# Algebraic Identities

Algebraic identities for addition and multiplication.

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Identify the Identity

Select the name of the identity used in the example and the statement of the identity.

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Expression | Identity | Name | Full Identity | Example |
---|---|---|---|---|

a+0 | a | Additive Identity | a+0=0 | 5+0=5 |

a+(-a) | 0 | Additive Inverse | a+(-a)=0 | 4+(-4)=0 |

(a+b)+c | a+(b+c) | Associativity of Addition | (a+b)+c=a+(b+c) | (1+2)+3=1+(2+3)=5 |

a+b | b+a | Commutativity of Addition | a+b=b+a | 6+8=8+6=14 |

a x 1 | a | Multiplicative Identity | a x 1=a | 7 x 1=7 |

a x (1/a) if a is not 0 | 1 | Multiplicative Inverse | a x (1/a)=1 if a is not 0 | 9 x (1/9)=1 |

a x 0 | 0 | Multiplication by 0 | a x 0=0 | 2 x 0=0 |

(a x b) x c | a x (b x c) | Associativity of Multiplication | (a x b) x c=a x (b x c) | (3 x 6) x 2=3 x (6 x 2)=36 |

a x b | b x a | Commutativity of Multiplication | a x b=b x a | 3 x 5=5 x 3=15 |

a x (b+c) | (a x b)+(a x c) | Distributive Law | a x (b+c) = (a x b)+(a x c) | 2 x (2+7)=(2 x 2)+(2 x 7)=18 |

a/b | a x (1/b) | Definition of Division | a/b=a x (1/b) | 9/3=9 x (1/3)=3 |