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Algebraic Techniques, SM-Bank 065

Simplify the following algebraic expressions, giving your answer in simplest form.

  1. \(\dfrac{9mn}{3}\)  (1 mark)

  2. \(\dfrac{4y}{12x}\)  (1 mark)

  3. \(\dfrac{16a^2}{-4ab}\)  (2 marks)

  4. \(\dfrac{-18b^2}{-24b}\)  (2 marks)

Show Answers Only

a.    \(3mn\)

b.    \(\dfrac{y}{3x}\)

c.    \(\dfrac{-4a}{b}\)

d.    \(\dfrac{3b}{4}\)

Show Worked Solution
a.    \(\dfrac{9mn}{3}\)  \(=\dfrac{3\times 3\times m\times n}{3}\)
    \(=3mn\)

 

b.    \(\dfrac{4y}{12x}\)  \(=\dfrac{4\times y}{4\times 3\times x} \)
    \(=\dfrac{y}{3x}\)

 

c.    \(\dfrac{16a^2}{-4ab}\) \(=\dfrac{4\times 4\times a\times a}{-4\times a\times b}\)
    \(=\dfrac{-4a}{b}\)

 

d.    \(\dfrac{-18b^2}{-24b}\)  \(=\dfrac{-6\times 3\times b\times b}{-6\times 4\times b}\)
    \(=\dfrac{3b}{4}\)