The multiplication property allows you to multiply both sides of an equation by any non-zero constant without affecting the solutions to the equation. In this context, division by any number (other than 0) is equally valid. These two properties are equivalent in the sense that dividing through by any non-zero number x is the same as multiplying through by 1/x.
These properties can be used to change the coefficients of the variables in simultaneous equations. The modified equations can then be added or subtracted together to eliminate one or more of the variables - provided at least one variable is left.
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multiplication is the Inverse operationof division so it could be used to check my work
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All the properties of multiplication may be used with money.
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.