Properties of Real Numbers

• The commutative property of addition states that numbers may be added in any order without affecting the sum.
• commutative property of multiplication states that numbers may be multiplied in any order without affecting the product.
• The associative property of multiplication tells us that it does not matter how we group numbers when multiplying. We can move the grouping symbols to make the calculation easier, and the product remains the same.
• The associative property of addition tells us that numbers may be grouped differently without affecting the sum.
• The distributive property states that the product of a factor times a sum is the sum of the factor times each term in the sum.
• The identity property of addition states that there is a unique number, called the additive identity (0) that, when added to a number, results in the original number.
• The identity property of multiplication states that there is a unique number, called the multiplicative identity (1) that, when multiplied by a number, results in the original number
• The inverse property of addition states that, for every real number a, there is a unique number, called the additive inverse (or opposite), denoted by (−a), that, when added to the original number, results in the additive identity, 0
• The inverse property of multiplication holds for all real numbers except 0 because the reciprocal of 0 is not defined. The property states that, for every real number a, there is a unique number, called the multiplicative inverse (or reciprocal), denoted that, when multiplied by the original number, results in the multiplicative identity, 1.