Fractions don’t have to have only numbers in them.
They can also have algebraic variables in them as well. And you also need to
be able to add, subtract, multiply and divide *algebraic* fractions
together just like you do with normal number only fractions. However, the
rules are the same as for working with number fractions.

### Adding algebraic fractions

Algebraic fraction addition problem Sponsored Links |

Calculate |

Solution |

First thing we have to is get the two fractions
to have a Now we’ve got a common denominator, we can do the rest of the calculation: Subtraction is just like addition – you need to make sure all the fractions have a common denominator. Now for multiplication and division. |

### Multiplying algebraic fractions

Calculate |

Solution |

Multiplication just means we have to multiply the tops by the tops (the numerators), and the bottoms by the bottoms (the denominators): We also need to simplify it by cancelling out bits. · 12 divided 6 becomes 2 on the top ·
‘a’ divided by ‘a ·
‘b |

### Dividing algebraic fractions

Calculate |

Solution |

The trick to dividing is to change it to a multiplication,
by swapping the top and bottom of the fraction Now we can just calculate an answer like a normal multiplication: |

Handy Hint #1 - Confusing ‘x’ and ‘×’

This is one of the most common
mistakes made in exams – when students don’t notice the difference between a
multiplication operation (×) and an ‘x’ symbol. When you’re doing algebraic
problems you want to make sure that these two things look *really, really
different*. And remember, even though *you* may be able to tell the
difference, what about your teacher, who may be marking your exam late at night
in bad lighting conditions when their eyes are tired. It’s best to play safe.
For instance, I draw my ‘x’s as if they were made up of two ‘c’s put together,
with one of the ‘c’s back to front. My multiplication symbols are smaller and
made up of two straight lines, like this:

You can use whatever style you want, as long as it is clear to anyone reading it what the difference is between the two symbols.