Algebraic Techniques, SM-Bank 107

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

\(\dfrac{5}{y}\ ÷\ \dfrac{4}{x}\) (1 mark)

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\(\dfrac{9a}{7}\ ÷\ \dfrac{c}{b}\) (1 mark)

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\(\dfrac{r}{3}\ ÷\ \dfrac{5}{4s}\) (2 marks)

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Show Answers Only

a. \(\dfrac{5x}{4y}\)

b. \(\dfrac{9ab}{7c}\)

c. \(\dfrac{4rs}{45}\)

Show Worked Solution

a.	\(\dfrac{5}{y}\ ÷\ \dfrac{4}{x}\)	\(=\dfrac{5}{y}\times \dfrac{x}{4}\)
		\(=\dfrac{5x}{4y}\)

b.	\(\dfrac{9a}{7}\ ÷\ \dfrac{c}{b}\)	\(=\dfrac{9a}{7}\times\dfrac{b}{c}\)
		\(=\dfrac{9ab}{7c}\)

c.	\(\dfrac{r}{3}\ ÷\ \dfrac{5}{4s}\)	\(=\dfrac{r}{3}\times \dfrac{4s}{5}\)
		\(=\dfrac{4rs}{15}\)