Question
What property of real numbers does the statement demonstrate? \( \begin{array}{ll}a+b=b+a \\ \text { A. Additive Inverse } \\ \begin{array}{ll}\text { B. Commutative Property of Addition } \\ \text { C. Associative Property of Addition }\end{array}\end{array} \) Distributive Property
Ask by Wright Schultz. in the United States
Jan 31,2025
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Answer
The statement \( a + b = b + a \) shows the **Commutative Property of Addition**.
Solution
The statement \( a + b = b + a \) demonstrates the **Commutative Property of Addition**.
**Explanation:**
- **Commutative Property of Addition:** This property states that the order in which two numbers are added does not change the sum. In other words, \( a + b = b + a \).
- **Additive Inverse:** This property involves adding a number and its inverse (e.g., \( a + (-a) = 0 \)), which is not relevant to the given statement.
- **Associative Property of Addition:** This property involves the grouping of three or more numbers, such as \( (a + b) + c = a + (b + c) \), which is also not related to the given statement.
- **Distributive Property:** This property involves multiplying a number by a sum, such as \( a \times (b + c) = a \times b + a \times c \), which is unrelated to the provided equation.
**Answer:**
**B. Commutative Property of Addition**
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The statement \( a+b=b+a \) showcases that the order of the numbers being added doesn't affect their sum, which is a super fun concept in mathematics! This means you can rearrange the order without any worries, like a dance party where everyone can swap partners and still have a blast! In real-world scenarios, this property is incredibly handy. For instance, if you're planning a group outing and each friend contributes a different amount to the bill, it doesn’t matter in which order you add their contributions together; you’ll still arrive at the same total amount. So, feel free to jumble those numbers without fear!
