GCSE Maths Practice: order-of-operations-bidmas

Question 6 of 9

This question combines brackets, fractions, and multiplication to test your full understanding of BIDMAS order.

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\( \begin{array}{l}\text{Work out } 4 + (\frac{6}{3}) \times 5 \text{ using BIDMAS.}\end{array} \)

Choose one option:

Always finish calculations inside brackets first, simplify any fractions, then complete multiplications and additions.

Mastering Multi-Step BIDMAS Problems

Once you understand the basics of BIDMAS, the next challenge is combining several layers at once. Expressions that include brackets and fractions test how well you can keep the order of operations organised. Fractions introduce hidden division, and brackets tell you which part to complete first. Keeping those priorities straight ensures accurate results in every calculation.

Breaking Down the Order

When you see a bracket that contains a fraction, start by simplifying the fraction before moving on. The horizontal line in a fraction means division, so the top (numerator) is divided by the bottom (denominator). Once that part is complete, replace the entire bracket with its simplified value and continue with the rest of the expression using normal BIDMAS rules.

Step-by-Step Strategy

  1. Brackets first: Complete everything inside the bracket, following BIDMAS within it if there are multiple operations.
  2. Fractions second: Simplify the numerator and denominator separately, then perform the division.
  3. Multiplication and division: Work from left to right for any remaining operations.
  4. Addition or subtraction: Finish by combining the final results.

This clear sequence helps prevent skipped steps and ensures that calculations remain structured.

Common Errors

  • Ignoring the fraction and multiplying before dividing.
  • Forgetting that the fraction line represents division.
  • Working from left to right without finishing the bracketed section first.

Writing one operation per line and checking off each step can help avoid these issues, especially under exam conditions.

Practical Applications

Fractions and brackets appear in many everyday contexts. In recipes, you might divide an ingredient amount before scaling up the total. In finance, you could adjust part of a bill within brackets before multiplying by a tax rate. The BIDMAS sequence guarantees that these multi-step processes give fair, consistent answers every time.

Building Confidence

Practising with multi-layer questions strengthens mental flexibility. Once you can quickly identify which operation comes first, you’ll find it easier to handle algebraic expressions and calculator problems later on. Remember that brackets reset BIDMAS for whatever sits inside them — treat each bracket like a mini-problem within the larger one.

FAQs

Q1: Which comes first: the bracket or the fraction?
A: Simplify the bracket first, but if the bracket contains a fraction, deal with the fraction as part of that internal process.

Q2: Do I always divide the numerator by the denominator before other steps?
A: Yes, unless there are brackets in either part — then simplify inside those brackets first.

Q3: Can multiplication come before the fraction?
A: No. The fraction (division) inside brackets has priority because the bracketed section must be finished before multiplying or adding outside.

Study Tip

When faced with an expression containing both a bracket and a fraction, imagine peeling layers off an onion: start from the inside and work outward. Simplify the deepest part first, rewrite the expression, and then move to the next operation. This careful, layered approach will make even complex BIDMAS problems feel straightforward and manageable.

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