GCSE Maths Practice: order-of-operations-bidmas

Using Subtraction Inside Brackets

Brackets play an essential role in controlling the order of operations. When a subtraction appears inside brackets, it must be completed before anything outside the brackets is calculated. This ensures the structure of the expression remains clear and avoids unnecessary confusion.

Why the Order Matters

Consider that subtraction and multiplication have different priorities in mathematics. Multiplication is normally done before subtraction unless brackets tell you otherwise. When a subtraction is written inside brackets, those brackets act like a set of instructions to pause and deal with that part first. Once the bracket is simplified to a single number, you can safely multiply or divide as the next step.

Understanding the Logic

Think of brackets as a small, self-contained problem. Inside them, handle every operation as if it were the only calculation you have. Once the bracket is simplified, you can treat its result like any other number. This way, even long problems can be broken down into clear, easy stages. The strategy prevents errors when signs change or when negative numbers appear later on.

Common Mistakes

• Ignoring the brackets and performing multiplication first.
• Subtracting incorrectly, especially when negatives are involved.
• Writing an incomplete expression without keeping the bracket around until the subtraction is complete.
• Forgetting that subtraction is sensitive to order—the difference between 6 − 2 and 2 − 6 is significant.

Checking every operation in order, and keeping your brackets visible until the inside is fully simplified, helps you stay accurate.

Practical Applications

Brackets and subtraction appear frequently in everyday contexts. For example, when adjusting totals in shopping receipts, you may subtract discounts before multiplying by quantity. In budgeting, you might find the difference between two figures before scaling that difference up or down. Following the correct order of operations ensures those calculations are meaningful and consistent.

How to Approach Multi-Step Problems

1. Identify any brackets.
2. Complete all additions or subtractions inside them first.
3. Replace the bracket with its simplified result.
4. Carry out multiplication or division next, then any remaining additions or subtractions.

Writing out each step on a separate line makes the order of operations easy to follow. Many errors happen when students skip writing one of these stages, so taking a few extra seconds to organise your work can save marks.

FAQs

Q1: What happens if there are two sets of brackets?
A: Start with the inner bracket, then move outward. Always complete one bracketed section before touching another.

Q2: Do subtraction and addition have the same level of priority?
A: Yes. They are handled in the order they appear, from left to right, after multiplication and division are finished.

Q3: How do I know whether to subtract or add first when both appear inside brackets?
A: Work from left to right, keeping the order of the signs exactly as written.

Study Tip

Before solving, scan for brackets and underline them. Inside each, underline subtraction or addition signs to highlight which step comes first. Then replace the bracket with its result before moving on. This clear, methodical process helps you apply BIDMAS correctly and reduces simple sign mistakes that often cost marks in foundation-level exams.