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Algebraic Techniques, SM-Bank 106

Simplify the following quotients, giving your answer as an algebraic fraction in simplest form.

  1. \(\dfrac{5m}{8}\ ÷\ \dfrac{m}{4}\)  (2 marks)

  2. \(\dfrac{14x}{3}\ ÷\ \dfrac{7y}{6}\)  (2 marks)

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a.    \(\dfrac{5}{2}\)

b.    \(\dfrac{8x}{y}\)

Show Worked Solution
a.    \(\dfrac{5m}{8}\ ÷\ \dfrac{m}{4}\) \(=\dfrac{5m}{8}\times \dfrac{4}{m}\)
    \(=\dfrac{20m}{8m}\)
    \(=\dfrac{5}{2}\)

 

b.    \(\dfrac{14x}{3}\ ÷\ \dfrac{7y}{6}\) \(=\dfrac{14x}{3}\times \dfrac{6}{7y}\)
    \(=\dfrac{7x\times 2\times 3\times 2}{7y\times 3}\)
    \(=\dfrac{4x}{y}\)