Multiplication is commutative and associative; further, it is distributive over addition and subtraction. The multiplicative identity is 1, since multiplying any number by 1 yields that same number. The multiplicative inverse for any number except  is the reciprocal of this number, because multiplying the reciprocal of any number by the number itself yields the multiplicative identity .  is the only number without a multiplicative inverse, and the result of multiplying any number and is again One says that is not contained in the multiplicative group of the numbers.