Math worksheet for dividing whole numbers by fractions using visual models.

Let's solve each problem on the worksheet "Dividing Whole Numbers by Fractions Using Models – Sheet 2" step-by-step, using fraction strips and visual models as intended. The goal is to divide a whole number by a fraction and determine how many times the fraction fits into the whole.

---

🔍 General Concept:

When dividing a whole number by a fraction (e.g., $ 4 \div \frac{1}{2} $), you are asking:
"How many groups of $ \frac{1}{2} $ are in 4?"

We can model this using fraction strips — each whole is divided into parts equal to the denominator of the fraction.

The rule is:
$$
\text{Whole} \div \frac{a}{b} = \text{Whole} \times \frac{b}{a}
$$
But here we're focusing on models, so we'll use visual reasoning.

---

✔ Problem 1: $ 4 \div \frac{1}{2} $

- Each whole is divided into 2 parts (since denominator is 2).
- So, each whole has 2 halves.
- We have 4 wholes → $ 4 \times 2 = 8 $ halves.
- So, $ \frac{1}{2} $ goes into 4 exactly 8 times.

✔ Answer: $ 8 $

👉 Draw 4 boxes, each split into 2 equal parts → total of 8 half pieces.

---

✔ Problem 2: $ 2 \div \frac{2}{5} $

- We need to see how many $ \frac{2}{5} $ fit into 2.
- First, divide each whole into 5 parts (denominator is 5).
- One whole has 5 fifths → 2 wholes = $ 2 \times 5 = 10 $ fifths.
- Each $ \frac{2}{5} $ uses 2 of those fifths.
- So, number of $ \frac{2}{5} $ in 10 fifths: $ 10 \div 2 = 5 $

✔ Answer: $ 5 $

👉 Draw 2 boxes, each split into 5 parts → total 10 parts. Group them into pairs (each pair is $ \frac{2}{5} $) → 5 groups.

---

✔ Problem 3: $ 6 \div \frac{3}{4} $

- Divide each whole into 4 parts (denominator = 4).
- 6 wholes → $ 6 \times 4 = 24 $ quarters.
- Each $ \frac{3}{4} $ uses 3 quarters.
- Number of $ \frac{3}{4} $ in 24 quarters: $ 24 \div 3 = 8 $

✔ Answer: $ 8 $

👉 Draw 6 boxes, each split into 4 parts → 24 parts. Group into sets of 3 → 8 groups.

---

✔ Problem 4: $ 3 \div \frac{3}{7} $

- Divide each whole into 7 parts.
- 3 wholes → $ 3 \times 7 = 21 $ sevenths.
- Each $ \frac{3}{7} $ uses 3 sevenths.
- Number of $ \frac{3}{7} $: $ 21 \div 3 = 7 $

✔ Answer: $ 7 $

👉 3 boxes, each split into 7 parts → 21 parts. Group into sets of 3 → 7 groups.

---

✔ Problem 5: $ 2 \div \frac{1}{6} $

- Divide each whole into 6 parts.
- 2 wholes → $ 2 \times 6 = 12 $ sixths.
- Each $ \frac{1}{6} $ is one part.
- So, $ 12 $ parts → $ 12 $ times $ \frac{1}{6} $

✔ Answer: $ 12 $

👉 2 boxes, each split into 6 parts → 12 small parts.

---

✔ Problem 6: $ 4 \div \frac{4}{7} $

- Divide each whole into 7 parts.
- 4 wholes → $ 4 \times 7 = 28 $ sevenths.
- Each $ \frac{4}{7} $ uses 4 sevenths.
- Number of $ \frac{4}{7} $: $ 28 \div 4 = 7 $

✔ Answer: $ 7 $

👉 4 boxes, each split into 7 parts → 28 parts. Group into sets of 4 → 7 groups.

---

✔ Problem 7: $ 5 \div \frac{1}{3} $

- Divide each whole into 3 parts.
- 5 wholes → $ 5 \times 3 = 15 $ thirds.
- Each $ \frac{1}{3} $ is one part.
- So, $ 15 $ times $ \frac{1}{3} $

✔ Answer: $ 15 $

👉 5 boxes, each split into 3 parts → 15 parts.

---

✔ Problem 8: $ 6 \div \frac{3}{5} $

- Divide each whole into 5 parts.
- 6 wholes → $ 6 \times 5 = 30 $ fifths.
- Each $ \frac{3}{5} $ uses 3 fifths.
- Number of $ \frac{3}{5} $: $ 30 \div 3 = 10 $

✔ Answer: $ 10 $

👉 6 boxes, each split into 5 parts → 30 parts. Group into sets of 3 → 10 groups.

---

📌 Final Answers:

| Problem | Expression | Answer |
|--------|--------------------|--------|
| 1 | $ 4 \div \frac{1}{2} $ | 8 |
| 2 | $ 2 \div \frac{2}{5} $ | 5 |
| 3 | $ 6 \div \frac{3}{4} $ | 8 |
| 4 | $ 3 \div \frac{3}{7} $ | 7 |
| 5 | $ 2 \div \frac{1}{6} $ | 12 |
| 6 | $ 4 \div \frac{4}{7} $ | 7 |
| 7 | $ 5 \div \frac{1}{3} $ | 15 |
| 8 | $ 6 \div \frac{3}{5} $ | 10 |

---

✔ How to Fill in the Strips:

For each problem:
- Draw the number of whole strips (equal to the whole number).
- Divide each strip into parts based on the denominator.
- Then group the parts into chunks of size equal to the numerator of the fraction.
- Count how many such chunks you get.

Example for #1:
```
[---] [---] [---] [---]
Each box represents 1 whole, split into 2 parts → 8 total half-pieces → 8 groups of 1/2.
```

---

Let me know if you'd like a printable version with drawn models!