Multiplication of Algebraic Fractions Revision Notes for Leaving Cert Mathematics

Multiplication of Algebraic Fractions

When two algebraic fractions are multiplied, we multiply the numerator with the numerator, and multiply the denominator with the denominator. In general :

\frac{a}{b} \cdot \frac{c}{d}=\frac{ac}{bd}

Example

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Simplify

\frac{3}{x} \cdot \frac{4x}{y}

Apply the rule for fraction multiplication :

\frac{3}{x} \cdot \frac{4x}{y}=\frac{12x}{xy}

Simplify :

\frac{12}{y}

Let's consider an interesting case : what happens when we want to multiply a non-fractional term with a fraction, such as :

Example

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Simplify :

3x\left( \frac{x}{2y}\right)

Any non-fraction term can be represented as a fraction because we can always divide that term by $1$ , making it a fraction. In general :

a=\frac{a}{1}

In other words, the non-fractional term just multiplies with the numerator of the fraction, and the denominator just multiplies with $1$ .

\frac{3x}{1} \cdot \frac{x}{2y}=\frac{3x^2}{2y}

Multiplication of Algebraic Fractions (Leaving Cert Mathematics): Revision Notes

Multiplication of Algebraic Fractions

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