Improper Fractions and Mixed Numbers

**Improper Fractions and Mixed Numbers**

An improper fraction can be written as a mixed number. The diagram below shows that a mixed number and an improper fraction can both represent the same amount.To change an improper fraction to a mixed number, divide the numerator by the denominator. The fraction bar stands for "divided by", then means "nine divided by four", then

9 4 = 2 with 1 as a remnant.

The 2 is the number of wholes and 1 is the number of fourths, so ^{9}/

_{4}is equal to 2

^{1}/

_{4}.

To write a mixed number as an improper fraction, just multiply and add. Lets take 2 ^{1}/_{4}: first multiply the denominator(4) of the fraction part by the whole-number part(2).

2 4 = 8

then add the numerator part of the fraction(1) to this amount

8 + 1 = 9

this becomes the new numerator of the improper fraction. The denominator remains the same, so

2 ^{1}/_{4}

**Try it yourself**

1.

Division | Improper Fraction | Mixed Number |

16 3 | ^{16}/_{3} |

Division | Improper Fraction | Mixed Number |

19 2 | 9 ^{1}/_{2} |

Division | Improper Fraction | Mixed Number |

^{11}/_{9} |

4.

Division | Improper Fraction | Mixed Number |

^{28}/_{7} |

5.

Division | Improper Fraction | Mixed Number |

4 ^{4}/_{5} |

**Answers**

1.

Division | Improper Fraction | Mixed Number |

5 ^{1}/_{3} |

Division | Improper Fraction | Mixed Number |

^{19}/_{2} |

3.

Division | Improper Fraction | Mixed Number |

11 9 | 1 ^{2}/_{9} |

4.

Division | Improper Fraction | Mixed Number |

28 7 | 4 |

5.

Division | Improper Fraction | Mixed Number |

24 5 | ^{24}/_{5} |