Functional Skills Maths · England

Formulae and the order of operations

Use formulae written in words, follow the correct order of operations, and — at Level 2 — substitute numbers, including negatives and decimals, into formulae and expressions written with letters.

Audience
Adults & apprentices
Levels
Level 1 (formulae in words) · Level 2 (letters)
Worked examples
4
Format
Print (A4/Letter) + answers

Learn

A formula is a set of instructions

A formula tells you how to work something out. Many everyday prices follow one: a plumber might charge a £45 call-out fee plus £30 for every hour. Written in words, that is: cost = £45 + £30 × number of hours. For 2.5 hours, the cost is £45 + £30 × 2.5 = £45 + £75 = £120. At Level 1, formulae are usually written in words like this.

The order of operations

When a calculation has more than one operation, the order matters. The usual memory aid is BIDMAS (or BODMAS): Brackets, Indices (powers such as squares), Division and Multiplication, then Addition and Subtraction. Division and multiplication have equal priority and are worked left to right; so do addition and subtraction.

So 6 + 4 × 5 is 6 + 20 = 26, not 10 × 5 = 50. And (12 − 4) × 5 is 8 × 5 = 40, because the brackets come first. Most scientific calculators follow this order automatically, but basic calculators may not, so it is safer to know it yourself.

Substituting into formulae with letters (Level 2)

At Level 2, formulae use letters. C = 25 + 18h means the cost C is £25 plus £18 for each hour h. To substitute, replace each letter with its number, keeping the operations. Writing two letters or a number and letter next to each other means multiply: 18h means 18 × h, and 2(l + w) means 2 × (l + w).

A temperature formula shows why order matters: F = 1.8C + 32 converts Celsius to Fahrenheit. For C = 25, do the multiplication first: 1.8 × 25 = 45, then add 32 to get 77. Negative numbers need extra care. With C = −5, 1.8 × −5 = −9, and −9 + 32 = 23. Putting negative values in brackets when you write them down — 1.8 × (−5) — helps avoid sign errors.

Squares apply only to what is directly next to them. In 3x² with x = 4, square first (16) and then multiply by 3 to get 48. In (2x)², the bracket is worked first.

You may also need to work backwards. If C = 30 + 12d and the bill is £126, take off the fixed £30 to leave £96, then divide by 12 to get d = 8 days. Undo the operations in the reverse order.

Worked example 1

Level 1: A plumber charges £45 call-out plus £30 per hour. How much is a 2.5 hour job?

  1. Cost = £45 + £30 × hours.
  2. Multiply first: £30 × 2.5 = £75.
  3. Add: £45 + £75 = £120.

Answer: £120.00

Worked example 2

Level 1: Work out 6 + 4 × 5.

  1. Multiplication comes before addition.
  2. 4 × 5 = 20.
  3. 6 + 20 = 26.

Answer: 26

Worked example 3

Level 2: Use F = 1.8C + 32 to convert 25 °C to Fahrenheit.

  1. Substitute: F = 1.8 × 25 + 32.
  2. Multiply: 1.8 × 25 = 45.
  3. Add: 45 + 32 = 77.

Answer: 77 °F

Worked example 4

Level 2: The perimeter of a rectangle is P = 2(l + w). Find P when l = 4.5 m and w = 3.2 m.

  1. Brackets first: 4.5 + 3.2 = 7.7.
  2. Multiply by 2: 2 × 7.7 = 15.4.

Answer: 15.4 m

Watch out

Common mistakes

  • Working strictly left to right and ignoring BIDMAS: 6 + 4 × 5 is 26, not 50.
  • Reading 18h as 18 + h. A number next to a letter means multiply.
  • Losing the minus sign when substituting a negative number; write it in brackets.
  • Squaring the coefficient as well: 3x² with x = 4 is 3 × 16, not 12².

Real life

Where you'll use this at work or home

  • Checking trade or hire quotes made of a fixed fee plus an hourly or daily rate.
  • Cooking: “20 minutes per 500 g plus 20 minutes” is a formula in words.
  • Spreadsheets at work, where every formula follows the order of operations.
  • Converting temperatures, working out phone or energy tariffs, or estimating materials.

Try it

Practice sheet

Functional Skills Maths · Level 1

Formulae and order of operations

NameDate

Show your working. Give money to the nearest penny and include units in every answer.

  1. 1.A taxi charges £3 plus £2 per mile. How much is a 7 mile journey?
  2. 2.Van hire is £40 per day plus £15 insurance. What is the cost for 3 days?
  3. 3.Roast chicken for 20 minutes per 500 g, plus 20 minutes. How long for a 2 kg chicken?
  4. 4.Work out 8 + 6 × 3.
  5. 5.Work out (12 − 4) × 5.
  6. 6.Weekly pay = £11 × hours + £25 bonus. What is the pay for 30 hours?
  7. 7.Work out 20 − 12 ÷ 4.
  8. 8.A phone plan costs £12 a month plus 5p for each extra text. What is the bill with 40 extra texts?
  9. 9.Number of fence posts = length in metres ÷ 2 + 1. How many posts for an 18 m fence?
  10. 10.Work out 3² + 4 × 2.
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Questions

Frequently asked questions

They mean the same thing. The I (indices) and O (orders) both refer to powers such as squares. Use whichever you were taught.

Simple working backwards, such as finding the number of days from a total bill, can appear at Level 2. Undo each operation in reverse order.

Multiply. 2(l + w) means work out l + w, then multiply the result by 2.

Level 1 usually uses formulae written in words. Letters and expressions are typically a Level 2 skill, though check your awarding body's specification.

Next steps

Area, perimeter and volumeRectangles, composite shapes, circles, cuboids and cylinders.Money, interest and budgetingBudgets, simple and compound interest, and income tax.Units, time and conversionsMetric units, time, imperial conversions, speed and density.All Functional Skills Maths topicsThe full learning path, Level 1 and Level 2.

Last reviewed: 9 October 2026

Editor: Paul Smeaton CMgr FCMI