State the properties used in the following statements: `456+(222+431)=(456+431)+222`

Answer

To solve the question, we need to identify the property used in the statement:

`456 + (222 + 431) = (456 + 431) + 222`.

### Step-by-Step Solution:

1. **Identify the Expression**: The expression given is `456 + (222 + 431) = (456 + 431) + 222`.

2. **Recognize the Grouping**: In the expression, you can see that the numbers are grouped differently on each side of the equation. On the left side, `222 + 431` is grouped together, while on the right side, `456 + 431` is grouped together.

3. **Understanding the Property**: The property that allows us to change the grouping of numbers in addition without changing the result is called the **Associative Property of Addition**.

4. **State the Property**: According to the associative property, when adding three or more numbers, the way in which the numbers are grouped does not change the sum.

5. **General Formula**: The general formula for the associative property can be expressed as:
\[ a + (b + c) = (a + b) + c \]
where `a`, `b`, and `c` are any numbers.

### Conclusion:
The property used in the statement `456 + (222 + 431) = (456 + 431) + 222` is the **Associative Property of Addition**.

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