GCSE Maths Practice: order-of-operations-bidmas

Question 9 of 10

This Higher-tier problem tests BIDMAS with nested brackets, powers, division, multiplication, and decimals — a key GCSE skill.

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\( \begin{array}{l}\text{Work out }8 + ((3^2 + 2) \div 5) \times 2\\\text{ using BIDMAS.}\end{array} \)

Choose one option:

Tackle the innermost brackets first, then move outward. Check your order carefully before adding the final term.

Mastering BIDMAS with Nested Brackets

This problem strengthens your understanding of BIDMAS when more than one layer of brackets is present. The acronym stands for Brackets, Indices, Division, Multiplication, Addition, Subtraction. When brackets are nested, always begin with the innermost set before working outward.

Why Order Matters

Mathematical operations follow a strict hierarchy. Without it, everyone could reach a different result from the same expression. Nested brackets test how confidently you can manage multiple operations in the correct sequence, which is crucial in higher-tier GCSE calculations.

Systematic Method

  1. Step 1: Work inside the innermost brackets.
  2. Step 2: Evaluate any powers or roots.
  3. Step 3: Complete division and multiplication from left to right.
  4. Step 4: Move outward, applying addition or subtraction last.

Worked Examples

Example 1: \(6 + ((2^3 + 1) \div 4) \times 3\)
Innermost power: \(2^3 = 8\). Inside brackets: \(8 + 1 = 9\). Divide: \(9 \div 4 = 2.25\). Multiply: \(2.25 \times 3 = 6.75\). Add outer term: \(6 + 6.75 = 12.75\).

Example 2: \(10 - ((5^2 - 5) \div 5) \times 2\)
Powers: \(5^2 = 25\). Inside brackets: \(25 - 5 = 20\). Divide: \(20 \div 5 = 4\). Multiply: \(4 \times 2 = 8\). Subtract: \(10 - 8 = 2\).

Example 3: \(4 + ((6^2 + 3) \div 9) \times 2\)
Evaluate power: \(6^2 = 36\). Inside brackets: \(36 + 3 = 39\). Division: \(39 \div 9 = 4.33\). Multiply: \(4.33 \times 2 = 8.66\). Add: \(4 + 8.66 ≈ 12.66\).

Common Pitfalls

  • Ignoring inner brackets and starting from the outside.
  • Multiplying before completing a division within the same bracket.
  • Forgetting to square a number before other steps.
  • Rounding mid-way—always round only at the end.

Where You Use This Skill

Nested-bracket reasoning appears in formula rearrangements, coding algorithms, and scientific calculations. Chemistry and physics equations often include squared terms and ratios that must be computed in order. In spreadsheets and calculators, the same BIDMAS sequence is built-in, so manual understanding ensures you can debug or check results confidently.

FAQ

Q1: What does 'nested' mean?
A: Brackets inside another set of brackets—solve the inner one first.

Q2: What if there are two operations at the same level?
A: Work left to right, performing division and multiplication before addition or subtraction.

Q3: Can decimal results occur?

A: Yes. Division often creates decimals; carry them through accurately rather than rounding too soon.

Exam Tip

Write each stage clearly beneath the previous one, checking the order at every line. In multi-step expressions, underline the part you’re solving. This approach prevents skipping operations under exam pressure.

Summary

BIDMAS is the foundation of all algebraic reasoning. Mastering nested brackets prepares you for complex formula work and ensures calculator-free accuracy in the GCSE Higher paper. Always move from inner to outer operations and maintain full precision until the last line.