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The answer to this question depends on the multiplication algorithm you are working with. If you are working with an algorithm for multiplying fractions, the answer of why it works the way it does is going to be different than if you are multiplying whole numbers. If you are looking to explain multiplication algorithms to young children (and even to explain algorithms to older children or to better understand them yourself), it is useful to use physical objects and play with multiplication. Once you work out a few of the type of problem you are doing (or a scaled down version if you are working with large numbers) it will likely become clearer to you why it works the way it does.

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