Pregunta
What property does the following equation show? \[ 5+7+9=7+5+9 \]
Ask by Sherman Gordon. in the United States
Jan 23,2025
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The equation shows that addition is commutative, meaning the order of the numbers does not change the sum.
Solución
The equation \( 5 + 7 + 9 = 7 + 5 + 9 \) demonstrates the **commutative property of addition**.
### Explanation:
1. **Commutative Property**: This property states that the order in which two numbers are added does not change the sum. In other words, for any numbers \( a \) and \( b \):
\[
a + b = b + a
\]
2. **Application in the Equation**:
- In the left-hand side of the equation, the numbers are added in the order \( 5, 7, 9 \).
- In the right-hand side, the numbers are rearranged to \( 7, 5, 9 \).
- Despite the different order, the sum remains the same, which is \( 21 \).
Thus, the equation illustrates that addition is commutative, as changing the order of the addends does not affect the total.
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Simplifique esta solución Mind Expander
This equation demonstrates the commutative property of addition, which states that the order in which you add numbers does not affect the sum. Whether you compute \(5 + 7 + 9\) or rearrange the numbers to \(7 + 5 + 9\), the result remains 21. It's a nifty little quirk of addition that makes math a bit more flexible and fun! Additionally, this property is foundational in algebra and is a key principle in simplifying expressions and solving equations. By knowing that you can rearrange terms, you can often simplify your calculations and find solutions more efficiently. It's like having your own mathematical magic trick!
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