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Translate between a description and an algebraic expression

Start a set of 8
Step 3 of 12

Keep the operation and the grouping

A pronumeral stands for a number. An expression records what to do with it. Read a grouped quantity before applying the operation outside it

Operation words

Sum means addition, product means multiplication and quotient means division

\[\begin{gathered}\text{sum}:\ r+s\\\text{product}:\ rs\\\text{quotient}:\ \frac{r}{s},\quad s\ne0\end{gathered}\]

Subtraction has an order

Start with the quantity named after less than, then subtract the other quantity

\[\text{Eleven less than }t:\ t-11\]

A coefficient multiplies

A number beside a pronumeral is a multiplying factor. The number on its own is the constant term

\[\underbrace{8}_{\text{coefficient}}r+\underbrace{9}_{\text{constant term}}\]

Group the complete sum

Brackets make the sum one factor. A fraction bar groups the whole numerator and denominator

\[\begin{gathered}k(r+s)\\\frac{r+s}{k},\quad k\ne0\end{gathered}\]
Year 9, Chapter 2, 4 difficulty levels, No calculatorBuild a worksheet

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

  1. Read the operation Translate sum, product and quotient as addition, multiplication and division \(\displaystyle \begin{gathered}r+s\\rs\\\frac{r}{s},\quad s\ne0\end{gathered}\)
  2. Read the order For subtraction and division, identify the starting quantity. Less than names the amount being removed before the starting quantity \(\displaystyle \text{Eleven less than }t:\ t-11\)
  3. Keep a whole quantity together Use brackets for a complete factor or base. A fraction bar and a root sign also group their contents \(\displaystyle \begin{gathered}k(r+s)\\\frac{r+s}{k},\quad k\ne0\\\sqrt{r+s},\quad r+s\ge0\end{gathered}\)
  4. 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 it
Dividing 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 sum
Reading 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 expression

Difficulty 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)