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Using the associative law, we can group the 25 with the 4. 25 x 4 = 100, and 77 x100 = 7700. So 77 x (25 x 4) = 7700

Another way, if the values don't lend themselves to such elegant manipulation, is to spilt the numbers into single-digit factors. Makes for more work but may sometimes be easier than long-multiplication.

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How can you use properties of multiplication to determine what the factors are with two same product?

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Multiplication properties, such as the commutative, associative, and distributive properties, simplify mental calculations. The commutative property allows you to rearrange numbers for easier computation, while the associative property lets you group numbers in a way that makes calculations simpler. The distributive property enables you to break down complex problems into smaller, more manageable parts, facilitating quicker mental math. By leveraging these properties, you can enhance your efficiency and accuracy in multiplying numbers mentally.


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