GCSE Maths Practice: order-of-operations-bidmas

Combining Brackets and Multiplication

At foundation level, the next step after simple brackets is to include more than one operation inside them. When both multiplication and addition appear within a single bracket, you must still follow BIDMAS inside that bracket before doing anything outside it. This ensures the entire expression is handled in the correct order and avoids confusion about which step to take first.

Nested Logic of BIDMAS

BIDMAS doesn’t apply only to the full expression; it also works within each bracket. That means if a bracket contains multiplication and addition, complete the multiplication first, then carry out the addition inside the same bracket. Only once the bracket has been simplified to one value should you continue with operations outside it.

Common Mistakes

• Adding numbers inside the bracket before performing multiplication.
• Forgetting that BIDMAS resets inside every bracketed section.
• Combining inside and outside steps too soon, which mixes priorities and changes the final result.
• Misreading the brackets or ignoring them entirely, which causes large errors even in simple problems.

To stay organised, draw a light underline beneath each bracketed part before starting and tick it off when that section is complete.

Everyday Examples

These ideas appear constantly in daily life. When working out total prices, you often multiply the number of items by the cost first, then add an extra fee such as delivery or tax. The concept is identical to performing multiplication before addition inside a bracket. In science, when calculating total energy or resistance, operations inside brackets often represent grouped values that must be processed together before combining with other quantities.

Step-by-Step Thinking

1. Look for the innermost or only bracket and handle all operations within it according to BIDMAS.
2. Simplify the bracket into one single number.
3. Use that result in the rest of the calculation, completing any remaining addition or subtraction.

This disciplined approach turns even multi-operation questions into a simple sequence of smaller steps.

Key Takeaways

• Brackets group parts of a calculation that must be completed first.
• Multiplication and division inside brackets take priority over addition or subtraction.
• Once a bracket is simplified, treat it as one number when continuing the calculation.

FAQs

Q1: Do I always start inside brackets first?
A: Yes. Finish everything inside brackets before moving outward.

Q2: What if there are two sets of brackets?
A: Work from the innermost bracket outward, simplifying each layer step by step.

Q3: Does BIDMAS change with decimals or fractions?
A: No, the order stays the same; only the type of numbers changes.

Study Tip

Write each stage on its own line: first simplify the bracket, then handle what remains outside. Checking one operation at a time will build accuracy and make it easier to identify where an error occurred. Mastering this process now prepares you for algebraic brackets later, where the same rules apply to letters as well as numbers.