To determine whether the expression \( (9 \times 5) + 8 + 3 \) follows the associative property, we first need to understand what the associative property entails.
The associative property refers to the way in which numbers are grouped in addition or multiplication without changing the result. Specifically:
- For addition: \( (a + b) + c = a + (b + c) \)
- For multiplication: \( (a \times b) \times c = a \times (b \times c) \)
Now, let's look at your expression \( (9 \times 5) + 8 + 3 \) and see if we can apply the associative property.
- Addition: You can group the numbers to see if it holds true:
- \(( (9 \times 5) + 8) + 3 = (45 + 8) + 3 = 53 + 3 = 56\)
- \(( 9 \times 5) + (8 + 3) = 45 + (8 + 3) = 45 + 11 = 56\)
Since both methods yield the same result, the associative property holds for the addition in this case.
- Multiplication: If we were to only consider the multiplication part:
- There is no need of grouping in your expression, as multiplication is applied first to \(9\) and \(5\).
In summary, the expression \( (9 \times 5) + 8 + 3 \) does follow the associative property in the context of addition. The multiplication is just a single operation and does not require grouping in this case.
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