## Subtracting Proper Fractions

#### 1. The video below explains how to subtract proper fractions.

A proper fraction is a fraction in which the numerator is smaller than the denominator.

#### 2. Monica had

1 |

4 |

3 |

4 |

How much more of the pie had Sarah than Monica?

Sarah =>

Monica =>

Sarah − Monica =>

−

=

=

=

(simplify)

=

Sarah had

3 |

4 |

Monica =>

1 |

4 |

Sarah − Monica =>

3 |

4 |

1 |

4 |

−

3 |

4 |

1 |

4 |

=

3 - 1 |

4 |

=

2 |

4 |

=

2 / 2 |

4 / 2 |

=

1 |

2 |

Sarah had

**a pie more than Monica.**

1 |

2 |

#### 3. Elly gives

1 |

2 |

1 |

3 |

How much more of the pizza does Elly give to Charlie than Derek?

Charlie =>

Derek =>

Charlie − Derek =>

−

1 |

2 |

Derek =>

1 |

3 |

Charlie − Derek =>

1 |

2 |

1 |

3 |

Both Charlie and Derek had 1 slice each but Charlie's slice was bigger than Derek's slice because Charlie's pizza was cut into 2 while Derek's pizza was cut into 3.

To compare the two slices, first cut both pizzas into equal number of slices.

To compare the two slices, first cut both pizzas into equal number of slices.

−

1 |

2 |

1 |

3 |

=

1 x 3 |

2 x 3 |

1 x 2 |

3 x 2 |

=

3 |

6 |

2 |

6 |

=

1 |

6 |

Elly gives

**of a pizza more to Charlie than to Derek.**

1 |

6 |

Since the two fractions,

and

are unlike fractions (as the denominators are different), we must first change them to like fractions before we can subtract them (that is, find a common denominator).

1 |

2 |

1 |

3 |