a. $$ 5 imes(6 imes 3) $$ and $$ (5 imes 6) imes 3 $$

Question

a. $$ 5 	imes(6 	imes 3) $$ and $$ (5 	imes 6) 	imes 3 $$

UpStudy AI · Accepted Answer

Certainly! Let's analyze and evaluate the two expressions you've provided:

### a. $$ 5 \times (6 \times 3) $$ and $$ (5 \times 6) \times 3 $$

These expressions demonstrate the **associative property of multiplication**, which states that the way in which numbers are grouped when multiplying does not change the product. In mathematical terms:

$$
a \times (b \times c) = (a \times b) \times c
$$

Let's evaluate both expressions step by step to verify this property.

#### 1. Evaluating $$ 5 \times (6 \times 3) $$:

- **Step 1:** Calculate the expression inside the parentheses first.
  
  $$
  6 \times 3 = 18
  $$

- **Step 2:** Multiply the result by 5.
  
  $$
  5 \times 18 = 90
  $$

So,

$$
5 \times (6 \times 3) = 90
$$

#### 2. Evaluating $$ (5 \times 6) \times 3 $$:

- **Step 1:** Calculate the expression inside the parentheses first.
  
  $$
  5 \times 6 = 30
  $$

- **Step 2:** Multiply the result by 3.
  
  $$
  30 \times 3 = 90
  $$

So,

$$
(5 \times 6) \times 3 = 90
$$

#### **Conclusion:**

Both expressions evaluate to **90**. This confirms that multiplication is associative because changing the grouping of the numbers (i.e., where you place the parentheses) does not change the product.

$$
5 \times (6 \times 3) = (5 \times 6) \times 3 = 90
$$

**Therefore,**

$$
5 \times (6 \times 3) = (5 \times 6) \times 3 = 90
$$

This illustrates the **associative property** of multiplication.
Both expressions equal 90.

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