# NCERT Class 8 Mathematics Chapter 1 Rational Numbers CBSE Board Sample Problems (For CBSE, ICSE, IAS, NET, NRA 2022)

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## Rational Numbers

Sr. no | Type of numbers | Description |

1. | Natural numbers | It is the counting numbers |

2. | Whole number | It is the counting numbers + zero |

3. | Integers | |

4. | Positive inters | |

5. | Negative integers | |

6. | Rational number | A number is called rational if it can be expressed in the form p/q where p and q are integers () . Example: etc. |

Sr. no | Terms | Descriptions |

1. | Additive identify/Role of Zero | Zero is called the identify for the addition of rational numbers. It is the additive identify for integers and whole numbers as well |

2. | Multiplicative indentify/role of the | 1 is the Multiplicative indentify for rational numbers. It is the Multiplicative indentify for integers and whole numbers as well |

3. | Reciprocal or multiplicative inverse | The multiplicative inverse of any rational number is Defined as b/a so that Zero does not have any reciprocal or multiplicative inverse |

### Properties of Rational Numbers

#### Closure Property

Numbers | Closed Under | |||

Addition | subtraction | multiplication | Division | |

Rational Numbers | Yes | Yes | Yes | No |

Integers | Yes | Yes | Yes | No |

Whole Numbers | Yes | No | Yes | No |

Natural Numbers | Yes | No | Yes | No |

#### Commutativity Property

Numbers | Commutative Under | |||

Addition | subtraction | multiplication | Division | |

Rational Numbers | Yes | No | Yes | No |

Integers | Yes | No | Yes | No |

Whole Numbers | Yes | No | Yes | No |

Natural Numbers | Yes | No | Yes | No |

#### Associativity Property

Numbers | Associative Under | |||

Addition | subtraction | multiplication | Division | |

Rational Numbers | Yes | No | Yes | No |

Integers | Yes | No | Yes | No |

Whole Numbers | Yes | No | Yes | No |

Natural Numbers | Yes | No | Yes | No |