# Division of fraction.

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## Division of fraction into natural number.

Definition.

To divide fraction into whole number, it is necessary to multiply denominator by a whole number, and to leave without modifications a numerator. Simplify the fraction if needed.### Examples of dividing of fractions into integer

Example 1.

Find the quotient of the fraction into integer:
3 | : 2 | = | 3 | = | 3 |

7 | 7 · 2 | 14 |

Example 2.

Find the quotient of the fraction into integer:
6 | : 3 | = | 6 | = | 2 · 3 | = | 2 |

11 | 11 · 3 | 11 · 3 | 11 |

Definition.

*To get the*

**reciprocal**of a fraction, just turn it upside down. In other words swap over the Numerator and Denominator.3 | - reciprocal fraction | 7 |

7 | 3 |

## Division of natural number into fraction.

Definition.

To divide natural number into fraction, it is necessary to multiply natural number by reciprocal of fraction.### Examples of dividing of integer into fraction

Example 3.

Find the quotient of the integer into fraction:
2: | 7 | = | 2· | 2 | = | 4 |

2 | 7 | 7 |

Example 4.

Find the quotient of the integer into fraction:
2: | 4 | = | 2· | 5 | = | 2 · 5 | = | 2 · 5 | = | 5 | = | 2 · 2 + 1 | = 2 | 1 |

5 | 4 | 4 | 2 · 2 | 2 | 2 | 2 |

## Division of fraction.

Definition.

To divide fractions, it is necessary to multiply first fraction by reciprocal of second fraction.### Examples of dividing of two fractions

Example 5.

Find the quotient of the two fractions:
3 | : | 4 | = | 3 | · | 5 | = | 3 · 5 | = | 15 |

7 | 5 | 7 | 4 | 7 · 4 | 28 |

Example 6.

Find the quotient of the two fractions:
6 | : | 4 | = | 6 | · | 7 | = | 6 · 7 | = | 3 · 2 | = | 3 | = | 2 + 1 | = 1 | 1 |

7 | 7 | 7 | 4 | 7 · 4 | 2 · 2 | 2 | 2 | 2 |

## Division of mixed numbers.

Definition.

- To divide mixed numbers:
- converting mixed numbers to improper fractions;
- to multiply first fraction by reciprocal of second fraction;
- simplify the fraction;
- if this fraction is improper then convert fraction to a mixed number.

### Examples of dividing of two mixed numbers

Example 7.

Find the quotient of the two mixed numbers:
1 | 1 | : | 2 | 2 | = | 1 · 2 + 1 | : | 2 · 3 + 2 | = | 3 | : | 8 | = | 3 | · | 3 | = | 3 · 3 | = | 9 |

2 | 3 | 2 | 3 | 2 | 3 | 2 | 8 | 2 · 8 | 16 |

Example 8.

Find the quotient of the mixed number into fraction:
2 | 1 | : | 3 | = | 2 · 7 + 1 | : | 3 | = | 15 | · | 5 | = | 15 · 5 | = | 25 | = 3 | 4 |

7 | 5 | 7 | 5 | 7 | 3 | 7 · 3 | 7 | 7 |

**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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