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multiplication is the Inverse operationof division so it could be used to check my work
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Not sure about the first part of the question, but when doing long division, the partial answer is multiplied by the divisor to get a product, which then is subtracted from the dividend, to see how much is left over.
Division by a number is the same as multiplication by its reciprocal. That is, n / a = n * (1/a) and as you should know, (1/a) is the reciprocal of a.