Variables, constants and terms | Year 7

01 / LEARN

Understand the idea.

A letter represents a number

A variable represents a number that can take different values. If $n$ is the number of notebooks, it might be $2$ , $5$ or $12$ ; it is a count, not a notebook. Use the same value for every occurrence of $n$ in one calculation.

A constant is fixed. In $4 n + 3$ , the coefficient $4$ multiplies the changing count, while $3$ is added once. The expression can change as $n$ changes, even though its written coefficient and constant remain fixed.

Terms and coefficients

An expression is built from terms joined by addition or subtraction. In $5 x + 8$ , the terms are $5 x$ and $8$ . The coefficient of $x$ is $5$ , meaning five copies of $x$ ; the constant term has no variable.

Keep a subtraction sign with its term. Writing $7 a - 2 b + 9$ as $7 a + (- 2 b) + 9$ exposes the three signed terms. The variables are $a$ and $b$ , and the coefficient of $b$ is $- 2$ .

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Read a cost rule

A booking costs $C = 6 t + 4$ dollars, where $t$ is the number of tickets. Name the coefficient of $t$ and the constant term.

Worked solution

1
Identify the term containing the ticket count.
$6 t = 6 \times t$
The variable term changes with the number of tickets.
2
Read its coefficient.
$Coefficient of t = 6$
The coefficient is the number multiplying the variable.
3
Identify the term without the variable.
$Constant term = 4$
The four-dollar amount is added once and does not depend on the ticket count.

Answer

Coefficient: 6. Constant term: 4.

EXAMPLE 02

Keep the subtraction sign

List the terms in $8 p - 3 q + 5$ and name its variables.

Worked solution

1
Rewrite subtraction as adding a signed term.
$8 p - 3 q + 5 = 8 p + (- 3 q) + 5$
The minus sign belongs to the complete variable term.
2
List the three terms.
$8 p, - 3 q, 5$
Addition now separates each signed term clearly.
3
Name the variables.
$p and q$
These letters represent the numerical quantities that can vary.

Answer

$8 p$ , $- 3 q$ , 5; variables $p$ and $q$ .

03 / YOUR TURN

Try it yourself.

Check your understanding

What is the constant term in $9 k + 11$ ?

Show answer & reasoning

The term $11$ contains no $k$ and remains fixed when $k$ changes. It is therefore the constant term in $9 k + 11$ .

Keep practising

6 worksheet questions · 9 marks

Open worksheet Worked solutions

Read the questions online

Name the variable in $4 x + 7$ .
1 mark
What is the coefficient of $m$ in $9 m + 2$ ?
1 mark
What is the constant term in $3 a + 12$ ?
1 mark
List the terms in $6 p - 4 q + 10$ .
2 marks
A delivery costs $5 b + 8$ dollars, where $b$ is the number of boxes. What does 8 represent?
2 marks
How many terms are in $2 r + 3 s + 4$ ? Name its variables.
2 marks

Read the worked solutions

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

Name the variable in $4 x + 7$ .
1 mark
The letter $x$ represents a number that may change.
$x$
What is the coefficient of $m$ in $9 m + 2$ ?
1 mark
The term $9 m$ means nine copies of $m$ .
9
What is the constant term in $3 a + 12$ ?
1 mark
The added 12 is independent of $a$ .
12
List the terms in $6 p - 4 q + 10$ .
2 marks
Addition and subtraction separate terms.
The minus sign stays with $4 q$ .
$6 p$ , $- 4 q$ , 10
A delivery costs $5 b + 8$ dollars, where $b$ is the number of boxes. What does 8 represent?
2 marks
The $5 b$ part changes with the number of boxes.
The 8 is added once regardless of $b$ .
A fixed delivery charge of 8 dollars.
How many terms are in $2 r + 3 s + 4$ ? Name its variables.
2 marks
The terms are $2 r$ , $3 s$ and 4.
The letters are $r$ and $s$ .
Three terms; variables $r$ and $s$ .

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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.

A letter represents a number

Terms and coefficients

See the method in action.

Read a cost rule

Identify the term containing the ticket count.

Read its coefficient.

Identify the term without the variable.

Keep the subtraction sign

Rewrite subtraction as adding a signed term.

List the three terms.

Name the variables.

Try it yourself.

Check your understanding

Keep practising