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| In this paper, the concept of scissor products is introduced and its fundamental properties are discussed. Combining with the smaller-than-smaller carry method, scissor products can be used in the numerical calculation to form a new and systematic rapid calculation method for the multiplication of integers, which is parallel to but superior to the well-known rapid calculation method of Shi Fengshou. The advantages of the new theory lie in the following two aspects: (1) the scissor products can be understood and remembered very easily with the help of the ordinary $9\times 9$ multiplication table; (2) the smaller-than-smaller carry method makes carrying very easy. Our theory of scissor products can be applied to the rapid multiplication in two ways, in which we use or do not use the virtual carry method respectively. |
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| Keywords:Number theory, rapid calculation, scissor product, smaller-than-smaller carry method, virtual carry method. |
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