Which equation shows the commutative property of addition?
[tex]$4+3=3+4$[/tex]
[tex]$1(3)=3$[/tex]
[tex]$(2+7)+12=2+(7+12)$[/tex]
[tex]$4+0=4$[/tex]
Answer (2)
The commutative property of addition states that a + b = b + a .
Examine each equation to see if it fits the commutative property.
4 + 3 = 3 + 4 demonstrates the commutative property.
The equation that shows the commutative property of addition is 4 + 3 = 3 + 4 .
Explanation
Understanding the Commutative Property The question asks us to identify which equation demonstrates the commutative property of addition. The commutative property states that changing the order of the addends does not change the sum. In other words, for any numbers a and b, a + b = b + a.
Analyzing Each Equation Let's examine each equation:
4 + 3 = 3 + 4 : This equation shows that changing the order of the addends (4 and 3) does not change the sum. This demonstrates the commutative property of addition.
1 ( 3 ) = 3 : This equation demonstrates the identity property of multiplication, where any number multiplied by 1 equals itself.
( 2 + 7 ) + 12 = 2 + ( 7 + 12 ) : This equation demonstrates the associative property of addition, where the grouping of addends does not affect the sum.
4 + 0 = 4 : This equation demonstrates the identity property of addition, where any number plus 0 equals itself.
Identifying the Correct Equation Therefore, the equation that shows the commutative property of addition is 4 + 3 = 3 + 4 .
Examples
The commutative property of addition is useful in everyday situations. For example, if you are buying items at a store, it doesn't matter if you add the prices in one order or another; the total cost will be the same. If you buy a drink for $2 and a snack for $3, the total cost is $2 + $3 = $5. Similarly, if you add the snack price first, $3 + $2 = $5. The commutative property ensures that the order in which you add the prices doesn't change the total amount you pay.
The commutative property of addition states that the order of addends does not change the sum, expressed as a + b = b + a . The equation that demonstrates this property is 4 + 3 = 3 + 4 . Therefore, the correct answer is 4 + 3 = 3 + 4 .
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