# Comparing fractions.

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## Comparing fractions with a common denominator

Definition.

*To*

**compare fraction with the common denominators**(bottom number of a fraction) you need to compare numerators and to see which fraction is greater.### Example of comparing fractions with the common denominators:

Example 1.

3 | < | 4 |

7 | 7 |

Example 2.

7 | > | 6 |

11 | 11 |

## Comparing fractions with a common numerator

Definition.

*The fraction with the smallest denominator is the larger fraction if the*

**numerators are the same**.### Example of comparing fractions with the common numerator:

Example 3.

4 | > | 4 |

7 | 9 |

Example 4.

1 | < | 1 |

31 | 20 |

## Comparing fractions

Definition.

To **compare fractions with different denominators**you need to make them the same finding the least common multiple (LCM) of the denominators (which is called the Least Common Denominator). Then to compare numerators and to see which fraction is greater.

### Example of comparing fractions:

Example 5.

8 | ? | 5 |

9 | 6 |

to reduce fractions to a common denominator

16 | ? | 15 |

18 | 18 |

as 16 > 15, then

8 | > | 5 |

9 | 6 |

Example 6.

3 | ? | 9 |

7 | 20 |

to reduce fractions to a common denominator

60 | ? | 63 |

140 | 140 |

as 60 < 63, then

3 | < | 9 |

7 | 20 |

**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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