Using the Distributive Property Worksheet for 6th - 9th Grade ... - Free Printable

The task involves solving a series of problems using the Distributive Property. The Distributive Property states that for any numbers \(a\), \(b\), and \(c\):

\[
a \cdot (b + c) = a \cdot b + a \cdot c
\]

This property allows us to distribute the multiplication over addition or subtraction. Let's solve each problem step by step.

---

Problem 1: \(5 \cdot (6 + 8)\)

Using the Distributive Property:
\[
5 \cdot (6 + 8) = 5 \cdot 6 + 5 \cdot 8
\]
Calculate each term:
\[
5 \cdot 6 = 30 \quad \text{and} \quad 5 \cdot 8 = 40
\]
Add the results:
\[
30 + 40 = 70
\]
So, the answer is:
\[
\boxed{70}
\]

---

Problem 2: \(9 \cdot (5 - 3)\)

Using the Distributive Property:
\[
9 \cdot (5 - 3) = 9 \cdot 5 - 9 \cdot 3
\]
Calculate each term:
\[
9 \cdot 5 = 45 \quad \text{and} \quad 9 \cdot 3 = 27
\]
Subtract the results:
\[
45 - 27 = 18
\]
So, the answer is:
\[
\boxed{18}
\]

---

Problem 3: \(7 \cdot (4 + 2)\)

Using the Distributive Property:
\[
7 \cdot (4 + 2) = 7 \cdot 4 + 7 \cdot 2
\]
Calculate each term:
\[
7 \cdot 4 = 28 \quad \text{and} \quad 7 \cdot 2 = 14
\]
Add the results:
\[
28 + 14 = 42
\]
So, the answer is:
\[
\boxed{42}
\]

---

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

Using the Distributive Property:
\[
6 \cdot (7 - 4) = 6 \cdot 7 - 6 \cdot 4
\]
Calculate each term:
\[
6 \cdot 7 = 42 \quad \text{and} \quad 6 \cdot 4 = 24
\]
Subtract the results:
\[
42 - 24 = 18
\]
So, the answer is:
\[
\boxed{18}
\]

---

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

Using the Distributive Property:
\[
8 \cdot (3 + 5) = 8 \cdot 3 + 8 \cdot 5
\]
Calculate each term:
\[
8 \cdot 3 = 24 \quad \text{and} \quad 8 \cdot 5 = 40
\]
Add the results:
\[
24 + 40 = 64
\]
So, the answer is:
\[
\boxed{64}
\]

---

Problem 6: \(4 \cdot (9 - 2)\)

Using the Distributive Property:
\[
4 \cdot (9 - 2) = 4 \cdot 9 - 4 \cdot 2
\]
Calculate each term:
\[
4 \cdot 9 = 36 \quad \text{and} \quad 4 \cdot 2 = 8
\]
Subtract the results:
\[
36 - 8 = 28
\]
So, the answer is:
\[
\boxed{28}
\]

---

Problem 7: \(3 \cdot (7 + 6)\)

Using the Distributive Property:
\[
3 \cdot (7 + 6) = 3 \cdot 7 + 3 \cdot 6
\]
Calculate each term:
\[
3 \cdot 7 = 21 \quad \text{and} \quad 3 \cdot 6 = 18
\]
Add the results:
\[
21 + 18 = 39
\]
So, the answer is:
\[
\boxed{39}
\]

---

Problem 8: \(2 \cdot (8 - 5)\)

Using the Distributive Property:
\[
2 \cdot (8 - 5) = 2 \cdot 8 - 2 \cdot 5
\]
Calculate each term:
\[
2 \cdot 8 = 16 \quad \text{and} \quad 2 \cdot 5 = 10
\]
Subtract the results:
\[
16 - 10 = 6
\]
So, the answer is:
\[
\boxed{6}
\]

---

Final Answers:

\[
\boxed{70, 18, 42, 18, 64, 28, 39, 6}
\]