Abstract

As early as fourth grade, we begin introducing students to the properties of arithmetic. The commutative property of addition and the commutative property of multiplication allow us to change the order of the numbers without changing the value of the expression. The associative property of addition and the associative property of multiplication state that regrouping numbers when adding and/or multiplying does not change the solution. The distributive property of multiplication over addition allows us either to find the addend of the numbers, then multiply by the factor, or to first multiply the factor by each addend, then find the sum. Finally, the identity properties of addition and multiplication state that the value of any real number remains unchanged if zero is added to it or if it is multiplied by one, respectively.

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