GCSE Maths Practice: order-of-operations-bidmas

Question 7 of 10

This Higher-tier exercise checks your understanding of BIDMAS, focusing on division, powers, and bracket handling with multiple steps.

‹ ›

\( \begin{array}{l}\text{Work out }3 + 6 \div 2 + (4 - 1)^2\text{ using BIDMAS.}\end{array} \)

Choose one option:

Always perform division and powers before adding or subtracting to avoid order errors.

Understanding the BIDMAS Rule

The BIDMAS order of operations ensures that mathematical expressions are solved consistently. The acronym stands for Brackets, Indices (powers), Division, Multiplication, Addition, and Subtraction. Each step follows a hierarchy so that every calculation leads to the same result, no matter who performs it.

Key Principle

Always begin by solving anything inside brackets. Next, evaluate powers or roots. After that, perform division and multiplication from left to right. Finally, complete addition and subtraction. Remember that division and multiplication share the same level of priority, as do addition and subtraction.

Step-by-Step Method

  1. Identify and simplify any brackets.
  2. Calculate powers (indices) inside or outside brackets.
  3. Carry out any division or multiplication in order from left to right.
  4. Finish with addition or subtraction operations.

Worked Examples

Example 1: \(2 + 8 \div 2 + (3 - 1)^2\).
Inside brackets: \(3 - 1 = 2\).
Powers: \(2^2 = 4\).
Division: \(8 \div 2 = 4\).
Now sum: \(2 + 4 + 4 = 10\).

Example 2: \(5 + 4 \times 2 + (6 - 2)^2\).
Brackets: \(6 - 2 = 4\).
Power: \(4^2 = 16\).
Multiplication: \(4 \times 2 = 8\).
Add results: \(5 + 8 + 16 = 29\).

Example 3: \(10 - 6 \div 3 + (5 - 2)^2\).
Brackets: \(5 - 2 = 3\).
Power: \(3^2 = 9\).
Division: \(6 \div 3 = 2\).
Final steps: \(10 - 2 + 9 = 17\).

Common Mistakes

  • Doing addition before division or multiplication.
  • Ignoring powers inside brackets.
  • Not following left-to-right order for division and multiplication.
  • Skipping brackets or expanding them incorrectly.

Why It Matters

Following BIDMAS prevents calculation errors in science, finance, and programming. For instance, in physics formulas or tax calculations, changing the order can completely alter results. Even spreadsheets and calculators follow BIDMAS internally.

FAQ

Q1: What happens if two operations have the same level?
A: Work from left to right. For example, with division and multiplication, do whichever appears first.

Q2: Can brackets override BIDMAS?
A: Yes, always solve brackets first; they can change the whole order of a problem.

Q3: Is there a quick way to check my answer?
A: Repeat the calculation slowly in steps or test it on a calculator—each stage should match the expected order.

Real-Life Connection

Every formula in technology, coding, or finance depends on a strict order of operations. For example, software that computes payroll or calculates compound interest uses this same structure behind the scenes.

Study Tip

Write each stage on a new line when solving complex expressions. Highlight or underline the operation you perform at each step to stay organised and avoid skipped operations. Practising this habit leads to perfect accuracy in exams.