YEAR 7 · ALGEBRAIC EXPRESSIONS AND FORMULAS · 12 MIN

Writing expressions from words

Translate words and simple situations into expressions, with the correct order of subtraction and division.

In this lesson

Translate operation phrases
Group a sum before multiplying or dividing
Define a variable in context

Before you start

Algebraic shorthand
Reading arithmetic instructions

01 / LEARN

Understand the idea.

Choose the operation and its order

Translate the operation as well as the numbers. “Five more than $n$ ” gives $n + 5$ ; “five times $n$ ” gives $5 n$ . For subtraction, start with the quantity being reduced: “five less than $n$ ” gives $n - 5$ .

Order matters in subtraction. “ $n$ less than five” instead gives $5 - n$ . Use a simple value to check your interpretation: when $n = 12$ , five less than $n$ should be $7$ , so $n - 5$ matches the words.

Keep a whole quantity together

Find the whole quantity affected by an operation. “Twice the sum of $x$ and $4$ ” means first form $x + 4$ , then multiply that entire sum: $2 (x + 4)$ . “One third of the sum” gives $\frac{x + 4}{3}$ .

In a situation, define what the variable counts and distinguish a repeated charge from a one-off charge. If $b$ buses each carry $40$ students, $40 b$ counts the students. An extra quantity is added once unless it occurs in every group.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Read 'less than' carefully

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

Worked solution

1
Translate the starting quantity.
$Three times x = 3 x$
Multiplication forms the quantity that will then be reduced.
2
Subtract seven from that quantity.
$3 x - 7$
Seven less than a quantity means take seven away from it.
3
Read the expression back.
Three times $x$ , then minus seven, follows the operation order stated in the question.

Answer

$3 x - 7$ .

EXAMPLE 02

One booking fee

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

Worked solution

1
Calculate the variable ticket cost.
$6 \times n = 6 n dollars$
There are $n$ tickets, each costing six dollars.
2
Add the booking fee once.
$6 n + 4 dollars$
The four-dollar fee belongs to the whole booking, rather than to every ticket.
3
Check the roles of the terms.
The six-dollar charge repeats with the ticket count, while the four-dollar charge remains fixed.

Answer

$6 n + 4$ dollars.

03 / YOUR TURN

Try it yourself.

Check your understanding

Write half the sum of $p$ and 8.

Show answer & reasoning

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

First form the entire sum $p + 8$ , then halve it: $\frac{p + 8}{2}$ . The fraction bar groups both terms, so neither is left outside the division.

Keep practising

6 worksheet questions · 8 marks

Open worksheet 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.
$8 b + 15$

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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 ↗

In this lesson

Understand the idea.

Choose the operation and its order

Keep a whole quantity together

See the method in action.

Read 'less than' carefully

Translate the starting quantity.

Subtract seven from that quantity.

Read the expression back.

One booking fee

Calculate the variable ticket cost.

Add the booking fee once.

Check the roles of the terms.

Try it yourself.

Check your understanding

Keep practising