Order Of Operations Bidmas Quizzes

GCSE Maths Foundation Quiz: Order of Operations (BIDMAS) Practice Questions

Difficulty: Foundation

Curriculum: GCSE

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Order of Operations BIDMAS Quiz 1

Difficulty: Higher

Curriculum: GCSE

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Visual overview of Order Of Operations Bidmas.

Introduction

The order of operations, known by the acronym BIDMAS (Brackets, Indices, Division/Multiplication, Addition/Subtraction), is a vital principle in GCSE Maths. It defines the correct sequence for carrying out operations in any calculation so that everyone reaches the same, correct answer. Without BIDMAS, the same expression could give different results depending on the order chosen.

For example, \(2 + 3 × 4 = 14\) when applying BIDMAS correctly (multiply before adding), but \(20\) if you add first — which is wrong. Mastering BIDMAS ensures accuracy in algebraic expressions, fractions, decimals, and multi-step arithmetic problems.

Core Concepts

The BIDMAS Order

  • B – Brackets: Solve anything inside brackets first.
  • I – Indices: Calculate powers and roots next (e.g., \(3^2, \sqrt{16}\)).
  • D / M – Division and Multiplication: Work from left to right.
  • A / S – Addition and Subtraction: Finally, complete these from left to right.
Tip: Division and multiplication share equal priority, as do addition and subtraction — always move left to right.

Brackets

Brackets group operations that must be performed first. They may appear in several forms:

  • Parentheses ( )
  • Square brackets [ ]
  • Curly braces { }

Example

\((2 + 3) × 4\)

Step 1: Inside brackets → \(2 + 3 = 5\)

Step 2: Multiply → \(5 × 4 = 20\)

Indices

Indices (powers or roots) come after brackets but before other operations. Always simplify exponents first.

  • \(3^2 + 4 = 9 + 4 = 13\)
  • \(2 × 5^2 = 2 × 25 = 50\)

Division and Multiplication

Perform these from left to right — neither has priority over the other.

Example

\(20 ÷ 4 × 3\)

Left to right → \(20 ÷ 4 = 5\), then \(5 × 3 = 15\)

Addition and Subtraction

Handled last, also from left to right, once all brackets, powers, and multiplication/division are complete.

Example

\(10 - 4 + 2\)

\(10 - 4 = 6\), then \(6 + 2 = 8\)

Combining All Operations

Follow BIDMAS carefully when multiple operations appear together.

Example

\(5 + (3 × 2)^2 - 8 ÷ 4\)

  1. Brackets → \(3 × 2 = 6\)
  2. Indices → \(6^2 = 36\)
  3. Division → \(8 ÷ 4 = 2\)
  4. Add/Subtract → \(5 + 36 - 2 = 39\)

Answer: \(39\)

Nested Brackets

When brackets appear inside other brackets, start from the innermost first and work outward.

Example

\([2 + (3 × 4)]^2\)

Innermost → \(3 × 4 = 12\); next → \(2 + 12 = 14\); finally \(14^2 = 196\)

Directed Numbers

With positive and negative numbers, multiply or divide before adding or subtracting, and keep track of signs.

Example

\(-3 + 5 × (-2)\)

\(5 × -2 = -10\); then \(-3 + (-10) = -13\)

Fractions and Decimals

BIDMAS applies exactly the same way. Multiplication and division come before addition and subtraction even in fractional or decimal form.

Example

\(\frac{1}{2} + \frac{3}{4} × 2\)

Multiply first → \(\frac{3}{4} × 2 = 1.5\)

Then add → \(0.5 + 1.5 = 2\)

Worked Examples

Example 1 (Foundation): Simple BIDMAS

\(2 + 3 × 4 = 14\)

Example 2 (Foundation): Brackets and Indices

\((2 + 3)^2 = 25\)

Example 3 (Higher): Mixed Operations

\(5 + 6 × 2^2 - 8 ÷ 4 = 27\)

Example 4 (Higher): Nested Brackets

\([3 + (2 × 4)]^2 - 5 = 116\)

Example 5 (Higher): Directed Numbers

\(-4 + 3 × (-2) = -10\)

Example 6 (Higher): Fractions and BIDMAS

\(\frac{2}{3} + \frac{1}{2} × 6 = 3.666…\)

Common Mistakes

  • Calculating strictly left to right without using BIDMAS.
  • Forgetting to complete powers before multiplying or dividing.
  • Ignoring negative signs when multiplying or dividing.
  • Adding or subtracting fractions before simplifying.
How to avoid: Write steps in order, underline brackets, handle powers early, and double-check negative signs before adding.

Applications

  • Algebra: Simplifying multi-term expressions.
  • Directed Numbers: Calculating temperature changes or gains/losses.
  • Fractions & Decimals: Common in science and finance questions.
  • Exams: Multi-step BIDMAS questions appear in both tiers.

Strategies & Tips

  • Memorise the BIDMAS order and follow it exactly.
  • Use extra brackets to make long calculations clearer.
  • Move left-to-right for operations of equal priority.
  • Check final answers using estimation or a calculator for sanity.
  • Practise with integers, fractions, and negative values.

Summary / Call-to-Action

BIDMAS ensures every calculation gives one correct answer. By understanding and applying the correct order of operations, you’ll avoid common mistakes and handle complex expressions confidently. Practise using a variety of numbers — whole, fractional, and negative — to strengthen your skills.

  • Try interactive BIDMAS quizzes to reinforce your learning.
  • Apply BIDMAS to algebraic and real-life problems.
  • Challenge yourself with nested-bracket and multi-step examples.

Consistent practice will make BIDMAS second nature and improve accuracy across all areas of GCSE Maths.