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Fill in the boxes in such a way that the...

Fill in the boxes in such a way that the multiplication process is simplified. Also, state the properties of multiplication used in the process.
`285 times 4 times 25=285 times square=square`

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To solve the problem step by step, we will simplify the multiplication of the numbers given and fill in the boxes accordingly. ### Step-by-Step Solution: 1. **Identify the Expression**: We start with the expression: \[ 285 \times 4 \times 25 \] 2. **Group the Multiplication**: We can group the numbers in a way that makes the multiplication easier. We can use the associative property of multiplication, which states that the way in which numbers are grouped does not change their product. We can group \(4\) and \(25\) together: \[ 285 \times (4 \times 25) \] 3. **Calculate \(4 \times 25\)**: Now, we calculate the multiplication of \(4\) and \(25\): \[ 4 \times 25 = 100 \] 4. **Rewrite the Expression**: Now we can rewrite the original expression using the result from the previous step: \[ 285 \times 100 \] 5. **Calculate \(285 \times 100\)**: Finally, we calculate \(285\) multiplied by \(100\): \[ 285 \times 100 = 28500 \] 6. **Fill in the Boxes**: Based on our calculations: - The first box (for \(4 \times 25\)) will be \(100\). - The second box (for the final result) will be \(28500\). ### Final Expression: Thus, we can fill in the boxes as follows: \[ 285 \times 4 \times 25 = 285 \times 100 = 28500 \] ### Properties of Multiplication Used: 1. **Associative Property of Multiplication**: This property allows us to group the numbers in a way that makes the calculation easier without changing the product. 2. **Commutative Property of Multiplication**: This property states that the order of multiplication does not affect the result, though it was not explicitly used in this case, it is an underlying principle of multiplication.
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