Distributive property of multiplication worksheets | Worsheets library - Free Printable

The task involves rewriting multiplication equations using the distributive property and then solving them. The distributive property states that:

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

This means we can break down a multiplication problem into smaller, easier-to-solve parts by splitting one of the factors into two addends.

Let's solve each problem step by step.

---

1. \( 20 \times 4 \)

We can split 20 into \( 10 + 10 \):

\[
20 \times 4 = (10 + 10) \times 4 = (10 \times 4) + (10 \times 4)
\]

Now calculate each part:

\[
10 \times 4 = 40
\]
\[
10 \times 4 = 40
\]

Add the results:

\[
40 + 40 = 80
\]

So, \( 20 \times 4 = 80 \).

---

2. \( 8 \times 14 \)

We can split 14 into \( 10 + 4 \):

\[
8 \times 14 = 8 \times (10 + 4) = (8 \times 10) + (8 \times 4)
\]

Now calculate each part:

\[
8 \times 10 = 80
\]
\[
8 \times 4 = 32
\]

Add the results:

\[
80 + 32 = 112
\]

So, \( 8 \times 14 = 112 \).

---

3. \( 7 \times 20 \)

We can split 20 into \( 10 + 10 \):

\[
7 \times 20 = 7 \times (10 + 10) = (7 \times 10) + (7 \times 10)
\]

Now calculate each part:

\[
7 \times 10 = 70
\]
\[
7 \times 10 = 70
\]

Add the results:

\[
70 + 70 = 140
\]

So, \( 7 \times 20 = 140 \).

---

4. \( 10 \times 15 \)

We can split 15 into \( 10 + 5 \):

\[
10 \times 15 = 10 \times (10 + 5) = (10 \times 10) + (10 \times 5)
\]

Now calculate each part:

\[
10 \times 10 = 100
\]
\[
10 \times 5 = 50
\]

Add the results:

\[
100 + 50 = 150
\]

So, \( 10 \times 15 = 150 \).

---

5. \( 8 \times 24 \)

We can split 24 into \( 20 + 4 \):

\[
8 \times 24 = 8 \times (20 + 4) = (8 \times 20) + (8 \times 4)
\]

Now calculate each part:

\[
8 \times 20 = 160
\]
\[
8 \times 4 = 32
\]

Add the results:

\[
160 + 32 = 192
\]

So, \( 8 \times 24 = 192 \).

---

6. \( 7 \times 16 \)

We can split 16 into \( 10 + 6 \):

\[
7 \times 16 = 7 \times (10 + 6) = (7 \times 10) + (7 \times 6)
\]

Now calculate each part:

\[
7 \times 10 = 70
\]
\[
7 \times 6 = 42
\]

Add the results:

\[
70 + 42 = 112
\]

So, \( 7 \times 16 = 112 \).

---

7. \( 6 \times 4 \)

We can split 4 into \( 2 + 2 \):

\[
6 \times 4 = 6 \times (2 + 2) = (6 \times 2) + (6 \times 2)
\]

Now calculate each part:

\[
6 \times 2 = 12
\]
\[
6 \times 2 = 12
\]

Add the results:

\[
12 + 12 = 24
\]

So, \( 6 \times 4 = 24 \).

---

8. \( 9 \times 8 \)

We can split 8 into \( 5 + 3 \):

\[
9 \times 8 = 9 \times (5 + 3) = (9 \times 5) + (9 \times 3)
\]

Now calculate each part:

\[
9 \times 5 = 45
\]
\[
9 \times 3 = 27
\]

Add the results:

\[
45 + 27 = 72
\]

So, \( 9 \times 8 = 72 \).

---

9. \( 5 \times 28 \)

We can split 28 into \( 20 + 8 \):

\[
5 \times 28 = 5 \times (20 + 8) = (5 \times 20) + (5 \times 8)
\]

Now calculate each part:

\[
5 \times 20 = 100
\]
\[
5 \times 8 = 40
\]

Add the results:

\[
100 + 40 = 140
\]

So, \( 5 \times 28 = 140 \).

---

10. \( 4 \times 8 \)

We can split 8 into \( 5 + 3 \):

\[
4 \times 8 = 4 \times (5 + 3) = (4 \times 5) + (4 \times 3)
\]

Now calculate each part:

\[
4 \times 5 = 20
\]
\[
4 \times 3 = 12
\]

Add the results:

\[
20 + 12 = 32
\]

So, \( 4 \times 8 = 32 \).

---

Final Answers

\[
\boxed{
\begin{aligned}
1. & \ 80 \\
2. & \ 112 \\
3. & \ 140 \\
4. & \ 150 \\
5. & \ 192 \\
6. & \ 112 \\
7. & \ 24 \\
8. & \ 72 \\
9. & \ 140 \\
10. & \ 32
\end{aligned}
}
\]