GCSE Maths Practice: order-of-operations-bidmas

Question 5 of 10

This higher-level BIDMAS question combines brackets, powers, fractions, and negative signs for a multi-layered challenge.

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\( \begin{array}{l}\text{Evaluate } \frac{1}{2} (5 + 3) \times (-(8 - 4))^2 \text{ using BIDMAS.}\end{array} \)

Choose one option:

Always resolve brackets first, then apply powers, then multiply or divide, and finish with addition or subtraction.

Advanced BIDMAS with Negatives, Powers, and Fractions

At higher GCSE level, expressions often combine several elements: brackets, powers, negatives, and fractions. These require careful attention to order and signs. The most common reason for mistakes is ignoring how negative signs interact with powers or forgetting to apply fractions to the whole expression rather than just part of it.

Understanding the Process

Let’s break down how to manage complex operations step by step:

  1. Brackets first: Always simplify anything inside brackets. This could include additions, subtractions, or even another power.
  2. Powers next: Apply indices (squares, cubes, etc.) immediately after completing brackets. Be especially cautious with negative numbers—(−4)² = +16 but −4² = −16 because the square applies only to the 4, not the negative sign.
  3. Multiplication and division: After all brackets and powers are handled, deal with multiplication and division, including fractional multipliers.
  4. Addition and subtraction last: Finish by combining any remaining values.

Each of these stages keeps your work structured, avoiding common order-of-operations errors that can flip signs or halve results incorrectly.

Fractions and Negative Powers

Fractions act as multipliers or divisors depending on where they appear. For example, multiplying by ½ is the same as dividing by 2. When a negative number is raised to a power, check whether the power is even or odd. An even power turns the result positive; an odd power keeps it negative. This interaction between signs and powers is one of the most tested elements at Higher tier.

Common Pitfalls

  • Squaring a number without brackets, turning what should be positive into negative.
  • Multiplying fractions incorrectly—forgetting to apply them to the full expression.
  • Adding before multiplying, which breaks the BIDMAS rule.

Always take time to rewrite expressions clearly. If you’re unsure whether a negative sign is included in the power, add your own brackets to show it explicitly.

Real-World Application

This kind of calculation mirrors real-life problem solving in physics and engineering. For instance, negative signs appear in direction or force, and powers represent area or volume. Fractions scale these values up or down. Following BIDMAS ensures your solution matches real measurements and doesn’t violate physical laws or proportions.

Checking Work

Once you have an answer, review the signs and powers: did every negative get squared correctly? Did every multiplication happen after the power step? Checking these two points alone eliminates over 80% of common mistakes.

FAQs

Q1: Why does (−4)² differ from −4²?
A: The first squares both the number and the sign; the second squares only the 4, leaving the negative outside.

Q2: How should I handle a fraction outside brackets?
A: Treat it as a multiplier applied to the result of the whole bracketed section.

Q3: What happens if two powers appear?

A: Evaluate each separately before combining their results through multiplication or addition.

Study Tip

When you see powers and fractions together, write out every stage on a separate line. Include brackets around negative values even if they aren’t shown. This guarantees correct sign handling and avoids confusion when typing into calculators. Consistent step-by-step working is what turns advanced BIDMAS questions from traps into easy marks.