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# Classifying Numbers

### Classifying the different types of real numbers

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

Real Numbers | All numbers that we deal with in Algebra are real numbers. |

Rational Numbers | Rational numbers are any number that can be written as a fraction. It includes positive and negative numbers, and any decimal that either terminates or repeats. (Ex. -2, 3.232323..., 7/8) |

Irrational Numbers | Irrational numbers are decimals that do not terminate and do not repeat. (Ex. pi, 3.1289368342...) |

Integers | Integers include positive numbers, negative numbers, and zero. Integers do not have a fraction or decimal part. (Ex. -4, 0, 2, 5) |

Whole Numbers | Whole Numbers include the positive integers and zero. (Ex. 0, 1, 2, 3...) |

Natural Numbers | Natural Numbers (also known as Counting Numbers) include only the positive integers. (Ex. 1, 2, 3, 4...) |

Identity Property of Addition | Adding zero to any number return the same number. a + 0 = a The ADDITIVE IDENTITY is 0 |

Identity Property of Multiplication | Multiplying any number by 1 returns the same number. a * 1 = a The MULTIPLICATIVE IDENTITY is 1 |

Inverse Property of Addition | A number plus its opposite is 0. a + -a = 0 |

Inverse Property of Addition | A number multiplied by its reciprocal is 1. a * (1/a) = 1 |

Commutative Property of Addition | When adding, the order is not important. a + b = b + a |

Commutative Property of Multiplication | When multiplying, the order is not important. ab = ba |

Associative Property of Addition | When adding, the grouping is not important. a + (b + c) = (a + b) + c |

Associative Property of Multiplication | When multiplying, the order is not important. a(bc) = (ab)c |

Created by:
mburke79