smc-4697-30-Add/Subtract

Algebraic Techniques, SM-Bank 103

For the expression $\dfrac{a}{2}+\dfrac{2a}{3}-\dfrac{a}{4}$, simplify and write an equivalent algebraic fraction. (3 marks)

Show Answers Only

$\dfrac{11a}{12}$

Show Worked Solution

$\dfrac{a}{2}+\dfrac{2a}{3}-\dfrac{a}{4}$	$=\dfrac{a}{2}\times \dfrac{6}{6}+\dfrac{2a}{3}\times \dfrac{4}{4}-\dfrac{a}{4}\times \dfrac{3}{3}$
	$=\dfrac{6a}{12}+\dfrac{8a}{12}-\dfrac{3a}{12}$
	$=\dfrac{11a}{12}$

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)

--- 1 WORK AREA LINES (style=lined) ---
Write an algebraic fraction to represent the amount he spent on movie tickets. (1 mark)

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

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

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{$5x}{6}$

Algebraic Techniques, SM-Bank 101

Yesterday Gareth walked $x$ kilometres in Kosciuszko National park.

He started at Thredbo village and walked up Merritts Nature Track to the Kosciuszko express chairlift. When he arrived at the chairlift he had complete $\dfrac{1}{5}$ of the total distance.

Gareth then joined a walking group and walked a further $\dfrac{1}{3}$ of the total distance before beginning his descent back to the village.

Write an algebraic fraction to represent the distance he walked to the Kosciuszko express chairlift. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
Write an algebraic fraction to represent the distance he walked with the walking group. (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
Using part (a) and (b) above, write a simplified algebraic fraction to represent the total distance Gareth covered in the first two legs of his walk. (2 marks)

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

Show Answers Only

a. $\dfrac{x}{5}\ \text{kilometres}$

b. $\dfrac{x}{3}\ \text{kilometres}$

c. $\dfrac{8x}{15}\ \text{kilometres}$

Show Worked Solution

a.	$\text{First leg}$	$=\dfrac{1}{5}\times x$
		$=\dfrac{x}{5}\ \text{kilometres}$

b.	$\text{Second leg}$	$=\dfrac{1}{3}\times x$
		$=\dfrac{x}{3}\ \text{kilometres}$

c.	$\text{Distance travelled}$	$=\dfrac{x}{5}+\dfrac{x}{3}$
		$=\dfrac{x}{5}\times \dfrac{3}{3}+\dfrac{x}{3}\times \dfrac{5}{5}$
		$=\dfrac{3x}{15}+\dfrac{5x}{15}$
		$=\dfrac{8x}{15}\ \text{kilometres}$

Algebraic Techniques, SM-Bank 100

For the sum $a+\dfrac{a}{4}$, simplify and write an equivalent algebraic fraction. (2 marks)

Show Answers Only

$\dfrac{5a}{4}$

Show Worked Solution

$a+\dfrac{a}{4}$	$=\dfrac{a}{1}\times \dfrac{4}{4}+\dfrac{a}{4}$
	$=\dfrac{4a}{4}+\dfrac{a}{4}$
	$=\dfrac{5a}{4}$

Algebraic Techniques, SM-Bank 099

For the difference $\dfrac{a}{3}-\dfrac{b}{4}$, simplify and write an equivalent algebraic fraction. (3 marks)

Show Answers Only

$\dfrac{4a-3b}{12}$

Show Worked Solution

$\dfrac{a}{3}-\dfrac{b}{4}$	$=\dfrac{a}{3}\times \dfrac{4}{4}-\dfrac{b}{4}\times \dfrac{3}{3}$
	$=\dfrac{4a}{12}-\dfrac{3b}{12}$
	$=\dfrac{4a-3b}{12}$

Algebraic Techniques, SM-Bank 098

For the difference $\dfrac{5r}{8}-\dfrac{3r}{8}$, simplify and write an equivalent algebraic fraction. (2 marks)

Show Answers Only

$\dfrac{r}{4}$

Show Worked Solution

$\dfrac{5r}{8}-\dfrac{3r}{8}$	$=\dfrac{2r}{8}$
	$=\dfrac{r}{4}$

Algebraic Techniques, SM-Bank 097

For the difference $\dfrac{m}{2}-\dfrac{m}{7}$, simplify and write an equivalent algebraic fraction. (2 marks)

Show Answers Only

$\dfrac{5m}{14}$

Show Worked Solution

$\dfrac{m}{2}-\dfrac{m}{7}$	$=\dfrac{m}{2}\times \dfrac{7}{7}-\dfrac{m}{7}\times \dfrac{2}{2}$
	$=\dfrac{7m}{14}-\dfrac{2m}{14}$
	$=\dfrac{5m}{14}$

Algebraic Techniques, SM-Bank 096

For the difference $\dfrac{a}{4}-\dfrac{a}{5}$, simplify and write an equivalent algebraic fraction. (2 marks)

Show Answers Only

$\dfrac{a}{20}$

Show Worked Solution

$\dfrac{a}{4}-\dfrac{a}{5}$	$=\dfrac{a}{4}\times \dfrac{5}{5}-\dfrac{a}{5}\times \dfrac{4}{4}$
	$=\dfrac{5a}{20}-\dfrac{4a}{20}$
	$=\dfrac{a}{20}$

Algebraic Techniques, SM-Bank 095

For the difference $\dfrac{2x}{3}-\dfrac{x}{4}$, simplify and write an equivalent algebraic fraction. (2 marks)

Show Answers Only

$\dfrac{5x}{12}$

Show Worked Solution

$\dfrac{2x}{3}-\dfrac{x}{4}$	$=\dfrac{2x}{3}\times \dfrac{4}{4}-\dfrac{x}{4}\times \dfrac{3}{3}$
	$=\dfrac{8x}{12}-\dfrac{3x}{12}$
	$=\dfrac{5x}{12}$

Algebraic Techniques, SM-Bank 094

For the sum $\dfrac{a}{2}+\dfrac{a}{3}+\dfrac{a}{4}$, simplify and write an equivalent algebraic fraction. (3 marks)

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

Show Answers Only

$\dfrac{13a}{12}$

Show Worked Solution

$\dfrac{a}{2}+\dfrac{a}{3}+\dfrac{a}{4}$	$=\dfrac{a}{2}\times \dfrac{6}{6}+\dfrac{a}{3}\times \dfrac{4}{4}+\dfrac{a}{4}\times \dfrac{3}{3}$
	$=\dfrac{6a}{12}+\dfrac{4a}{12}+\dfrac{3a}{12}$
	$=\dfrac{13a}{12}$

Algebraic Techniques, SM-Bank 093

For the sum $\dfrac{b}{3}+\dfrac{5b}{6}$, simplify and write an equivalent algebraic fraction. (2 marks)

Show Answers Only

$\dfrac{7b}{6}$

Show Worked Solution

$\dfrac{b}{3}+\dfrac{5b}{6}$	$=\dfrac{b}{3}\times \dfrac{2}{2}+\dfrac{5b}{6}$
	$=\dfrac{2b}{6}+\dfrac{5b}{6}$
	$=\dfrac{7b}{6}$

Algebraic Techniques, SM-Bank 092

For the sum $\dfrac{2x}{3}+\dfrac{x}{5}$, simplify and write an equivalent algebraic fraction. (2 marks)

Show Answers Only

$\dfrac{13x}{15}$

Show Worked Solution

$\dfrac{2x}{3}+\dfrac{x}{5}$	$=\dfrac{2x}{3}\times \dfrac{5}{5}+\dfrac{x}{5}\times \dfrac{3}{3}$
	$=\dfrac{10x}{15}+\dfrac{3x}{15}$
	$=\dfrac{13x}{15}$

Algebraic Techniques, SM-Bank 091

For the sum $\dfrac{a}{4}+\dfrac{a}{2}$, simplify and write an equivalent algebraic fraction. (2 marks)

Show Answers Only

$\dfrac{3a}{4}$

Show Worked Solution

$\dfrac{a}{4}+\dfrac{a}{2}$	$=\dfrac{a}{4}+\dfrac{a}{2}\times \dfrac{2}{2}$
	$=\dfrac{a}{4}+\dfrac{2a}{4}$
	$=\dfrac{3a}{4}$

Algebraic Techniques, SM-Bank 090

For the sum $\dfrac{m}{3}+\dfrac{m}{2}$, simplify and write an equivalent algebraic fraction. (2 marks)

Show Answers Only

$\dfrac{5m}{6}$

Show Worked Solution

$\dfrac{m}{3}+\dfrac{m}{2}$	$=\dfrac{m}{3}\times \dfrac{2}{2}+\dfrac{m}{2}\times \dfrac{3}{3}$
	$=\dfrac{2m}{6}+\dfrac{3m}{6}$
	$=\dfrac{5m}{6}$

\(\dfrac{a}{2}+\dfrac{2a}{3}-\dfrac{a}{4}\)	\(=\dfrac{a}{2}\times \dfrac{6}{6}+\dfrac{2a}{3}\times \dfrac{4}{4}-\dfrac{a}{4}\times \dfrac{3}{3}\)
	\(=\dfrac{6a}{12}+\dfrac{8a}{12}-\dfrac{3a}{12}\)
	\(=\dfrac{11a}{12}\)

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

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

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

a.	\(\text{First leg}\)	\(=\dfrac{1}{5}\times x\)
		\(=\dfrac{x}{5}\ \text{kilometres}\)

c.	\(\text{Distance travelled}\)	\(=\dfrac{x}{5}+\dfrac{x}{3}\)
		\(=\dfrac{x}{5}\times \dfrac{3}{3}+\dfrac{x}{3}\times \dfrac{5}{5}\)
		\(=\dfrac{3x}{15}+\dfrac{5x}{15}\)
		\(=\dfrac{8x}{15}\ \text{kilometres}\)

\(a+\dfrac{a}{4}\)	\(=\dfrac{a}{1}\times \dfrac{4}{4}+\dfrac{a}{4}\)
	\(=\dfrac{4a}{4}+\dfrac{a}{4}\)
	\(=\dfrac{5a}{4}\)

\(\dfrac{a}{3}-\dfrac{b}{4}\)	\(=\dfrac{a}{3}\times \dfrac{4}{4}-\dfrac{b}{4}\times \dfrac{3}{3}\)
	\(=\dfrac{4a}{12}-\dfrac{3b}{12}\)
	\(=\dfrac{4a-3b}{12}\)

\(\dfrac{5r}{8}-\dfrac{3r}{8}\)	\(=\dfrac{2r}{8}\)
	\(=\dfrac{r}{4}\)