Grouping with brackets | Year 7

01 / LEARN

The idea, step by step

A bracket creates one quantity

In $4 (x + 3)$ , add $x$ and 3 before multiplying by 4. It describes four equal groups, each containing $x + 3$ . In $4 x + 3$ , there are four copies of $x$ but only one extra 3. Brackets change the meaning.

When $x = 2$ , the first expression is $4 (2 + 3) = 20$ . The second is $4 \times 2 + 3 = 11$ . Checking both values shows why brackets cannot simply be removed.

Count groups after writing one group

If one set contains an item costing $p$ dollars and another costing 2 dollars, the set costs $p + 2$ . Three sets cost $3 (p + 2)$ . Write the whole cost of one set first, then multiply by the set number.

Brackets also show which amount is divided or subtracted. In $(a + b) \div 2$ , share the combined amount. In $20 - (x + 4)$ , take both $x$ and 4 away from 20. Follow the group before the surrounding operation.

A common trap

Omitting brackets when the whole sum is repeated.

Instead: Write one complete group, bracket it, then multiply by the number of groups.

02 / WORKED EXAMPLES

See the thinking

Example 1

Three sets

A pen costs $p$ dollars and a notebook costs 4 dollars. Write the cost of three sets, each with one pen and one notebook.

One set costs $p + 4$ .
Multiply that whole sum by 3.

3 (p + 4)

dollars.

Example 2

Two similar-looking expressions

Evaluate $2 (n + 5)$ and $2 n + 5$ when $n = 4$ .

$2 (4 + 5) = 2 \times 9 = 18$ .
$2 \times 4 + 5 = 13$ .
The extra 5 is counted twice only in the first expression.

18 and 13, respectively.

Check your understanding

Which means five times the sum of $x$ and 2: $5 x + 2$ or $5 (x + 2)$ ?

Show answer

$5 (x + 2)$

The whole sum is multiplied by 5.

03 / WORKSHEET

Your turn

6 questions · 10 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Write four times the sum of $a$ and 6.
1 mark
Evaluate $3 (n + 2)$ for $n = 5$ .
2 marks
Evaluate $3 n + 2$ for $n = 5$ .
1 mark
Each pack has $x$ red counters and 3 blue counters. Write the total in six equal packs.
2 marks
For $x = 4$ , compare $20 - (x + 5)$ and $20 - x + 5$ .
2 marks
A student writes $2 p + 7$ for two boxes, each with $p$ pencils and 7 pens. Explain the error and correct it.
2 marks

Read the worked solutions

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

Write four times the sum of $a$ and 6.
1 mark
The sum is $a + 6$ . Multiply all of it by 4.
$4 (a + 6)$
Evaluate $3 (n + 2)$ for $n = 5$ .
2 marks
$3 (5 + 2) = 3 \times 7 = 21$ .
21
Evaluate $3 n + 2$ for $n = 5$ .
1 mark
$3 \times 5 + 2 = 17$ .
17
Each pack has $x$ red counters and 3 blue counters. Write the total in six equal packs.
2 marks
One pack contains $x + 3$ .
Six packs contain six copies of that sum.
$6 (x + 3)$
For $x = 4$ , compare $20 - (x + 5)$ and $20 - x + 5$ .
2 marks
$20 - (4 + 5) = 11$ .
$20 - 4 + 5 = 21$ .
11 and 21, respectively.
A student writes $2 p + 7$ for two boxes, each with $p$ pencils and 7 pens. Explain the error and correct it.
2 marks
Each box contains $p + 7$ items.
$2 p + 7$ counts the pens only once.
The pens must be counted in both boxes. Correct expression: $2 (p + 7)$ .

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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 ↗

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