Distributive Property Of Multiplication 3Rd Grade Worksheet - Free Printable

Problem Overview:

The task involves using the distributive property of multiplication to solve multiplication problems. The distributive property states that for any numbers \( a \), \( b \), and \( c \):

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

We will break down each problem step by step using this property.

---

Solution:

#### Problem ①: \( 12 \times 4 \)

1. Break the larger number into two addends:
\[
12 = 10 + 2
\]
So, we rewrite the expression:
\[
12 \times 4 = (10 + 2) \times 4
\]

2. Apply the distributive property:
\[
(10 + 2) \times 4 = (10 \times 4) + (2 \times 4)
\]

3. Calculate each product:
\[
10 \times 4 = 40
\]
\[
2 \times 4 = 8
\]

4. Add the products:
\[
40 + 8 = 48
\]

5. Final Answer:
\[
12 \times 4 = 48
\]

---

#### Problem ②: \( 4 \times 14 \)

1. Break the larger number into two addends:
\[
14 = 10 + 4
\]
So, we rewrite the expression:
\[
4 \times 14 = 4 \times (10 + 4)
\]

2. Apply the distributive property:
\[
4 \times (10 + 4) = (4 \times 10) + (4 \times 4)
\]

3. Calculate each product:
\[
4 \times 10 = 40
\]
\[
4 \times 4 = 16
\]

4. Add the products:
\[
40 + 16 = 56
\]

5. Final Answer:
\[
4 \times 14 = 56
\]

---

#### Problem ③: \( 3 \times 18 \)

1. Break the larger number into two addends:
\[
18 = 10 + 8
\]
So, we rewrite the expression:
\[
3 \times 18 = 3 \times (10 + 8)
\]

2. Apply the distributive property:
\[
3 \times (10 + 8) = (3 \times 10) + (3 \times 8)
\]

3. Calculate each product:
\[
3 \times 10 = 30
\]
\[
3 \times 8 = 24
\]

4. Add the products:
\[
30 + 24 = 54
\]

5. Final Answer:
\[
3 \times 18 = 54
\]

---

#### Problem ④: \( 22 \times 8 \)

1. Break the larger number into two addends:
\[
22 = 20 + 2
\]
So, we rewrite the expression:
\[
22 \times 8 = (20 + 2) \times 8
\]

2. Apply the distributive property:
\[
(20 + 2) \times 8 = (20 \times 8) + (2 \times 8)
\]

3. Calculate each product:
\[
20 \times 8 = 160
\]
\[
2 \times 8 = 16
\]

4. Add the products:
\[
160 + 16 = 176
\]

5. Final Answer:
\[
22 \times 8 = 176
\]

---

#### Problem ⑤: \( 4 \times 25 \)

1. Break the larger number into two addends:
\[
25 = 20 + 5
\]
So, we rewrite the expression:
\[
4 \times 25 = 4 \times (20 + 5)
\]

2. Apply the distributive property:
\[
4 \times (20 + 5) = (4 \times 20) + (4 \times 5)
\]

3. Calculate each product:
\[
4 \times 20 = 80
\]
\[
4 \times 5 = 20
\]

4. Add the products:
\[
80 + 20 = 100
\]

5. Final Answer:
\[
4 \times 25 = 100
\]

---

#### Problem ⑥: \( 18 \times 6 \)

1. Break the larger number into two addends:
\[
18 = 10 + 8
\]
So, we rewrite the expression:
\[
18 \times 6 = (10 + 8) \times 6
\]

2. Apply the distributive property:
\[
(10 + 8) \times 6 = (10 \times 6) + (8 \times 6)
\]

3. Calculate each product:
\[
10 \times 6 = 60
\]
\[
8 \times 6 = 48
\]

4. Add the products:
\[
60 + 48 = 108
\]

5. Final Answer:
\[
18 \times 6 = 108
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
&① \ 12 \times 4 = 48 \\
&② \ 4 \times 14 = 56 \\
&③ \ 3 \times 18 = 54 \\
&④ \ 22 \times 8 = 176 \\
&⑤ \ 4 \times 25 = 100 \\
&⑥ \ 18 \times 6 = 108
\end{aligned}
}
\]