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Math Lesson 6.5.1 - What Are Algebraic Fractions?

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Welcome to our Math lesson on What Are Algebraic Fractions?, this is the first lesson of our suite of math lessons covering the topic of Algebraic Fractions, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.

What Are Algebraic Fractions? What do you need to Keep in Mind when Dealing with Algebraic Fractions?

As the name itself suggests, algebraic fractions are those fractions that contain algebraic expressions in at least one of their components (numerator or/and denominator). This means they contain at least one letter (variable) in their structure.

For example,

3a/7; 2-x/5y; 3xy2/12 - 4x; x - 6/y2 - 1

etc., are all algebraic fractions as they contain at least one variable.

We deal with algebraic fractions in the same way as we do with numerical fractions. The only thing to bear in mind when dealing with algebraic fractions is that the denominator must, necessarily, be different from zero to avoid division by zero. As we know, a fraction is another form of representing division. Since division by zero is meaningless we must avoid making the denominator zero.

The values of variables for which the denominator of an algebraic fraction becomes zero are known as 'disallowed values'. We must first identify them before continuing with other operations such as simplification, factorisation, etc.

Example 1

Identify the disallowed values (if any) of the following algebraic fractions.

5x - 2/6
5 - 2x/x - 4
4x - 3y + z/x2 yz3

Solution 1

The condition for a variable to be a disallowed value is when the denominator becomes zero. In the algebraic fraction

5x - 2/6

there are no variables in the denominator, so this algebraic fraction has no disallowed values.

Again, we must look for values that make the denominator zero. We have

x - 4 = 0
x = 4

This (x = 4) is the only disallowed value for this algebraic fraction.

The condition for this algebraic fraction to have disallowed values is that

x2 yz3 = 0

This condition occurs when either variable is zero, i.e.

x = 0
y = 0

and

z = 0

More Algebraic Fractions Lessons and Learning Resources

Expressions Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
6.5Algebraic Fractions
Lesson IDMath Lesson TitleLessonVideo
Lesson
6.5.1What Are Algebraic Fractions?
6.5.2Operations with Algebraic Fractions

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