smc-4697-20-Multiply/Divide

Algebraic Techniques, SM-Bank 108

Simplify \(\dfrac{3x}{2}\times \dfrac{8}{5x}\ ÷\ \dfrac{4}{x}\) giving your answer as an algebraic fraction in simplest form. (2 marks)

Show Answers Only

\(\dfrac{3x}{5}\)

Show Worked Solution

\(\dfrac{3x}{2}\times \dfrac{8}{5x}\ ÷\ \dfrac{4}{x}\)	\(=\dfrac{3x}{2}\times \dfrac{8}{5x}\times \dfrac{x}{4}\)
	\(=\dfrac{3x}{5}\)

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)

--- 2 WORK AREA LINES (style=lined) ---
\(\dfrac{9a}{7}\ ÷\ \dfrac{c}{b}\) (1 mark)

--- 2 WORK AREA LINES (style=lined) ---
\(\dfrac{r}{3}\ ÷\ \dfrac{5}{4s}\) (2 marks)

--- 2 WORK AREA LINES (style=lined) ---

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

Algebraic Techniques, SM-Bank 106

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

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

--- 4 WORK AREA LINES (style=lined) ---
\(\dfrac{14x}{3}\ ÷\ \dfrac{7y}{6}\) (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

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

Algebraic Techniques, SM-Bank 105

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

\(\dfrac{2b}{3}\times \dfrac{9c}{5}\) (2 marks)

--- 3 WORK AREA LINES (style=lined) ---
\(\dfrac{8x}{5}\times \dfrac{25y}{12}\) (2 marks)

--- 3 WORK AREA LINES (style=lined) ---

Show Answers Only

a. \(\dfrac{6bc}{5}\)

b. \(\dfrac{10xy}{3}\)

Show Worked Solution

a.	\(\dfrac{2b}{3}\times \dfrac{9c}{5}\)	\(=\dfrac{2b\times 9c}{3\times 5}\)
		\(=\dfrac{18bc\ ÷\ 3}{15\ ÷\ 3}\)
		\(=\dfrac{6bc}{5}\)

b.	\(\dfrac{8x}{5}\times \dfrac{25y}{12}\)	\(=\dfrac{8x\times 25y}{5\times 12}\)
		\(=\dfrac{200xy\ ÷\ 20}{60\ ÷\ 20}\)
		\(=\dfrac{10xy}{3}\)

Algebraic Techniques, SM-Bank 104

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

\(\dfrac{a}{2}\times \dfrac{1}{5}\) (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
\(\dfrac{3x}{5}\times \dfrac{2y}{7}\) (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
\(\dfrac{5r}{9}\times \dfrac{4s}{5}\) (2 marks)

--- 1 WORK AREA LINES (style=lined) ---

Show Answers Only

a. \(\dfrac{a}{10}\)

b. \(\dfrac{6xy}{35}\)

c. \(\dfrac{4rs}{9}\)

Show Worked Solution

\(\dfrac{a}{2}\times \dfrac{1}{5}\)

\(=\dfrac{a\times 1}{2\times 5}=\dfrac{a}{10}\)

\(\dfrac{3x}{5}\times \dfrac{2y}{7}\)

\(=\dfrac{3x\times 2y}{5\times 7}=\dfrac{6xy}{35}\)

\(\dfrac{5r}{9}\times \dfrac{4s}{5}\)

\(=\dfrac{5r\times 4s}{9\times 5}=\dfrac{4rs}{9}\)