Expressions, formulae and equations
Using expressions and formulae
A formula is a rule written in algebra. Put numbers in, and the answer falls out.
Substituting
To SUBSTITUTE means to replace each letter with its number, then work the answer out. If x = 5, then: • x + 3 = 5 + 3 = 8 • 4x = 4 × 5 = 20 • x/5 = 5 ÷ 5 = 1 • 2x + 1 = 2 × 5 + 1 = 11
Order matters
Do the multiplying and dividing BEFORE the adding and subtracting. 2x + 3 when x = 4: First 2 × 4 = 8, then 8 + 3 = 11. (Not 2 × 7 = 14.) If there are brackets, do those first of all.
Formulae
A formula gives a rule for working something out. The perimeter of a rectangle: P = 2(l + w) With l = 7 and w = 3: P = 2(7 + 3) = 2 × 10 = 20 The area of a rectangle: A = lw With l = 7 and w = 3: A = 7 × 3 = 21 The same formula works for every rectangle — that is the point of writing it with letters.
Worked examples
Work out 4x when x = 5
- 4x means 4 × x.
- 4 × 5 = 20.
Answer: 20
Work out 2x + 1 when x = 5
- Multiply first: 2 × 5 = 10.
- Then add: 10 + 1 = 11.
Answer: 11
Work out 2x + 3 when x = 4
- Multiplying comes before adding.
- 2 × 4 = 8, then 8 + 3 = 11.
- It is NOT 2 × 7 = 14.
Answer: 11
P = 2(l + w) with l = 7 and w = 3
- Brackets first: 7 + 3 = 10.
- Then 2 × 10 = 20.
Answer: P = 20
A = lw with l = 7 and w = 3
- lw means l × w.
- 7 × 3 = 21.
Answer: A = 21
Work out x/5 when x = 5
- x/5 means x ÷ 5.
- 5 ÷ 5 = 1.
Answer: 1
Where you see this in real life
- A recipe scaled for p people uses 75p grams of rice — one formula covering any number of guests.
- Converting temperature, distance or currency all use formulae: put your number in, read your answer out.
Key words
- Substitute
- replace a letter with its number value
- Formula
- a rule written using letters
- Evaluate
- work out the value of an expression
- Expression
- letters and numbers combined, with no equals sign
- Order of operations
- brackets, then × and ÷, then + and −