Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

According to the Commutative Property, what can be said about the addition of two numbers?

1. The order of addition does not change the sum

2. The sum is always zero

3. The result is dependent on the first number

4. Grouping of numbers must be changed

The correct answer is: The order of addition does not change the sum

The Commutative Property of addition states that the order in which two numbers are added does not affect the sum. This means that if you have two numbers, say \(a\) and \(b\), you can add them in either order: \(a + b\) will yield the same sum as \(b + a\). This property highlights the flexibility in the arrangement of terms when performing addition, making it a fundamental concept in arithmetic. In contrast, other options do not accurately reflect the Commutative Property. For instance, stating that the sum is always zero would only apply in specific cases (such as when both numbers are zero), but it does not generally apply to all addition scenarios. Additionally, claiming that the result depends on the first number contradicts the essence of the Commutative Property, as it emphasizes that both arrangements yield the same result. Lastly, the grouping of numbers relates to the Associative Property, not the Commutative Property, which focuses solely on the order of addition without altering how the numbers are grouped. Hence, the correct assertion is that the order of addition does not change the sum.