Reading and writing expressions
An expression combines numbers and pronumerals using operations. A term keeps its sign. A coefficient multiplies a pronumeral; a constant term has no pronumeral
- Read the operation Translate sum, product and quotient as addition, multiplication and division \(\displaystyle \begin{gathered}r+s\\rs\\\frac{r}{s},\quad s\ne0\end{gathered}\)
- Read the order For subtraction and division, identify the starting quantity. Less than names the amount being removed before the starting quantity \(\displaystyle \text{Eleven less than }t:\ t-11\)
- Keep a whole quantity together Use brackets for a complete factor or base. A fraction bar and a root sign also group their contents \(\displaystyle \begin{gathered}k(r+s)\\\frac{r+s}{k},\quad k\ne0\\\sqrt{r+s},\quad r+s\ge0\end{gathered}\)
- Distinguish powers and reciprocals Read which quantity is squared, cubed or used as the denominator. Do not expand a grouped power merely to name it \(\displaystyle \begin{gathered}(r+s)^2\\r^2+s^2\\(r+s)^3\\\frac{1}{r+s},\quad r+s\ne0\end{gathered}\)
Common mistakes
Reversing a subtraction
✕\(\displaystyle \text{Eleven less than }t:\ 11-t\)✓\(\displaystyle \text{Eleven less than }t:\ t-11\)
The variable is the starting quantity, and the stated amount is removed from itDividing only one term
✕\(\displaystyle \begin{gathered}\text{Divide the sum by six:}\\r+\frac{s}{6}\end{gathered}\)✓\(\displaystyle \begin{gathered}\text{Divide the sum by six:}\\\frac{r+s}{6}\end{gathered}\)
The fraction bar must cover the whole sumReading a squared sum as separate squares
✕\(\displaystyle \text{Square the sum}:\ h^2+j^2\)✓\(\displaystyle \text{Square the sum}:\ (h+j)^2\)
The complete sum is the base. Separate squares describe another expressionDifficulty levels
introRecognise sums, products and quotients with one pronumeral and a number
standardKeep subtraction order and group sums in products, quotients and equal shares
challengeRecognise powers, roots and reciprocals of complete quantities
examChoose a matching expression or description from four options using the same grouping ideas
Questions about this topic
What is a pronumeral?+
It is a letter used to stand for a number. It is also called a variable
Why does less than change the order?+
It names the amount being removed first. Start with the quantity after those words, then subtract
When does a sum need grouping?+
Group it when the next operation acts on the entire sum. Brackets, fraction bars and root signs can all show grouping
Can I use a calculator?+
No. This topic is practised without a calculator
Which year level and chapter is this?+
Year 9 Mathematics, chapter 2: Linear equations
In this chapter
Translate between a description and an algebraic expressionEvaluate an algebraic expression by substitutionSimplify algebraic terms and collect like termsExpand brackets and collect like terms2D Two-step linear equations: Solve a linear equation2E Linear equations with brackets: Solve a linear equationSet up and solve a practical linear equationSolve and interpret a linear inequationRepresent and read inequalities on a number lineSubstitute values into a formulaSolve for an unknown or recognise a rearranged formulaSolve a pair of simultaneous linear equations (optional extension)Solve a pair of simultaneous linear equations by elimination (optional extension)Set up a pair of simultaneous equations from a description (optional extension)Solve a practical problem with simultaneous equations (optional extension)