To determine which equation illustrates the commutative property of addition, let's first understand what the commutative property of addition is.
The commutative property of addition states that changing the order of the numbers being added does not change the sum. In other words, for any two numbers [tex]\( A \)[/tex] and [tex]\( B \)[/tex],
[tex]\[ A + B = B + A \][/tex]
Let's analyze each of the given options one by one:
1. [tex]\( 12 + 6 + 15 = 12 + 15 + 6 \)[/tex]
- In this equation, we see that the numbers on the left-hand side (LHS) are [tex]\( 12 \)[/tex], [tex]\( 6 \)[/tex], and [tex]\( 15 \)[/tex], and they appear in a different order on the right-hand side (RHS) as [tex]\( 12 \)[/tex], [tex]\( 15 \)[/tex], and [tex]\( 6 \)[/tex].
- The order of addition is different, but the numbers are the same. Therefore, this equation correctly demonstrates the commutative property of addition.
2. [tex]\( 12 + 6 + 15 = 12 + (6 + 15) \)[/tex]
- This equation involves the use of parentheses to group [tex]\( 6 \)[/tex] and [tex]\( 15 \)[/tex] together on the RHS.
- While this is a correct mathematical statement due to the associative property (grouping of numbers does not affect the sum), it does not specifically illustrate the commutative property (changing the order of numbers).
3. [tex]\( 12 + 6 + 15 = 18 + 15 \)[/tex]
- This equation changes the numbers on the LHS and RHS.
- The sum on the LHS is [tex]\( 33 \)[/tex], and the sum on the RHS is also [tex]\( 33 \)[/tex], but this does not illustrate the commutative property since the individual terms have combined values.
4. [tex]\( 12 + 6 + 15 = 12 + 6 + 15 \)[/tex]
- This equation merely repeats the same expression on both the LHS and RHS without changing the order.
- This does not demonstrate the commutative property as nothing has been rearranged.
Based on the analysis, the equation that correctly illustrates the commutative property of addition is:
[tex]\[ 12 + 6 + 15 = 12 + 15 + 6 \][/tex]
Therefore, the correct choice is:
Option 1: [tex]\( 12 + 6 + 15 = 12 + 15 + 6 \)[/tex]
