First, let's carefully examine the given equation:
[tex]\[ 4 \times 12 = 12 \times 4 \][/tex]
By looking at the equation, we can see that the order of the numbers being multiplied has been reversed:
- On the left side, we multiply 4 by 12.
- On the right side, we multiply 12 by 4.
However, the result of both multiplications is the same. This suggests that the order in which the two numbers are multiplied does not affect the outcome.
### Step-by-Step Analysis
1. Identify the Numbers:
- The two numbers are 4 and 12.
2. Multiplication:
- Multiply 4 by 12, which gives [tex]\( 4 \times 12 = 48 \)[/tex].
- Multiply 12 by 4, which gives [tex]\( 12 \times 4 = 48 \)[/tex].
3. Compare the Results:
- Both [tex]\( 4 \times 12 \)[/tex] and [tex]\( 12 \times 4 \)[/tex] equal 48, confirming the equality.
### Conclusion
The property that allows for the multiplication of numbers to yield the same product regardless of the order in which they are multiplied is known as the commutative property of multiplication.
This property states:
[tex]\[ a \times b = b \times a \][/tex]
### Determining the Correct Choice
Among the options provided:
- Identity
- Associative
- Commutative
- Property
- Property
- Property
The term “commutative” is the specific property demonstrated by the equation [tex]\( 4 \times 12 = 12 \times 4 \)[/tex].
### Answer
The property demonstrated is the commutative property, which is the third option in the given list. Therefore, the correct answer is:
#### commutative
And the respective choice number is:
#### 3
Thus, the detailed solution for the question is that it demonstrates the commutative property of multiplication, and the respective choice is number 3.
