Mathematical notation and implied multiplication | Year 7

01 / LEARN

The idea, step by step

Multiplication without a sign

Algebra writes a number beside a letter to mean multiplication. Thus $6 a$ means $6 \times a$ . Put the numerical coefficient first. The product of 3, $p$ and $q$ is $3 p q$ . A number beside a bracket also means multiply: $2 (n + 5)$ multiplies the whole bracket by 2.

This shorthand works when letters or brackets identify the factors. Do not write 34 to mean $3 \times 4$ : 34 is already a different number. Between numerical factors, keep the multiplication sign when it is needed.

Powers and division

The product $a \times a$ is $a^{2}$ , read as a squared. It is different from $2 a$ , which means $a + a$ . A coefficient multiplies the power: $3 a^{2}$ means $3 \times a \times a$ . Calculate the power before multiplying by the coefficient.

A fraction bar represents division and groups its full numerator. The expression $\frac{x}{4}$ means $x \div 4$ . To divide a whole sum, write all of it above the bar: $\frac{x + 3}{4}$ .

A common trap

Reading $x^{2}$ as $2 x$ .

Instead: Write out the multiplication: $x^{2} = x \times x$ , whereas $2 x = x + x$ .

02 / WORKED EXAMPLES

See the thinking

Example 1

Write a product

Write $4 \times b \times c$ in algebraic shorthand.

Put the numerical coefficient first.
Write the variable factors beside it; changing their order does not change the product.

4 b c

Example 2

Square or double?

Compare $a^{2}$ and $2 a$ when $a = 5$ .

$a^{2} = 5 \times 5 = 25$ .
$2 a = 2 \times 5 = 10$ .
Squaring multiplies a number by itself; doubling multiplies it by 2.

a^{2} = 25

and

2 a = 10

Check your understanding

Write $7 \times t$ in algebraic shorthand.

Show answer

$7 t$

The coefficient comes before the variable.

03 / WORKSHEET

Your turn

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

Worksheet PDF Worked solutions

Read the questions online

Write $8 \times y$ in shorthand.
1 mark
Write $a \times b$ in shorthand.
1 mark
Write $5 \times k \times k$ in shorthand.
2 marks
Show the multiplication sign in $3 (p + 2)$ .
1 mark
Evaluate $4 b$ when $b = 6$ .
1 mark
For $x = 3$ , find $x^{2}$ and $2 x$ . Are they equal?
2 marks

Read the worked solutions

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

Write $8 \times y$ in shorthand.
1 mark
Put the coefficient before the letter.
$8 y$
Write $a \times b$ in shorthand.
1 mark
The variable factors may be written beside one another.
$a b$
Write $5 \times k \times k$ in shorthand.
2 marks
The repeated factor gives $k^{2}$ .
Keep 5 as the coefficient.
$5 k^{2}$
Show the multiplication sign in $3 (p + 2)$ .
1 mark
The 3 multiplies the whole bracket.
$3 \times (p + 2)$
Evaluate $4 b$ when $b = 6$ .
1 mark
$4 b = 4 \times 6 = 24$ .
24
For $x = 3$ , find $x^{2}$ and $2 x$ . Are they equal?
2 marks
$x^{2} = 3 \times 3 = 9$ .
$2 x = 2 \times 3 = 6$ .
9 and 6; they are not equal.

Checking saved progress…

Continue learning

Writing expressions from words

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