When we divide algebraic fractions, we use the same method as when we divide numerical fractions.

Remember the **KFC** rule:** Keep **the first fraction, **flip** the second fraction and **change** the sign.

First, we invert the second fraction and then turn the ÷ sign into a x sign.

Then we try to reduce or cancel down any top term with a bottom term that has a common factor.

**Example**

Simplify:

a^{3} |
÷ | 7a^{2} |

10 | 5 |

**Answer**

Invert the second fraction and change the ÷ sign to a x sign.

a^{3} |
x | 5 |

10 | 7a^{2} |

Now multiply the numerators to get 5a^{3}

And multiply the denominators to get 70a^{2}

This gives us:

5a^{3} |

70a^{2} |

Now we simplify this by dividing the numbers by a common factor.

5 is a common factor of 5 and 70, so divide them both by 5. This gives us 1 as the numerator and 14 as the denominator.

Remember the rule for dividing by powers? a^{3} ÷ a^{2} = a^{3-2} = a

We end up with

a |

14 |

Let's try some questions.