Distributive Property:Math Worksheets - Free Printable

The task involves solving the given problems using the distributive property. The distributive property states that:

$$
a(b + c) = ab + ac
$$

This means you multiply the number outside the parentheses by each term inside the parentheses and then add or subtract as needed.

Let's solve each problem step by step:

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Problem 1: \( 8(3+5) \)

1. Apply the distributive property:
$$
8(3+5) = 8 \cdot 3 + 8 \cdot 5
$$

2. Perform the multiplications:
$$
8 \cdot 3 = 24, \quad 8 \cdot 5 = 40
$$

3. Add the results:
$$
24 + 40 = 64
$$

Answer:
$$
\boxed{64}
$$

---

Problem 2: \( 4(5-2) \)

1. Apply the distributive property:
$$
4(5-2) = 4 \cdot 5 - 4 \cdot 2
$$

2. Perform the multiplications:
$$
4 \cdot 5 = 20, \quad 4 \cdot 2 = 8
$$

3. Subtract the results:
$$
20 - 8 = 12
$$

Answer:
$$
\boxed{12}
$$

---

Problem 3: \( 3(8-1) \)

1. Apply the distributive property:
$$
3(8-1) = 3 \cdot 8 - 3 \cdot 1
$$

2. Perform the multiplications:
$$
3 \cdot 8 = 24, \quad 3 \cdot 1 = 3
$$

3. Subtract the results:
$$
24 - 3 = 21
$$

Answer:
$$
\boxed{21}
$$

---

Problem 4: \( 7(7-4) \)

1. Apply the distributive property:
$$
7(7-4) = 7 \cdot 7 - 7 \cdot 4
$$

2. Perform the multiplications:
$$
7 \cdot 7 = 49, \quad 7 \cdot 4 = 28
$$

3. Subtract the results:
$$
49 - 28 = 21
$$

Answer:
$$
\boxed{21}
$$

---

Problem 5: \( 2(9+9) \)

1. Apply the distributive property:
$$
2(9+9) = 2 \cdot 9 + 2 \cdot 9
$$

2. Perform the multiplications:
$$
2 \cdot 9 = 18, \quad 2 \cdot 9 = 18
$$

3. Add the results:
$$
18 + 18 = 36
$$

Answer:
$$
\boxed{36}
$$

---

Problem 6: \( 5(2+8) \)

1. Apply the distributive property:
$$
5(2+8) = 5 \cdot 2 + 5 \cdot 8
$$

2. Perform the multiplications:
$$
5 \cdot 2 = 10, \quad 5 \cdot 8 = 40
$$

3. Add the results:
$$
10 + 40 = 50
$$

Answer:
$$
\boxed{50}
$$

---

Problem 7: \( 6(9-4) \)

1. Apply the distributive property:
$$
6(9-4) = 6 \cdot 9 - 6 \cdot 4
$$

2. Perform the multiplications:
$$
6 \cdot 9 = 54, \quad 6 \cdot 4 = 24
$$

3. Subtract the results:
$$
54 - 24 = 30
$$

Answer:
$$
\boxed{30}
$$

---

Problem 8: \( 3(0+8) \)

1. Apply the distributive property:
$$
3(0+8) = 3 \cdot 0 + 3 \cdot 8
$$

2. Perform the multiplications:
$$
3 \cdot 0 = 0, \quad 3 \cdot 8 = 24
$$

3. Add the results:
$$
0 + 24 = 24
$$

Answer:
$$
\boxed{24}
$$

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Final Answers:

1. \( \boxed{64} \)
2. \( \boxed{12} \)
3. \( \boxed{21} \)
4. \( \boxed{21} \)
5. \( \boxed{36} \)
6. \( \boxed{50} \)
7. \( \boxed{30} \)
8. \( \boxed{24} \)

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Explanation:

The distributive property simplifies calculations by breaking down complex expressions into simpler parts. By multiplying the outer number with each term inside the parentheses and then combining the results, we can efficiently solve these problems. Each step ensures clarity and accuracy in the solution process.