7)
- 5 circles, each divided into 8
- First four full → 4 wholes
- Fifth has 1/8 shaded → $ 4\frac{1}{8} = \frac{33}{8} $

✔ $ \frac{33}{8} $

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#### 8)
- 2 circles, each divided into 10 parts (since 10 sections)
- First full → 1 whole
- Second has 1/10 shaded → $ 1\frac{1}{10} = \frac{11}{10} $

✔ $ \frac{11}{10} $

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#### 9)
- 3 full circles (divided into 8), and 1/8 shaded in fourth
- $ 3 + \frac{1}{8} = \frac{25}{8} $

✔ $ \frac{25}{8} $

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#### 10)
- 2 full circles (divided into 8), and 1/8 shaded in third
- $ 2 + \frac{1}{8} = \frac{17}{8} $

✔ $ \frac{17}{8} $

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#### 11)
- 4 full circles (divided into 3), and 1/3 shaded in fifth
- $ 4 + \frac{1}{3} = \frac{13}{3} $

✔ $ \frac{13}{3} $

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#### 12)
- 4 full circles (divided into 8), and 1/8 shaded in fifth
- $ 4 + \frac{1}{8} = \frac{33}{8} $

✔ $ \frac{33}{8} $

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✔ Final Answer Key:

| Number | Mixed Number | Improper Fraction |
|--------|--------------|-------------------|
| 1) | $ 3\frac{2}{3} $ | $ \frac{11}{3} $ |
| 2) | $ 3\frac{2}{5} $ | $ \frac{17}{5} $ |
| 3) | $ 3\frac{1}{4} $ | $ \frac{13}{4} $ |
| 4) | $ 2\frac{1}{8} $ | $ \frac{17}{8} $ |
| 5) | $ 2\frac{1}{8} $ | $ \frac{17}{8} $ |
| 6) | $ 3\frac{1}{8} $ | $ \frac{25}{8} $ |
| 7) | $ 4\frac{1}{8} $ | $ \frac{33}{8} $ |
| 8) | $ 1\frac{1}{10} $ | $ \frac{11}{10} $ |
| 9) | $ 3\frac{1}{8} $ | $ \frac{25}{8} $ |
| 10) | $ 2\frac{1}{8} $ | $ \frac{17}{8} $ |
| 11) | $ 4\frac{1}{3} $ | $ \frac{13}{3} $ |
| 12) | $ 4\frac{1}{8} $ | $ \frac{33}{8} $ |

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📌 Summary of Steps:

To convert any mixed number to improper fraction:
1. Multiply the whole number by the denominator.
2. Add the numerator.
3. Place over the original denominator.

Example: $ 3\frac{2}{5} = \frac{(3 \times 5) + 2}{5} = \frac{15 + 2}{5} = \frac{17}{5} $

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Let me know if you'd like this formatted as a printable answer key!