Complex Fractions - SS2 Mathematics Lesson Note

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Complex fractions are fractions containing fractions.

Example:

Simplify \(\frac{\frac{x}{2} + \frac{x}{5}}{2x - \frac{3x}{10}}\)

Solution:

Given \(\frac{\frac{x}{2} + \frac{x}{5}}{2x - \frac{3x}{10}}\),

Resolving the numerator, \(\frac{x}{2} + \frac{x}{5} = \ \frac{5x + 2x}{10} = \ \frac{7x}{10}\)

Resolving the denominator, \(2x - \frac{3x}{10} = \ \frac{20x - 3x}{10} = \frac{17x}{10}\)

So \(\frac{\frac{x}{2} + \frac{x}{5}}{2x - \frac{3x}{10}} = \ \frac{\frac{7x}{10}}{\frac{17x}{10}} = \ \frac{7x}{10} \times \frac{10}{17x} = \ \frac{7x}{17x} = \ \frac{7}{17}\)