Writing expressions from words | Year 7

01 / LEARN

The idea, step by step

Choose the operation and its order

Five more than $n$ is $n + 5$ , while five times $n$ is $5 n$ . Subtraction order matters: five less than $n$ is $n - 5$ , while $n$ less than five is $5 - n$ . Start with the quantity being changed, then apply the instruction.

Check a phrase by choosing a sensible number. If $n = 12$ , five less than $n$ should be 7. The expression $n - 5$ gives 7, while $5 - n$ does not. The numerical check helps interpret the words.

Keep a whole quantity together

The sum of $x$ and 4 is $x + 4$ . Twice that sum is $2 (x + 4)$ because the whole result is doubled. Dividing that sum by 3 gives $\frac{x + 4}{3}$ . The bracket or fraction bar shows which quantities are grouped.

In a situation, define what the letter counts. If $b$ is the number of buses and each bus carries 40 students, the student number is $40 b$ . A one-off extra quantity is added only once unless the situation says it occurs in every group.

A common trap

Writing $6 - n$ for six less than $n$ .

Instead: Start with $n$ , then subtract 6. With $n = 10$ , the phrase should give 4.

02 / WORKED EXAMPLES

See the thinking

Example 1

Read 'less than' carefully

Write an expression for seven less than three times $x$ .

Three times $x$ is $3 x$ .
Subtract 7 from that result.

3 x - 7

Example 2

One booking fee

A class buys $n$ tickets at 6 dollars each and pays one booking fee of 4 dollars. Write the total cost.

The tickets cost $6 n$ dollars.
The one-off fee adds 4 once.

6 n + 4

dollars.

Check your understanding

Write half the sum of $p$ and 8.

Show answer

$\frac{p + 8}{2}$

Add first, then divide the entire sum by 2.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Write nine more than $a$ .
1 mark
Write four times $b$ .
1 mark
Write three less than $2 x$ .
1 mark
Write 12 decreased by $t$ .
1 mark
Write the sum of $m$ and 5, divided by 4.
2 marks
Bottles cost 8 dollars each, plus one delivery fee of 15 dollars. Let $b$ be the number of bottles. Write the total cost.
2 marks

Read the worked solutions

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

Write nine more than $a$ .
1 mark
Add 9 to the starting number.
$a + 9$
Write four times $b$ .
1 mark
Multiply $b$ by 4.
$4 b$
Write three less than $2 x$ .
1 mark
Start with $2 x$ , then subtract 3.
$2 x - 3$
Write 12 decreased by $t$ .
1 mark
Subtract $t$ from 12.
$12 - t$
Write the sum of $m$ and 5, divided by 4.
2 marks
First form $m + 5$ .
Divide the whole sum by 4.
$\frac{m + 5}{4}$
Bottles cost 8 dollars each, plus one delivery fee of 15 dollars. Let $b$ be the number of bottles. Write the total cost.
2 marks
The bottles cost $8 b$ .
Add the delivery charge once.
$8 b + 15$

Checking saved progress…

Continue learning

Grouping with brackets

Next lesson

Curriculum reference & lesson scope

Australian Curriculum v9.0 / SA Curriculum Mathematics

Year 7 variables, expression notation, substitution, simple equivalence and formula tables. Digital methods are explained with supplied data; the topic test works by hand.

Official curriculum source ↗

Back to Algebraic expressions and formulas