Give an example to justify whether:
whole numbers are associative under division?

Answer

To determine whether whole numbers are associative under division, we can follow these steps:

### Step 1: Understand Associative Property
The associative property states that for three numbers \( a \), \( b \), and \( c \), the way in which the numbers are grouped does not change the result of the operation. For example, in addition, \( (a + b) + c = a + (b + c) \). We need to check if this holds true for division.

### Step 2: Choose Whole Numbers
Let's choose three whole numbers. For this example, we will use:
- \( a = 6 \)
- \( b = 3 \)
- \( c = 2 \)

### Step 3: Calculate \( (a \div b) \div c \)
First, we will calculate \( (a \div b) \div c \):
1. Calculate \( a \div b \):
\[ 6 \div 3 = 2 \]
2. Now, take the result and divide by \( c \):
\[ 2 \div 2 = 1 \]
So, \( (a \div b) \div c = 1 \).

### Step 4: Calculate \( a \div (b \div c) \)
Next, we will calculate \( a \div (b \div c) \):
1. First, calculate \( b \div c \):
\[ 3 \div 2 = 1.5 \]
2. Now, take \( a \) and divide by this result:
\[ 6 \div 1.5 = 4 \]
So, \( a \div (b \div c) = 4 \).

### Step 5: Compare the Results
Now we compare the results from Step 3 and Step 4:
- \( (a \div b) \div c = 1 \)
- \( a \div (b \div c) = 4 \)

Since \( 1 \neq 4 \), we conclude that:
\[ (a \div b) \div c \neq a \div (b \div c) \]

### Conclusion
Whole numbers are **not associative under division**.

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