distributive property of multiplication Worksheets - Free Printable

Problem Overview:

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

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

In this worksheet, each problem is broken down into simpler parts using the distributive property, and the results are calculated step by step.

Solution Explanation:

#### Example Problem:
The example provided is:
\[
9 \times 18 = (9 \times 8) + (9 \times 10)
\]
- Break down \( 18 \) into \( 8 + 10 \).
- Apply the distributive property: \( 9 \times 18 = 9 \times (8 + 10) = (9 \times 8) + (9 \times 10) \).
- Calculate each part:
- \( 9 \times 8 = 72 \)
- \( 9 \times 10 = 90 \)
- Add the results: \( 72 + 90 = 162 \).

Thus, \( 9 \times 18 = 162 \).

#### Step-by-Step Solutions for Each Problem:

1. Problem: \( 13 \times 5 \)
- Break down \( 13 \) into \( 8 + 5 \).
- Apply the distributive property: \( 13 \times 5 = (8 \times 5) + (5 \times 5) \).
- Calculate each part:
- \( 8 \times 5 = 40 \)
- \( 5 \times 5 = 25 \)
- Add the results: \( 40 + 25 = 65 \).

Answer: \( 65 \)

2. Problem: \( 14 \times 3 \)
- Break down \( 14 \) into \( 7 + 7 \).
- Apply the distributive property: \( 14 \times 3 = (7 \times 3) + (7 \times 3) \).
- Calculate each part:
- \( 7 \times 3 = 21 \)
- \( 7 \times 3 = 21 \)
- Add the results: \( 21 + 21 = 42 \).

Answer: \( 42 \)

3. Problem: \( 17 \times 9 \)
- Break down \( 17 \) into \( 8 + 9 \).
- Apply the distributive property: \( 17 \times 9 = (8 \times 9) + (9 \times 9) \).
- Calculate each part:
- \( 8 \times 9 = 72 \)
- \( 9 \times 9 = 81 \)
- Add the results: \( 72 + 81 = 153 \).

Answer: \( 153 \)

4. Problem: \( 16 \times 3 \)
- Break down \( 16 \) into \( 9 + 7 \).
- Apply the distributive property: \( 16 \times 3 = (9 \times 3) + (7 \times 3) \).
- Calculate each part:
- \( 9 \times 3 = 27 \)
- \( 7 \times 3 = 21 \)
- Add the results: \( 27 + 21 = 48 \).

Answer: \( 48 \)

5. Problem: \( 5 \times 14 \)
- Break down \( 14 \) into \( 8 + 6 \).
- Apply the distributive property: \( 5 \times 14 = (5 \times 8) + (5 \times 6) \).
- Calculate each part:
- \( 5 \times 8 = 40 \)
- \( 5 \times 6 = 30 \)
- Add the results: \( 40 + 30 = 70 \).

Answer: \( 70 \)

6. Problem: \( 9 \times 17 \)
- Break down \( 17 \) into \( 7 + 10 \).
- Apply the distributive property: \( 9 \times 17 = (9 \times 7) + (9 \times 10) \).
- Calculate each part:
- \( 9 \times 7 = 63 \)
- \( 9 \times 10 = 90 \)
- Add the results: \( 63 + 90 = 153 \).

Answer: \( 153 \)

7. Problem: \( 4 \times 18 \)
- Break down \( 18 \) into \( 9 + 9 \).
- Apply the distributive property: \( 4 \times 18 = (4 \times 9) + (4 \times 9) \).
- Calculate each part:
- \( 4 \times 9 = 36 \)
- \( 4 \times 9 = 36 \)
- Add the results: \( 36 + 36 = 72 \).

Answer: \( 72 \)

8. Problem: \( 18 \times 3 \)
- Break down \( 18 \) into \( 9 + 9 \).
- Apply the distributive property: \( 18 \times 3 = (9 \times 3) + (9 \times 3) \).
- Calculate each part:
- \( 9 \times 3 = 27 \)
- \( 9 \times 3 = 27 \)
- Add the results: \( 27 + 27 = 54 \).

Answer: \( 54 \)

9. Problem: \( 13 \times 5 \)
- Break down \( 13 \) into \( 8 + 5 \).
- Apply the distributive property: \( 13 \times 5 = (8 \times 5) + (5 \times 5) \).
- Calculate each part:
- \( 8 \times 5 = 40 \)
- \( 5 \times 5 = 25 \)
- Add the results: \( 40 + 25 = 65 \).

Answer: \( 65 \)

10. Problem: \( 6 \times 14 \)
- Break down \( 14 \) into \( 4 + 10 \).
- Apply the distributive property: \( 6 \times 14 = (6 \times 4) + (6 \times 10) \).
- Calculate each part:
- \( 6 \times 4 = 24 \)
- \( 6 \times 10 = 60 \)
- Add the results: \( 24 + 60 = 84 \).

Answer: \( 84 \)

Final Answer:

\[
\boxed{65, 42, 153, 48, 70, 153, 72, 54, 65, 84}
\]