YEAR 7 · ALGEBRAIC EXPRESSIONS AND FORMULAS · 12 MIN

Substituting into expressions/formulas

Substitute numerical values consistently, follow operation order and interpret formula answers with units.

In this lesson

Replace every occurrence of a variable
Evaluate formulas with several variables
State meaningful units

Before you start

Algebraic notation
Brackets
Order of operations

01 / LEARN

Understand the idea.

Replace every matching letter

Substitution replaces each occurrence of a variable by its stated value. To evaluate $3 x + 2$ at $x = 4$ , write $3 \times 4 + 2$ first. Showing the multiplication prevents confusing $3 x$ with either $3 + x$ or the number $34$ .

Use the same replacement everywhere the letter appears. In $x^{2} + x$ at $x = 3$ , both occurrences become $3$ . Preserve the expression's brackets and follow the order of operations: brackets, powers, multiplication or division, then addition or subtraction.

Follow the formula and its meaning

Before using a formula, identify each required quantity and its unit. In $P = 2 (l + w)$ , substitute the length for $l$ and width for $w$ , add the two lengths, then double that sum to count all four sides.

Attach the unit of the quantity calculated. Perimeter measures length, area measures square units and cost measures money. Check the result against the situation: for example, a rectangle's perimeter must include two lengths and two widths, not just one of each.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

A repeated variable

Evaluate $2 a^{2} + a$ when $a = 3$ .

Worked solution

1
Replace every occurrence of the variable.
$2 a^{2} + a = 2 \times 3^{2} + 3$
The same value three replaces both occurrences, while the coefficient remains two.
2
Calculate the power first.
$3^{2} = 9, 2 \times 3^{2} + 3 = 2 \times 9 + 3$
The exponent applies to three, before the multiplication by two.
3
Complete multiplication, then addition.
$2 \times 9 + 3 = 18 + 3 = 21$
Multiplication precedes the final addition.

Answer

21.

EXAMPLE 02

A perimeter formula

Use $P = 2 (l + w)$ for length 8 cm and width 5 cm.

Worked solution

1
Substitute both dimensions.
$P = 2 (8 + 5)$
The formula requires the eight-centimetre length and five-centimetre width.
2
Calculate the bracketed sum.
$P = 2 \times 13$
One length plus one width is thirteen centimetres.
3
Double the sum and state the unit.
$P = 26 cm$
Doubling counts the other length and width, so the perimeter is a length in centimetres.

Answer

26 cm.

03 / YOUR TURN

Try it yourself.

Check your understanding

Evaluate $5 n + 6$ when $n = 4$ .

Show answer & reasoning

Replace $n$ by four and multiply before adding: $5 n + 6 = 5 \times 4 + 6 = 20 + 6 = 26$ . The coefficient five remains a multiplier.

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

Evaluate $4 x + 3$ for $x = 5$ .
1 mark
Evaluate $7 a - 2$ for $a = 4$ .
1 mark
Evaluate $b^{2} + 2 b$ for $b = 6$ .
2 marks
Evaluate $3 (p + 4)$ for $p = 7$ .
2 marks
A museum charges $C = 4 n + 6$ dollars for $n$ children. Find the cost for 7 children.
2 marks
A rectangle is 9 cm long and 4 cm wide. Use $A = l w$ and $P = 2 (l + w)$ to find its area and perimeter.
3 marks

Read the worked solutions

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

Evaluate $4 x + 3$ for $x = 5$ .
1 mark
$4 \times 5 + 3 = 23$ .
23
Evaluate $7 a - 2$ for $a = 4$ .
1 mark
$7 \times 4 - 2 = 26$ .
26
Evaluate $b^{2} + 2 b$ for $b = 6$ .
2 marks
$6^{2} + 2 \times 6 = 36 + 12 = 48$ .
48
Evaluate $3 (p + 4)$ for $p = 7$ .
2 marks
$3 (7 + 4) = 3 \times 11 = 33$ .
33
A museum charges $C = 4 n + 6$ dollars for $n$ children. Find the cost for 7 children.
2 marks
$C = 4 \times 7 + 6 = 34$ .
The result is a cost in dollars.
34 dollars
A rectangle is 9 cm long and 4 cm wide. Use $A = l w$ and $P = 2 (l + w)$ to find its area and perimeter.
3 marks
$A = 9 \times 4 = 36$ cm².
$P = 2 (9 + 4) = 26$ cm.
Area 36 cm²; perimeter 26 cm.

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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.

Replace every matching letter

Follow the formula and its meaning

See the method in action.

A repeated variable

Replace every occurrence of the variable.

Calculate the power first.

Complete multiplication, then addition.

A perimeter formula

Substitute both dimensions.

Calculate the bracketed sum.

Double the sum and state the unit.

Try it yourself.

Check your understanding

Keep practising