Before You Watch

This video covers how to add fractions involving algebra, when the letters are on the top (the numerator) and when they are on the bottom (the denominator).

Before watching this video, it is recommended that you refresh your memory of how to add fractions without using a calculator! The skill of adding fractions without a calculator is necessary when the fractions involve algebra.

A guide on how to add fractions can be found here:

https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/fractions-unlike-denom-pre-alg/v/adding-fractions-with-10-and-100-as-denominators

This topic also builds on the fundamental concepts of algebra, so make sure you've seen Introduction to Algebra before watching this video.

The Video

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Some Practice Questions

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Now What?

This video introduces working with algebraic fractions, but only deals with addition.

However, subtraction and addition of fractions with algebra are very similar to subtraction and addition of fractions with common, everyday numbers. Multiplication and division of algebraic fractions is also similar to fractions with common, everyday numbers: multiplication of algebraic fractions is done by multiplying the denominators and multiplying the numerators, and division is done by the process of inverse and multiply.

When you're confident with adding algebraic fractions, the next step is to become familiar with subtraction, multiplication and division. Again, this is best done by refreshing your memory of how to subtract, multiply and divide with common, everyday numbers first, then moving onto algebraic fractions after that.

To practise adding, subtracting, multiplying and dividing fractions, see the Other Links section.

But When I am Going to Use This

Just like fractions with everyday numbers, fractions with algebra appear in countless different situations. What if you’re splitting the bill of “m” dollars between “n” people? Then the bill per person is m/n. The old formula for gradient, m=rise/run is an algebraic fraction. When you pay off a home loan you must divide the total cost over “n” number of months, creating another fraction. Any time you are dividing by an unknown quantity (represented by a letter), or dividing an unknown quantity, you are creating an algebraic fraction.

Other Links

Sophia.org gives several different tutorial videos for each concept, and also has as a quiz so you can test yourself.

Mathspace has several worked video examples for addition and subtraction of algebraic fractions, as well as multiplication and division of algebraic fractions. Mathspace is also available on the App Store, Google Play or Microsoft Store. It has questions to test yourself, however, signing up is required to access those features.

Maths Is Fun provides simple and well-written summaries of the rules, worked examples, and a small selection of sample questions. This page gives a summary of addition, subtraction, multiplication and division, and also explains each operation separately.