Sure, let's examine the given examples and understand the property they are illustrating.
The commutative property of addition states that the order of the numbers being added does not affect the sum. We can swap the numbers around, and the sum remains the same.
Let's inspect the examples provided:
1. [tex]\( 7 + 8 + 3 = 7 + 3 + 8 \)[/tex]
On the left side, we have:
[tex]\( 7 + 8 + 3 \)[/tex]
On the right side, we have:
[tex]\( 7 + 3 + 8 \)[/tex]
Notice that the numbers [tex]\( 7, 8, \)[/tex] and [tex]\( 3 \)[/tex] are simply rearranged. According to the commutative property of addition, the order of addition does not matter. Hence, [tex]\( 7 + 8 + 3 = 7 + 3 + 8 \)[/tex].
2. [tex]\( 4.6 + 11.4 = 11.4 + 4.6 \)[/tex]
On the left side, we have:
[tex]\( 4.6 + 11.4 \)[/tex]
On the right side, we have:
[tex]\( 11.4 + 4.6 \)[/tex]
Again, the numbers [tex]\( 4.6 \)[/tex] and [tex]\( 11.4 \)[/tex] are rearranged. The commutative property assures that [tex]\( 4.6 + 11.4 = 11.4 + 4.6 \)[/tex].
Now, let’s compare the possible statements given in the question:
a) [tex]\( a + b = a - b \)[/tex]
This statement is incorrect because it implies subtraction. Addition and subtraction are different operations.
b) [tex]\( a + (b + c) = (a + b) + c \)[/tex]
This statement represents the associative property of addition, not the commutative property. The associative property deals with how numbers are grouped.
c) [tex]\( a + b = a + c \)[/tex]
This statement is incorrect because it suggests two sums with different addends are equal, which is generally not true.
d) [tex]\( a + b = b + a \)[/tex]
This is the correct statement that describes the commutative property of addition. It indicates that the order in which two numbers are added does not change the sum.
Hence, the statement that best describes the commutative property of addition is:
[tex]\[ a + b = b + a \][/tex]
So, the correct choice is:
[tex]\[ \boxed{d} \][/tex]
