# Simplifying fractions

Definition.

Any fraction can be fully reduced to its lowest terms by dividing both the numerator and denominator by their **greatest common divisor**. This is called

**reducing**or

**simplifying**of the fraction.

4 | = | 2 | = | 1 |

20 | 10 | 5 |

Definition.

A fraction in which the numerator and denominator are coprime [this means that for faction ## Examples of tasks to simplify fractions

Example 1. Simplify the fraction | 4 | . |

8 |

gcd(4, 8) = 4 then,

4 | = | 4÷4 | = | 1 | . |

8 | 8÷4 | 2 |

Example 2. Simplify the fraction | 15 | . |

40 |

gcd(15, 40) = 5 then,

15 | = | 15÷5 | = | 3 | . |

40 | 40÷5 | 8 |

Example 3. Simplify the fraction | 126 | . |

426 |

gcd(126, 426) = 6 then,

126 | = | 126÷6 | = | 21 | . |

426 | 426÷6 | 71 |

Example 4. Simplify the fraction | 7 | . |

9 |

gcd(7, 9) = 1 then,

7 | - can not be simplified. |

9 |

**Fraction**

**Forms of fractions (vulgar fraction, proper fraction, improper fractions, mixed numbers, decimals)**

**The basic property of fraction**Simplifying fractions Least common denominator of fractions Converting improper fractions (composed fractions) to mixed numbers Converting mixed numbers to improper fractions (composed fractions) Addition and Subtraction of fractions Multiplication of fractions Division of fractions Comparing fractions Convert Decimals to Common Fractions

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