5th Grade Division Worksheet: Multiplication & Division Fact Families

Let's solve the "Multiplication & Division Fact Families" worksheet step by step. Each triangle represents a fact family using three numbers: two factors and their product (or dividend, divisor, and quotient). The goal is to write all four related multiplication and division equations.

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🔷 Fact Family Rule

For any three numbers in a fact family:
- If $ a \times b = c $, then:
- $ b \times a = c $
- $ c \div a = b $
- $ c \div b = a $

We'll use this pattern for each triangle.

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✔ Problem 1: Triangle with numbers 66, 11, 6

The top number is the product (66), and the two bottom numbers are the factors (11 and 6).

So:
- $ 11 \times 6 = 66 $
- $ 6 \times 11 = 66 $
- $ 66 \div 11 = 6 $
- $ 66 \div 6 = 11 $

Answer:
```
11 × 6 = 66
6 × 11 = 66
66 ÷ 11 = 6
66 ÷ 6 = 11
```

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✔ Problem 2: Triangle with numbers 63, 9, 7

Top = 63, bottom = 9 and 7

- $ 9 \times 7 = 63 $
- $ 7 \times 9 = 63 $
- $ 63 \div 9 = 7 $
- $ 63 \div 7 = 9 $

Answer:
```
9 × 7 = 63
7 × 9 = 63
63 ÷ 9 = 7
63 ÷ 7 = 9
```

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✔ Problem 3: Triangle with numbers 40, 5, 8

Top = 40, bottom = 5 and 8

- $ 5 \times 8 = 40 $
- $ 8 \times 5 = 40 $
- $ 40 \div 5 = 8 $
- $ 40 \div 8 = 5 $

Answer:
```
5 × 8 = 40
8 × 5 = 40
40 ÷ 5 = 8
40 ÷ 8 = 5
```

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✔ Problem 4: Triangle with numbers 72, 6, 12

Top = 72, bottom = 6 and 12

- $ 6 \times 12 = 72 $
- $ 12 \times 6 = 72 $
- $ 72 \div 6 = 12 $
- $ 72 \div 12 = 6 $

Answer:
```
6 × 12 = 72
12 × 6 = 72
72 ÷ 6 = 12
72 ÷ 12 = 6
```

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📝 Final Answers (Fill in the blanks):

#### 1.
```
11 × 6 = 66
6 × 11 = 66
66 ÷ 11 = 6
66 ÷ 6 = 11
```

#### 2.
```
9 × 7 = 63
7 × 9 = 63
63 ÷ 9 = 7
63 ÷ 7 = 9
```

#### 3.
```
5 × 8 = 40
8 × 5 = 40
40 ÷ 5 = 8
40 ÷ 8 = 5
```

#### 4.
```
6 × 12 = 72
12 × 6 = 72
72 ÷ 6 = 12
72 ÷ 12 = 6
```

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✔ These are all correct multiplication and division fact families! This helps students understand how multiplication and division are inverse operations.