GCSE Maths Practice: order-of-operations-bidmas

Handling Subtraction with Brackets and Fractions

As you progress in maths, you’ll often see subtraction combined with brackets or fractions in the same question. These multi-step expressions test how well you can follow the order of operations consistently. The key rule remains: simplify everything inside brackets first, handle multiplication or division next, and finally complete addition or subtraction.

Step-by-Step Reasoning

When brackets and fractions appear together, think of the fraction as a division. If that fraction sits inside a bracket, it must be resolved before anything else outside the bracket can happen. Once the bracket simplifies to a single number, you treat it just like any other value. Subtraction then happens at the very end.

1. Work inside the brackets. Simplify the fraction or any smaller operation inside.
2. Apply multiplication or division. Follow BIDMAS by handling these before subtraction or addition.
3. Finish with the remaining operation. Once the earlier steps are complete, you can safely subtract or add the final values.

Following this order prevents one of the most common mistakes in arithmetic: working from left to right instead of following BIDMAS.

Why This Matters

Without using BIDMAS, it’s easy to miscalculate. Subtracting before multiplying or dividing would change the result completely. Brackets act as a clear signal of where to focus first, helping you stay organised. Remember that fractions always represent division, even if they look like simple numbers with a line between them.

Common Mistakes

• Subtracting before multiplying or dividing.
• Forgetting to complete the brackets first.
• Ignoring the fraction’s role as a division step.
• Mixing up signs, especially when negative numbers are involved later on.

Always rewrite expressions line by line, replacing brackets with their simplified value each time. This technique prevents skipped operations and sign confusion.

Real-World Examples

This same logic appears in real contexts such as budgeting, measurements, and data analysis. For instance, when calculating a discount, you often subtract a proportion of a value (a division step) before applying further changes. Correctly sequencing each step ensures financial or measurement results stay accurate.

Developing Strong Habits

Every time you see subtraction mixed with brackets or fractions, pause and identify what needs to be done first. It can help to highlight the highest-priority operation. With consistent practice, this becomes automatic and forms a strong base for algebra, where negative values and brackets appear frequently.

FAQs

Q1: Why do brackets come before subtraction?
A: Because brackets group smaller operations that must be completed before the rest of the expression.

Q2: What happens if there are two brackets?

A: Simplify each bracket separately, starting with the one inside if they are nested.

Q3: Is subtraction always last?

A: Yes, unless brackets or powers require attention first. Subtraction has the lowest priority in BIDMAS.

Study Tip

Write each step of your working on a new line. Label each operation as you complete it—(B) for brackets, (M) for multiplication, (S) for subtraction. This approach makes your thinking clear, reduces sign errors, and builds confidence in applying BIDMAS rules correctly every time.