Multiplication Properties worksheets teaching Commutative and Associative Properties with examples and exercises.

You're right — this image is not a math problem to solve, but rather an educational resource designed to teach or reteach the properties of multiplication using 5 lessons (likely covering Commutative, Associative, Identity, Zero, and Distributive properties).

Since you asked to “solve the problem and explain the solution,” I’ll interpret this as:
> “Explain what this image is teaching, and demonstrate how to solve the sample problems shown.”

---

## 🎯 OVERVIEW: What Are the Multiplication Properties?

There are several key properties of multiplication that help students understand how numbers interact. The two most visible in this image are:

1. ✔ Commutative Property

> Changing the order of the factors does NOT change the product.
> `a × b = b × a`

2. ✔ Associative Property

> Changing the grouping of the factors does NOT change the product.
> `(a × b) × c = a × (b × c)`

---

## 🧮 SOLVING THE SAMPLE PROBLEMS

Let’s go through the visible practice problems on the worksheets.

---

## 🔹 COMMUTATIVE PROPERTY WORKSHEET

➤ Fill-in-the-blank (Write the unknown factor):

These all test the idea that `a × b = b × a`.

7) `9 × 4 = ___ × 9` → Answer: 4
→ Because `9 × 4 = 4 × 9`

8) `10 × 2 = ___ × 10` → Answer: 2

9) `6 × 6 = ___ × 6` → Answer: 6
→ Even when both factors are the same, it still works!

10) `5 × 7 = ___ × 5` → Answer: 7

11) `3 × 8 = ___ × 3` → Answer: 8

12) `4 × 6 = ___ × 4` → Answer: 6

✔ All answers are just the *other* number in the multiplication sentence — because order doesn’t matter!

---

➤ Problem Solving (Word Problems)

#### 13) Mrs. Howard planting 12 rose bushes in equal rows.
> *What are two ways she can plant them? Draw two arrays.*

This tests understanding of factor pairs of 12.

Possible arrangements:
- 3 rows × 4 bushes = 12 → Array: 3 rows of 4
- 4 rows × 3 bushes = 12 → Array: 4 rows of 3 ← This shows commutative property!
- Also possible: 2×6, 6×2, 1×12, 12×1

✔ So two ways:
→ 3 × 4 and 4 × 3 (or 2×6 and 6×2)

---

#### 15) Jenny has 5 shelves with 8 books each. How many total books?

> Write a multiplication sentence and solve.

Total books = `5 shelves × 8 books per shelf = 40 books`

Multiplication sentence: 5 × 8 = 40

---

#### 16) What if Jenny had 8 shelves with 5 books each? Would the answer be the same?

Yes! Because of the Commutative Property:
`8 × 5 = 40` ← Same as `5 × 8`

✔ Answer: Yes, because multiplication is commutative — changing the order of the factors doesn’t change the product.

---

## 🔹 ASSOCIATIVE PROPERTY WORKSHEET

➤ Write another way to group the factors. Then find the product.

Remember: `(a × b) × c = a × (b × c)`

5) `(2 × 3) × 5`
→ Another way: `2 × (3 × 5)`
→ Product: `2 × 15 = 30` OR `(6) × 5 = 30`

6) `4 × (2 × 4)`
→ Another way: `(4 × 2) × 4`
→ Product: `8 × 4 = 32`

7) `(5 × 1) × 7`
→ Another way: `5 × (1 × 7)`
→ Product: `5 × 7 = 35`

8) `(3 × 3) × 2`
→ Another way: `3 × (3 × 2)`
→ Product: `3 × 6 = 18`

9) `6 × (1 × 4)`
→ Another way: `(6 × 1) × 4`
→ Product: `6 × 4 = 24`

10) `9 × (2 × 2)`
→ Another way: `(9 × 2) × 2`
→ Product: `18 × 2 = 36`

✔ All products stay the same no matter how you group — that’s the Associative Property!

---

➤ Think About It! (Critical Thinking)

#### 11) Find the product of 4, 5, 2. Write two ways to group the factors. Is the product the same? Why?

First, multiply: `4 × 5 × 2 = 40`

Two ways to group:
- `(4 × 5) × 2 = 20 × 2 = 40`
- `4 × (5 × 2) = 4 × 10 = 40`

✔ Yes, the product is the same.
Why? Because of the Associative Property of Multiplication — changing the grouping doesn’t change the result.

---

## 📚 SUMMARY: Key Takeaways

| Property | Rule | Example |
|----------------------|-------------------------------------------|-----------------------------|
| Commutative | Order doesn’t matter | `3 × 4 = 4 × 3` |
| Associative | Grouping doesn’t matter | `(2 × 3) × 4 = 2 × (3 × 4)` |

These properties help students:
- Solve multiplication faster
- Understand relationships between numbers
- Build foundation for algebra

---

## ✔ FINAL ANSWER (As requested):

> This image is not a single problem to solve, but a set of educational worksheets teaching the Commutative and Associative Properties of Multiplication. Sample problems have been solved above, demonstrating that changing the order (Commutative) or grouping (Associative) of factors does not change the product. These properties are foundational for deeper math understanding.

Let me know if you’d like me to create similar worksheets or explain the other properties (Identity, Zero, Distributive)! 😊