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# 1.2 Properties

### Properties of Real Numbers

Question | Answer |
---|---|

4+(a+b)=(a+b)+4 | Commutative Property of Addition |

14+16=16+14 | Commutative Property of Addition |

(math) x (1/math) = 1 | Inverse Property of Multiplication |

xy=yx | Commutative Property of Multiplication |

a+b+(-a) = b | Inverse Property of Addition |

Can 0 be a multiplicative identity? Why or not? | No, because a number multiplied by 0 equals 0, not the original value of the number. |

(4+y)+z = 4+(y+z) | Associative Property of Addition |

1(a+b) = a+b | Multiplicative Identity |

ab+cd+(-ab) = cd | Inverse Property of Addition |

Can 1 be the additive identity? Why or why not? | No, because 1 does not give the original value of the number. It only increases the value 1. |

−41+0 = −41 | Additive Identity |

Zero plus seven equals seven | Additive Identity |

(6a)(8x)(1/6a) = 8x | Inverse Property of Multiplication |

Can a property ever be false? Why or why not? | No, a property is a statement that is true for every real number. |

1(b) = b | Multiplicative Identity |

(5+q)+(-3)=(q+5)+(-3) | Commutative Property of Addition |

(12)(−8)=(−8)(12) | Commutative Property of Multiplication |

3•(9•0)=(3•9)•0 | Associative Property of Multiplication |

(-3+4)+5 = 5+(-3+4) | Commutative Property of Addition |

(4m)n=4(mn) | Associative Property of Multiplication |

(a+b)+c=a+(b+c) | Associative Property of Addition |

2(3+6) = 2•3 + 2•6 | Distributive Property |

2(5a)+2(4b)=2(5a+4b) | Distributive Property |

Use the distributive property to rewrite −4(x+2) | -4x - 8 |