Division: Arrays for Division (Part One) | Worksheet - Free Printable

Let's solve the division problems using arrays as shown in the worksheet. The idea is to use equal groups of X’s to represent the division, where:

- The divisor tells you how many X’s to draw in each row.
- The total number of X’s should equal the dividend.
- The quotient is the number of rows (how many groups you can make).

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🔹 Step-by-step Solutions

#### 1. 28 ÷ 7 = ?
- We need to draw 7 X’s per row until we reach a total of 28 X’s.
- How many rows of 7 make 28?
- 7 × 4 = 28 → So, 4 rows.
- ✔ Answer: 4

```
X X X X X X X
X X X X X X X
X X X X X X X
X X X X X X X
```

#### 2. 16 ÷ 4 = ?
- Draw 4 X’s per row, total 16 X’s.
- 4 × 4 = 16 → 4 rows.
- ✔ Answer: 4

```
X X X X
X X X X
X X X X
X X X X
```

#### 3. 18 ÷ 2 = ?
- Draw 2 X’s per row, total 18 X’s.
- 2 × 9 = 18 → 9 rows.
- ✔ Answer: 9

```
X X
X X
X X
X X
X X
X X
X X
X X
X X
```

#### 4. 10 ÷ 5 = ?
- Draw 5 X’s per row, total 10 X’s.
- 5 × 2 = 10 → 2 rows.
- ✔ Answer: 2

```
X X X X X
X X X X X
```

#### 5. 12 ÷ 3 = ?
- Draw 3 X’s per row, total 12 X’s.
- 3 × 4 = 12 → 4 rows.
- ✔ Answer: 4

```
X X X
X X X
X X X
X X X
```

#### 6. 20 ÷ 5 = ?
- Draw 5 X’s per row, total 20 X’s.
- 5 × 4 = 20 → 4 rows.
- ✔ Answer: 4

```
X X X X X
X X X X X
X X X X X
X X X X X
```

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🔹 Now, interpret the arrays at the bottom

We are given three arrays and asked: What division problems do they represent?

#### Array 1:
```
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
```
- There are 4 rows of 10 X’s each.
- Total = 4 × 10 = 40
- So, this represents: 40 ÷ 10 = 4 or 40 ÷ 4 = 10
- But since the divisor tells us how many in each row, and here each row has 10, the divisor is 10.
- ✔ Division problem: 40 ÷ 10 = 4

#### Array 2:
```
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
```
- 5 rows of 10 X’s → Total = 50
- Each row has 10 X’s → Divisor = 10
- So, 50 ÷ 10 = 5
- ✔ Division problem: 50 ÷ 10 = 5

#### Array 3:
```
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
X X X X X X X X X X
```
- 6 rows of 10 X’s → Total = 60
- Divisor = 10
- So, 60 ÷ 10 = 6
- ✔ Division problem: 60 ÷ 10 = 6

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✔ Final Answers:

#### Fill-in-the-blank Problems:
1. 28 ÷ 7 = 4
2. 16 ÷ 4 = 4
3. 18 ÷ 2 = 9
4. 10 ÷ 5 = 2
5. 12 ÷ 3 = 4
6. 20 ÷ 5 = 4

#### What division problems do the arrays represent?
1. 40 ÷ 10 = 4
2. 50 ÷ 10 = 5
3. 60 ÷ 10 = 6

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This method helps visualize division as grouping — very helpful for understanding the concept! 🎉