Algebraic Techniques, SM-Bank 102

Ben recieved \($x\) for his birthday.

He spent \(\dfrac{1}{2}\) of his money on shoes and \(\dfrac{1}{3}\) on Gold Class movie tickets.

Write an algebraic fraction to represent the amount he spent on shoes. (1 mark)

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Write an algebraic fraction to represent the amount he spent on movie tickets. (1 mark)

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Using part (a) and (b) above, write a simplified algebraic fraction to represent the total amount of money he has spent so far. (2 marks)

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Show Answers Only

a. \(\dfrac{$x}{2}\)

b. \(\dfrac{$x}{3}\)

c. \(\dfrac{$5x}{6}\)

Show Worked Solution

a.	\(\text{Shoes}\)	\(=\dfrac{1}{2}\times x\)
		\(=\dfrac{$x}{2}\)

b.	\(\text{Movie tickets}\)	\(=\dfrac{1}{3}\times x\)
		\(=\dfrac{$x}{3}\)

c.	\(\text{Total Spent}\)	\(=\dfrac{x}{2}+\dfrac{x}{3}\)
		\(=\dfrac{x}{2}\times \dfrac{3}{3}+\dfrac{x}{3}\times \dfrac{2}{2}\)
		\(=\dfrac{3x}{6}+\dfrac{2x}{6}\)
		\(=\dfrac{$5x}{6}\)