Writing expressions with operations and brackets

01 / LEARN

The idea, step by step

Give each quantity a symbol

A variable, such as $x$ , represents a quantity that can take different values. A constant is a fixed number. In $x + 7$ , $x$ is the variable and $7$ is the constant term.

An expression describes a calculation, such as $x + 7$ . An equation states that two expressions are equal, such as $x + 7 = 12$ . When asked to write an expression, you do not need to find $x$ .

Translate the operation and its order

Read which quantity the operation acts on. Subtracting $5$ from $n$ gives $n - 5$ ; subtracting $n$ from $5$ gives $5 - n$ . Dividing $n$ by $5$ gives $\frac{n}{5}$ , while dividing $5$ by $n$ gives $\frac{5}{n}$ , with $n \neq 0$ .

Write multiplication compactly: $4 \times n$ becomes $4 n$ . Put the number before the variable. Write $x$ rather than $1 x$ , and $t$ rather than $1 t$ . The expression $4 n$ means multiplication; $4 + n$ means addition.

Keep grouped quantities together

Use brackets when a whole sum or difference is multiplied or divided. Three times the sum of $x$ and $2$ is $3 (x + 2)$ : add first, then multiply the whole result by $3$ .

Two more than three times $x$ is $3 x + 2$ : multiply first, then add $2$ . The brackets change which quantity is multiplied. Leave a grouped expression in brackets when that clearly represents the situation.

A common trap

'Three times the sum of $x$ and $2$ ' is $3 x + 2$ .

Instead: The whole sum must be multiplied, so write $3 (x + 2)$ . In $3 x + 2$ , only $x$ is multiplied by $3$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Translate addition and subtraction

Let $n$ represent a number. Write expressions for (a) seven more than $n$ , and (b) subtract $n$ from $12$ .

For (a), start with $n$ and add $7$ .
For (b), start with $12$ and take away $n$ . The word 'from' tells us which quantity comes first in the subtraction.

(a)

n + 7

; (b)

12 - n

Example 2

Represent a fixed fee and a changing cost

One ticket costs $t$ dollars. Write an expression for the cost, in dollars, of five tickets plus one booking fee of $2$ dollars.

Five tickets cost $5 \times t = 5 t$ dollars.
The booking fee is paid once, so add the constant $2$ to the ticket cost.

5 t + 2

dollars.

Example 3

Decide whether brackets are needed

Write expressions for (a) three times the sum of $x$ and $2$ , and (b) two more than three times $x$ .

For (a), form the sum $x + 2$ first. Multiply that whole sum by $3$ , giving $3 (x + 2)$ .
For (b), multiply $x$ by $3$ first, giving $3 x$ . Then add $2$ , giving $3 x + 2$ .

(a)

3 (x + 2)

; (b)

3 x + 2

Check your understanding

Write an expression for: add $4$ to $y$ , then divide the whole result by $2$ .

Show answer

$\frac{y + 4}{2}$ , or $(y + 4) \div 2$ .

The addition happens first. The fraction bar groups the whole numerator $y + 4$ , so both parts belong to the quantity being divided.

03 / WORKSHEET

Your turn

8 questions · 19 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

In $x + 7$ , name the variable and the constant term. Is $x + 7$ an expression or an equation? Explain briefly.
3 marks
Let $p$ represent a number. Write expressions for
1. (a)eight more than $p$ , and
2. (b)subtract $6$ from $p$ .
2 marks
Rewrite using usual algebra notation:
1. (a) $1 \times x$ ,
2. (b) $5 \times t$ ,
3. (c) $n \div 4$ .
3 marks
Write expressions for
1. (a)divide $a$ by $5$ , and
2. (b)divide $5$ by $a$ . Assume $a \neq 0$ .
2 marks
Write expressions for
1. (a)three times the sum of $n$ and $4$ , and
2. (b)four more than three times $n$ .
2 marks
Each of four boxes holds $b$ blue tokens and $2$ red tokens. Write an expression for the total number of tokens in all four boxes. Explain your brackets.
2 marks
A ribbon is $m$ centimetres long, where $m > 9$ . Cut off $9$ centimetres, then divide the remaining ribbon into three equal pieces. Write an expression for the length of one piece.
2 marks
A shopper buys $x$ notebooks at $3$ dollars each and $y$ pens at $2$ dollars each. The total cost is no more than $20$ dollars. Write an expression for the change from $20$ dollars, showing how you formed it.
3 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

In $x + 7$ , name the variable and the constant term. Is $x + 7$ an expression or an equation? Explain briefly.
3 marks
$x$ represents the quantity that can vary. (1 mark)
$7$ is the fixed number added to $x$ . (1 mark)
It is an expression because it describes a calculation without an equality statement. (1 mark)
Variable: $x$ . Constant term: $7$ . It is an expression.
Let $p$ represent a number. Write expressions for
1. (a)eight more than $p$ , and
2. (b)subtract $6$ from $p$ .
2 marks
(a) Start with $p$ and add $8$ : $p + 8$ . (1 mark)
(b) Start with $p$ and take away $6$ : $p - 6$ . (1 mark)
1. (a) $p + 8$ ;
2. (b) $p - 6$ .
Rewrite using usual algebra notation:
1. (a) $1 \times x$ ,
2. (b) $5 \times t$ ,
3. (c) $n \div 4$ .
3 marks
(a) Multiplying by $1$ leaves the quantity unchanged; omit the coefficient $1$ : $x$ . (1 mark)
(b) Put the numerical coefficient before the variable and omit the multiplication sign: $5 t$ . (1 mark)
(c) Put the quantity being divided above the divisor: $\frac{n}{4}$ . (1 mark)
1. (a) $x$ ;
2. (b) $5 t$ ;
3. (c) $\frac{n}{4}$ .
Write expressions for
1. (a)divide $a$ by $5$ , and
2. (b)divide $5$ by $a$ . Assume $a \neq 0$ .
2 marks
(a) $a$ is divided into five equal parts, giving $\frac{a}{5}$ . (1 mark)
(b) $5$ is the quantity being divided, and $a$ is the divisor, giving $\frac{5}{a}$ . (1 mark)
1. (a) $\frac{a}{5}$ ;
2. (b) $\frac{5}{a}$ .
Write expressions for
1. (a)three times the sum of $n$ and $4$ , and
2. (b)four more than three times $n$ .
2 marks
(a) Form $n + 4$ , then multiply the whole sum by $3$ : $3 (n + 4)$ . (1 mark)
(b) Form $3 n$ , then add $4$ : $3 n + 4$ . (1 mark)
1. (a) $3 (n + 4)$ ;
2. (b) $3 n + 4$ .
Each of four boxes holds $b$ blue tokens and $2$ red tokens. Write an expression for the total number of tokens in all four boxes. Explain your brackets.
2 marks
One box contains $b + 2$ tokens. (1 mark)
There are four copies of that whole quantity, so the total is $4 (b + 2)$ . The brackets keep the tokens in one box together. (1 mark)
$4 (b + 2)$ tokens.
A ribbon is $m$ centimetres long, where $m > 9$ . Cut off $9$ centimetres, then divide the remaining ribbon into three equal pieces. Write an expression for the length of one piece.
2 marks
After the cut, the remaining length is $m - 9$ centimetres. (1 mark)
Divide that whole remaining length by $3$ : $\frac{m - 9}{3}$ centimetres. The fraction bar groups the subtraction. (1 mark)
$\frac{m - 9}{3}$ centimetres.
A shopper buys $x$ notebooks at $3$ dollars each and $y$ pens at $2$ dollars each. The total cost is no more than $20$ dollars. Write an expression for the change from $20$ dollars, showing how you formed it.
3 marks
The notebooks cost $3 x$ dollars. (1 mark)
The pens cost $2 y$ dollars, so the total cost is $3 x + 2 y$ dollars. (1 mark)
Subtract the whole cost from the amount paid: $20 - (3 x + 2 y)$ dollars. Accept the equivalent expression $20 - 3 x - 2 y$ . (1 mark)
$20 - (3 x + 2 y)$ dollars.

Checking saved progress…

Continue learning

Solving and checking linear equations

Next lesson

Curriculum reference & lesson scope

Australian Curriculum, Assessment and Reporting Authority (ACARA) · Australian Curriculum v9.0

AC9M7A02: Formulate algebraic expressions using constants, variables, operations and brackets

Formulating expressions from words and familiar situations, including conventional notation and grouping. Expressions and equations are distinguished, but solving equations, expanding and factorising are not taught in this lesson.

Official curriculum source ↗

Source checked 2026-11-02. Schools may sequence content differently.

Back to Algebra